SHAPECOEXISTENCEINTHENEUTRON-RICHNICKELISOTOPESNEARN=40ByChristopherJohnProkopADISSERTATIONSubmittedtoMichiganStateUniversityinpartialfulllmentoftherequirementsforthedegreeofChemistry-DoctorofPhilosophy2016ABSTRACTSHAPECOEXISTENCEINTHENEUTRON-RICHNICKELISOTOPESNEARN=40ByChristopherJohnProkopTheevolutionofnuclearstructurewithchangingprotonandneutronnumberisofcommoninterestacrossthenuclearsciencecommunity.Withintheshellmodel,protonsandneutronsoccupycollectionsofsingle-particlestatesseparatedbyrelativelylargeenergygaps,givingrisetothesocalled\magic"numbers.Analogoustothenoblegasesinchemistry,whichhaveenhancedchemicalinertness,unstablenucleipossessingclosed-shellnucleoncongu-rationsaregenerallysphericalinshapeandexhibitincreasedstability.Closedshellnucleiexhibitlargernucleonseparationenergies,andwhenradioactivetheyhavelongerhalf-lives.Theenergyofthesingle-particlestatesalsomigratewithchangingnumbersofprotonsandneutronsduetostrongproton-neutronresidualinteractions.Themigrationofsingle-particleenergiesleadstoshellevolutionandcandrivenucleifromsphericaltodeformedshapes.Withinasinglenucleus,theredistributionofnucleonscangiverisetointruderstatespossessingdierentshapesthanthatofthegroundstateconguration.Theseintruderstatesowetheirexistencetothedelicatebalancebetweenthecostofexcitingnucleonsintothehigher-lyingsingle-particlestatesandthestabilizingeectofresidualproton-neutroninteractions.Iftheenergyoftheintruderstatedescendsfarenough,stateswithnucleoncongurationsassociatedwithdierentnuclearshapescancoexistatsimilarexcitationen-ergyinaphenomenoncalledshapecoexistence.Ineven-evennuclei,thehallmarkofshapecoexistenceismultiplelow-lying0+states.Recently,theNiisotopicchainhasbeenthefocusofmanyexperimentalandtheoreticalinvestigationsstudyingtheevolutionofnuclearstructureawayfromstability.Inparticular,68NihaselicitedsignicantattentionduetothepresenceofboththeZ=28protonshellclosureandtheN=40neutronsubshellclosure.In68Ni,three0+states,withenergiesof0,1603,and2511keVhavebeenidentied.Advancedshell-modelcalculations,utilizingthefullfpg9=2d5=2modelspaceforbothprotonsandneutrons,predictaspherical0+
1groundstate,oblate-deformed0+
2state,andprolate-deformed0+
3state.Thecongurationoftheoblate-deformed0+
2stateispredictedtobepredominatelytheexcitationoftwoneutronsacrossN=40intothe0g9=2orbit,whilethetheprolate-deformed0+
3stateisexpectedtocontainmultipleparticle-holeexcitationsdominatedbytheexcitationoftwoprotonsacrossZ=28intothe0ˇf5=2orbit.Transitioningto70Ni,withtheadditionofonlytwoneutrons,thesameshell-modelcalculationspredicttheprolatedeformed0+statetodropprecipitouslyfromthemeasuredenergyof2511keVin68Nidowntoapredictedenergyof1525keVin70Ni.Thisisexplainedbythereductionoftheenergyspacingbetweenthe0ˇf7=2and0ˇf5=2single-particlestatesduetothestrengtheningoftheattractive0g9=20ˇf5=2andrepulsive0g9=20ˇf7=2monopoleinteractionsofthetensorforcewithincreasedoccupancyofthe0g9=2orbital.Inordertovalidatethesepredictionsandexperimentallyinvestigateshapecoexistencein68;70Ni,twocomplimentaryexperimentswereperformedattheNationalSuperconductingCyclotronLaboratory.Asaresultoftheseexperiments,anew(0+
2)statewasdiscoveredat1567-keVin70Ni,ingoodagreementwiththeoreticalpredictions.Transitionprobabilitiesdeducedfromnewlifetimeandbranchingratiomeasurementsof0+statesin68;70Nipro-videstringenttestsforcompetingtheoreticaldescriptions.Theseresultsconstitutetherstquantitativedescriptionsofthese0+statesandsupportthepredictionsofshapecoexistencein68;70Ni.InlovingmemoryofmyfatherHaroldD.ProkopivACKNOWLEDGMENTSThelistofpeoplethathavebeeninstrumentaltomysuccessingraduateschool,presentedherein,islongandwithoutadoubtnotexhaustivesoIwouldliketobeginbythankingeveryoneasawholefortheircontributions,bothlargeandsmall,thatmadethisdissertationpossible.First,IwouldliketothankmyadvisorSeanLiddickforyourcontinuoussupportthrough-outmytenureasagraduatestudent.Theguidanceandtrainingyouhavegivenmehasbeeninstrumentalforpreparingmyforroadahead.Yourwillingnesstoanswerthecountless,per-hapsevensomefoolish,questionsduringthemanytimesIstoppedbyyourocehasbeengreatlyappreciated.Thankyouforbeingapproachableandalwayswillingtohelp.BeforemovingontoanyoneelseIwouldliketothankmyfatherHarold.SomuchofwhoIhavebecomeisdirectlybecauseofyouandnoamountofwordscanexpresshowmuchImissyou.TherearecountlesslifeskillsIlearnedworkingwithyouonenumerablehouseholdprojects.Iattributealotofmyproblemsolvingabilitytoyourteaching.OutsideofworkmyabilitiesasacompetentmechanicandcarpenterareadirectresultofthetimeIspentwithyou.DespitebeingsurroundedbyveryintelligentpeopleonadailybasisduringgraduateschoolIalwaysregardedyouasoneofthemostintelligentpeopleIknow.ThoughIknowyouwerealwaysproudofme,Icanthelpbutwishyouwereheretoseemegraduate.NextIwanttothankmymomCarlawhoiswithoutadoubtthemostcaringandcompassionatepersonIknow.AnytimeIhaveaproblem,whetherpersonalorprofessional,IknowIcanturntoyouforhelp.WordscannotexpresshowmuchIappreciateyou.Losingmyfather,onedayaftermy27thbirthdayandjusttwomonthsbeforemythesisexperiment,wasthehardestthingIhaveeverexperiencedandmakesallofgraduateschool(includingvwritingthisdissertation)looklikeawalkintheparkonawarmsummerday.Icantimaginewhatthatwaslikeforyoumombutsomehowyouremainedpositiveandsupportive.YoubelonginaspecialcategoryamongpeoplemomandIoweyouaninnitedebtofgratitude.IcantcontinuewithoutthankingmylittlesisterLindsey.YouarecertainlythefunniestpersonIknow.WheneverIamstressed,tired,depressed,oracombinationthereofIcantalktoyouandsomehowfeelbetteralmostinstantly.Peoplealwaysrefertousas"twinseightyearsapart"soitsnosurpriseIamveryproudofyou.IknowloosingdadwashardonyouaswellsoIappreciateyouhelpingmomaroundthehouseandforhelpingmewithprojectswhenIcomehome.Iknowthatyouandmomarealwaysinmycorner.NextIwanttothankmywonderfulgirlfriendAlex.IloveyouandIappreciateyoursupportandcompanionshipthroughoutourrelationship.ByvirtueofcomingintomylifeinmythirdyearofgraduateschoolyouhavehadtheneprivilegeofdealingwithmeduringthemorestressfulportionofitandIthankyouforgoingthroughitwithme.IappreciatethetimesyoukeptmecompanyinmyocesomeofthosedayswhenIwasworkinglate.ThoughIamsurethereweremoreinterestingorexcitingthingsyoucouldhavedone,Iamgladyouspentthetimewithme.YoumakemylifebetterandIlookforwardtoourfuturetogether.Whilegraduateschooltendstominimizefreetimeforactivitiessuchasvideogames,IwanttosaythankstomycousinsTylerandTrevorforalwaysbeingtherewhentheopportunitypresentsitself.PlayingCallOfDuty,GrandTheftAuto,andBattleeldwithyouguyshasalwaysbeenstressreliefinitsnestform.IalsowanttothankJuanManfrediforbeinganexcellentfriend,colleague,androommatethroughoutgraduateschool.IwanttothankBenCriderforbeingmycolleagueandfriend.Witheachofusrespon-sibleforrunningoneofthecomplimentaryexperimentsdiscussedinthisdissertationthereviweremanylonghoursofcollaborativework.Iappreciateyourassistanceobtainingthere-sultspresentedhereinandyourandcompanionshipthroughout.Ialsowanttothanktheremainingmembersofthebeta-decaygroupandallotherswhosatshiftoneitherexperi-ment.Scienceiscertainlyacollaborativeeortandwithoutyourhelptheseresultswouldnotbepossible.IwanttothankRobertJanssensandBillWaltersfortheircontributionstomanuscriptdraftsandforthelettersofrecommendationyouwroteformewhenIwassearchingforpostdocpositions.IalsowanttothankAlexBrownandMortenHjorth-Jensonforprovidingmewiththeorycalculationsandforhelpingmeunderstandtheunderlyingnuclearphysicsconceptsbehindthem.LookingbackonwhatleadmetograduateschoolIwanttothankmyundergraduateresearchadvisorAndrewRoberts.Itwasworkingwithhimthatgavememyrstexperienceworkinginnuclearscienceandthedesiretopursueacareerintheeld.IalsowanttothankTrentVorlicekforsuggestingIattendthedepartmentofenergynuclearsummerschool.ItwastherethatImetPaulManticaanditwasthroughinteractingwithhimIchosetocometoMichiganState.Paulalsodeservesasecondthankyouforservingasthesecondreaderonmyguidancecommittee.Iwouldliketothanktheothertwomembersofmycommittee,DaveMorrisseyandRemcoZegers,fortheirservice.EvenbeforecollegeIwasinspiredbysomewonderfuleducators.FirstandforemostIthankMarkFrantaforbeinganexcellentphysicsteacherandforprovidingmetheinspirationtomajorinphysics.IalsowanttothankRogerSchoenfelder,TomPlocker,andCindyAllevanforthereoutstandingteachinginChemistry,Math,andEnglish,respectively.LastbutnotleastIwanttothankallthepeoplethatperformtheday-to-dayoperationsatthelab.Ithankthebeamphysicists,cyclotronoperators,designgroup,machinists,oceviista,andallothersthatcontributetothesuccessfuloperationofthelab.Withoutthesepeoplenoneofthesciencewouldbepossible.ThereiscertainlysomethingtobeproudofbeingpartofaworldclassfacilitysuchastheNSCLanditsbeenawonderfulexperienceworkingwithyouall.viiiTABLEOFCONTENTSLISTOFTABLES....................................xiiLISTOFFIGURES...................................xvChapter1Introduction...............................11.1NuclearShellStructure..............................11.2NuclearShellEvolution..............................41.3NuclearShapeCoexistence............................61.4NuclearStructureNearN=40andZ=28...................71.5GoalsoftheExperiment.............................11Chapter2NuclearDecayModes.........................122.1Decay......................................122.1.1-DelayedParticleEmission.......................182.2Decay......................................192.3InternalConversion................................222.4InternalPairFormation.............................242.5E0Transitions..................................24Chapter3ExperimentalDescription.......................283.1IsotopeProduction,Identication,andDeliveryattheNationalSupercon-ductingCyclotronLaboratory(NSCL).....................293.2NSCLe14039ExperimentalSetup........................313.3NSCLe14057ExperimentalSetup........................333.4NSCLDigitalDataAcquisitionSystem(DDAS)................363.4.1Triggering.................................36
3.4.2EnergyExtraction............................38
3.4.3FastTimingCapabilitiesofDDAS...................393.5PlanarGermaniumDouble-SidedStripDetector(GeDSSD)..........423.5.1InstrumentationandTriggeringConditions...............423.5.2EventLocalizationandCorrelation...................433.5.3CrosstalkCalibration...........................463.5.4EnergyCalibration............................503.5.5PulseShapeAnalysis...........................523.6SegmentedPlasticScintillatorandPosition-SensitivePhoto-MultiplierTube(PSPMT).....................................64
3.6.1InstrumentationandTriggeringConditions...............643.6.2EventLocalizationandCorrelation...................653.6.3PulseShapeAnalysis...........................703.7SegmentedGermaniumArray(SeGA).....................73ix3.7.1SeGAInstrumentationandTriggeringConditions...........733.7.2SeGAEnergyCalibrations.......................743.7.3SeGAAbsoluteEciencyCalibrations.................753.8LanthanumBromideArray............................813.8.1InstrumentationandTriggeringConditions...............813.8.2LaBr3EnergyCalibrations.......................813.8.3AbsoluteLaBr3EciencyCalibrations.................833.9LevelLifetimeMeasurementTechniques....................843.9.1TimeWalkCorrections..........................843.9.2DepthofInteractionCorrections....................883.9.3NewAnalysisMethodforLifetimeTechniques...........923.9.4DemonstrationoftheTechniqueonaPromptTransition.......943.9.5BenchmarkingtheTechniqueonaTwoExcitedStateswithKnownLifetimes..................................97Chapter4ExperimentalResults..........................1044.1Decayof68Co..................................1044.1.1DecayoftheLong-Lived68CoIsomer..................1044.1.2Half-LifeMeasurements.........................1304.1.2.1AssessingSpuriousCorrelations................1304.1.2.2\ExclusionTechnique"forCorrelations............1314.1.2.3Half-Lifeof68Fe........................1354.1.2.4Half-LifeoftheLong-Lived68CoIsomer...........1404.1.2.5A=68DecayCurves.....................1424.1.2.6Half-Lifeofthe0+
2statein68Ni................1464.1.2.7Half-Lifeofthe0+
3statein68Ni................1494.2Decayof70Co..................................1534.2.1-DecayingIsomersin70Co.......................1574.2.2A=70DecayCurves...........................1654.2.370CoIsomerDeconvolution.......................1674.2.4DecayoftheShort-Lived70CoIsomer.................1764.2.5DecayoftheLong-Lived70CoIsomer..................1804.2.6Half-Lifeofthe(0+
2)statein70Ni....................189Chapter5DiscussionandOutlook........................1965.1ShapeCoexistencein68;70Ni...........................1965.2Analysisof-DecayStrengthandIntensityDistributionsin68;70Ni.....2005.2.1Short-Lived,High-Spin,70CoIsomer..................2025.2.2Long-Lived,Low-Spin,70CoIsomer...................2045.2.3Long-Lived,Low-Spin,68CoIsomer...................2075.3Outlook......................................211xAPPENDICES......................................213AppendixAIdenticationofAdditionalPeaksObservedinPulseShapeAnalysisNotliatedWiththe0+
2!0+
1Transitionin68Ni..............214AppendixBand-double-pulseCoincidencesObservedFollowingthe-DecayoftheLong-Lived,Low-Spin,68CoIsomer...............219AppendixCCoincidencesObservedFollowingthe-DecayoftheShort-Lived,High-Spin,70CoIsomer..............................245AppendixDCoincidencesObservedFollowingthe-DecayoftheLong-Lived,Low-Spin,70CoIsomer...............................250BIBLIOGRAPHY....................................257xiLISTOFTABLESTable2.1:-decayselectionrules,adaptedfromRef.[25]............14Table2.2:Classicationof-decaytransitionsandassociatedlog10(f0t)values,adaptedfromRef.[24]..........................17Table2.3:Selectionrulesandelectromagnetictransitionrates,assumingasingle-particletransitionfromaninitialstatetoanalstate,fortherstfourmultipolaritiesofelectricandmagnetictransitions.isthemul-tipolarityofthetransition,ˇisthechangeinparitybetweentheinitialandnalstates,Eisthe-rayenergyinMeV,andAisthemassnumberofthenucleus.[24]....................22Table3.1:NumberofionsofeachisotopeimplantedintotheGeDSSDcrystalovertheninedaysofbeamtimeduringe14039.............33Table3.2:Numberofionsofeachisotopeimplantedintothesegmentedplasticscintillatoroverthesixdaysofbeamtimeduringe14057........35Table3.3:RatiosofinducedsignalsintheGeDSSDbystripnonadjacentstrips(n+1)or(n1).Whenmultipliedbythesignalamplitudeofstripnthesevaluescorrecttheamplitudeofthesignalpresentonstripsn+1orn1...............................48Table3.4:SummingcorrectionsusedforabsoluteeciencycalibrationwithSRMsource.TotalecienciesatagivenenergyEaredenotedas[E]whilephoto-peakecienciesaredenotedasfEg.Thecorrectedeciencyisobtainedbydividingtheexperimentaleciencybythevalueofthesummingcorrection....................77Table3.5:ValuesusedinEq.3.10toparameterizethe-raydetectioneciencyofSeGAfore14039and14057......................80Table4.1:Energiesandabsoluteintensitiesofthe-raytransitionsplacedin68Nifollowingthedecayofthelong-lived,low-spin,68Coisomerselectivelypopulatedbythedecayof68Fe.Theenergiesoftheinitialandnalstatesforeachtransitionarealsolisted........112Table4.2:Summaryofobserved-raycoincidencesfollowingthedecayofthelong-lived,low-spin,68Coisomerpopulatedbythedecayof68Fe..116xiiTable4.3:Energiesandabsoluteintensitiesof-raytransitionsplaced68Ni,detectedincoincidencewiththe0+
2!0+
1E0transition,followingthedecayofthelong-lived,low-spin,68Coisomer.Theenergiesoftheinitialandnalstatesbetweenwhicheachtransitionoccursarealsolisted.................................123Table4.4:Energiesandrelativeintensities(I1139:2=100%)ofunplaced-raytransitionscoincidentwiththe0+
2!0+
1E0transition,followingthedecayofthelong-lived,low-spin,68Coisomer............124Table4.5:Summaryof-double-pulsecoincidencesin68Nifollowingthede-cayofthelong-lived,low-spin,68Coisomer...............124Table4.6:Summaryofunplacedrayspotentiallyaliatedwiththedecayofthelong-lived,low-spin,68Coisomer..................129Table4.7:Decaycurveintegrationresultsandcorrectionfactorsfor68Niineachexperiment.The\corrected"numberofdecaysisobtainedbymul-tiplyingtheintegratednumberofcountsbythespuriouscorrelationandexclusiontechniquecorrelationfactors.Thecorrectednumberofdecaysisthendirectlycomparabletothenon-exclusionanalysis-delayed-raystatistics.........................146Table4.8:Decaycurvetresultsandcorrectionfactorsfor70Niine14039.The\corrected"numberofdecaysisobtainedbymultiplyingtheintegratednumberofcountsbythespuriouscorrelationandexclu-siontechniquecorrelationfactors.Thecorrectednumberofdecaysisthendirectlycomparabletothenon-exclusionanalysis-delayed-raystatistics..............................167Table4.9:Energiesandabsoluteintensitiesofthe-raytransitionsidentiedin70Nifollowingthedecayoftheshort-lived,high-spin,70Coiso-mer.Theenergiesoftheinitialandnalstatesbetweenwhicheachtransitionoccursarealsolisted.....................177Table4.10:Summaryof-raycoincidencesobservedfollowingthedecayoftheshort-lived,high-spin,70Coisomer...................178Table4.11:Energiesandabsoluteintensitiesofthe-raytransitionsidentiedin70Nifollowingthedecayofthelong-lived,low-spin,70Coiso-mer.Theenergiesoftheinitialandnalstatesbetweenwhicheachtransitionoccursarealsolisted.....................181xiiiTable4.12:Summaryof-raycoincidencesobservedfollowingthedecayofthelong-lived,low-spin,70Coisomer....................188Table4.13:Summaryofunplacedrayspotentiallyaliatedwiththedecayofthelong-lived,low-spin,70Coisomer..................189Table5.1:Half-lives,branchingratios,andeitherabsoluteB(E2)ine2fm4orˆ2(E0),dependingonthenatureofthetransition...........197xivLISTOFFIGURESFigure1.1:(a)Firstionizationenergyplottedasafunctionofatomicnumber.Thenoble-gaselementsandtheiratomicnumbers,correspondingtoclosedelectronshellcongurations,arelabeled.Allionizationen-ergiesweretakenfromRef.[2].(b)Dierentialneutronseparationenergiesasafunctionofneutronnumberforavarietyofeven-evennucleiadaptedfromRef.[3].Nucleialongthesameisotopicchainsareconnectedwithlines.........................2Figure1.2:Schematicrepresentationoftheeectofthemonopolecomponentofthetensorforce..............................4Figure1.3:ShellevolutionalongtheHgisotopicchain..............6Figure1.4:Systematicsof(a)2+
1stateenergiesand(b)B(E2;0+
1!2+
1)valuesasafunctionofneutronnumberfortheCr,Fe,andNiisotopes.DatatakenfromRef.[13]............................8Figure3.1:SchematicrepresentationoftheCoupledCyclotronFacility(CCF)[36]andA1900fragmentseparator[37]atNSCL...........29Figure3.2:Normalizedimplantationdepthdistributionsfor68Feand70CoionsdepositedinsidetheGeDSSDcrystalduringe14039..........31Figure3.3:ParticleidenticationplotforionsdepositedintheGeDSSDcrystalduringe14039.ThedatashownwereobtainedfromtheenergylossinformationprovidedbytherstPINdetectorandtheTOFmeasuredbetweentheextendedfocalplanescintillatorintheA1900andtherstPINdetector.Asaconditionontheplot,theGeDSSDhadto
recordcoincidentimplantenergydepositioninatleastonefrontandonebackstrip...............................32Figure3.4:Normalizedimplantationdepthdistributionsfor68Feand70Coionsdepositedinsidethesegmentedplasticscintillatorduringe14057...33Figure3.5:Particleidenticationplotforionsdepositedinthesegmentedplasticscintillatorduringe14057.ThedatashownwereobtainedfromtheenergylossinformationprovidedbytherstPINdetectorandtheTOFmeasuredbetweenthescintillatoratthedispersiveimageoftheA1900andtherstPINdetector.Asaconditionontheplot,the
segmentedplasticscintillatorhadtorecordimplantenergydeposition.34xvFigure3.6:ExampleofDDASdigitallteringalgorithms.AsampledetectorsignalacquiredfromtheplanarGeDSSDbya14-bit250MSPSis
showninblack.TheresponseoftheDDAStrigger-lteralgorithmisshownindarkredalongwiththeuser-denedtriggerlterthresholdillustratedasablackdashedline.ShownindarkblueistheresponseoftheDDASenergylteralgorithm.Keypointsintimerelatedtotriggeringandenergyextractionarelabeled..............37Figure3.7:ExampleoftheDDASdigitalconstantfractiondiscriminator(CFD)algorithm.AsampledetectorsignalacquiredfromaLaBr3detectorbya12-bit500MSPSisshowninblack.TheresponseoftheDDAS
CFDalgorithmisshowninredalongwiththeuser-denedCFD
thresholdillustratedasablackdashedline.Keypointsintimerelatedtoprecisiontimeextractionarelabeled.................40Figure3.8:DDASElectronicstimeresolutionforLaBr3detectortypesignals,generatedbyaAgilent33522Aarbitrarywaveformgenerator,asafunctionofinputsignalamplituderelativetothedynamicrangeoftheADC.Forsignalamplitudesoccupying>10%oftheADCdy-namicrangetheelectronicscontributiontothedetectorsystemtimeresolutionisessentiallynegligible....................41Figure3.9:Two-dimensionalhistogramshowingthemaximumlow-gainfrontchannelvs.themaximumlow-gainbackchannelforalllow-gaineventsine14039.Projectionsontothefront-andback-stripaxesareshowntotherightandabovethetwo-dimensionalhistogram,respec-tively.Thereisaclearregionofmissingeventsduetochargetrappingasaresultofcrystaldamage.......................44Figure3.10:Two-dimensionalhistogramshowingthemaximumhigh-gainfrontchannelvs.themaximumhigh-gainbackchannelforallhigh-gaineventsine14039.Projectionsontothefront-andback-stripaxesareshowntotherightandabovethetwo-dimensionalhistogram,respectively.Theregionofmissingeventsduetochargetrappingasaresultofcrystaldamageislessevidentduetothefactthattheelectronsandrayscantraveloutsidethelocalizeddamagedregionandcandepositenergyacrossthedepthofthedetector........45Figure3.11:RepresentativecrosstalkexamplefortheGeDSSDshowing(b)afullenergydepositionofa662-keVrayinstrip11.Panels(a)and(c)showinducedsignalsinstrips10and12respectively.Theseinducedsignalsyieldlow-energypeaksintheGeDSSDstripenergyspectraandmustbecalibratedout........................46xviFigure3.12:Representativesampleofcrosstalkcalibrationsusingstrip10onthebackoftheGeDSSD.Panels(a)and(b)showtheratioofthesignalinducedonstrips9and11,respectively,byasignalpresentonstrip10.47Figure3.13:ResultsofthecrosstalkcalibrationforarepresentativestripofthebackoftheGeDSSD.Theuncorrectedandcorrectedspectrafor137Csareshownin(a)and(b),respectively.Foreachspectrumaninsetexpandsthelowenergyregionanddemonstratestheexistenceandsubsequentremovalofthecrosstalkinducedpeaks...........49Figure3.14:Uncalibrated,crosstalkcorrected,energyspectraforall16backstripsoftheGeDSSDfora137Cssource.Strips4through9clearlyexhibitmultiplepeakswhichresultfromdierencesinchargecollectionalongthedamagedregionsofthosestrips.EnergieswereobtainedfromtheDDASdigitallter............................50Figure3.15:EnergyspectraofGeDSSDbackstrip7takenwitha137CssourceandhistogrammedbyinteractionlocationfromthefrontoftheGeDSSD.Theblack,green,cyan,magenta,red,andbluespectracorrespondtopositionsalongthelengthofbackstrip7basedonthecoincidentsignalinfrontstrips1,4,7,10,13,and16,respectively.Thelocationofthe662-keVphotopeakisidenticalforstrips1,13,and16butislowerinenergyforstrip4.Eventsoccurringinbackstrip7localizedtostrips7and10onthefrontdonotdisplayaphotopeak......51Figure3.16:Calibrated,crosstalkcorrected,energyspectraforall16backstripsoftheGeDSSDfora137Cssource....................52Figure3.17:Selectedlevelschemefor68NishowingthersttwolevelsandtheE0transitionthatconnectsthem......................53Figure3.18:Exampledouble-pulsesignalrecordedintheGeDSSDduringe14039.53Figure3.19:Responseofthetriggerlteralgorithmusedfortransientrejectionintheanalysisto(a)large-amplitudesinglepulse,(b)low-amplitudesin-glepulse,(c)negativetransient,and(d)positivetransientGeDSSDsignals.Detectorsignalsareshowninblackwhilethetriggerlterre-sponsesareshowninred.Triggerlterresponseshavebeenreducedbyafactoroftenandthebaselineofthesignalhasbeenadded...55Figure3.20:SampleresponseoftheGeDSSDtoasingleeventrecordedusinga137Cssource................................56xviiFigure3.21:Distributionof˜2dividedbysignalamplitude(˜2
n)forthetofhigh-gainGeDSSDsignalswithasingledetectorpulse.Alltsabovethereddashedlinearetwiththelinearcombinationoftwosingledetectorpulseswhilealltsbelowtheredsolidlineareconsideredgoodsingle-pulseevents.........................56Figure3.22:Single-pulsetresultsforavarietyofdierentsignaltypesintheGeDSSD.(a)Goodtofasinglepulsebyasingle-pulset.(b)Fitofatransientwithasinglepulse.(c)Fitofalowamplitudesignalwithasingle-pulset.(d)Fitofadouble-pulseeventwithasinglepulse.Detectorsignalsareshowninblackwhilethetsareshowninred.The˜2
nislabeledoneacht....................57Figure3.23:EnergyspectrumobtainedfromthetofGeDSSDsignalsbyasingletemplatedetectorsignalwhere˜2
n<250.MostofthecountsarefromthecontinuouselectronenergydistributionsfromdecayandfromCompton-scatteredrays.Thepeakat92.6-keVisfromthedecayofthe93.3-keV1=2statein67Znand141.4-keVtransitioncomesfromthedecayofthe242.6-keVisomericstatein70Cu.The185.0-keV,239.2-keV,and352.1-keVareroombackgroundlinesfrom226Ra,212Pb,and214Pb,respectively.................58Figure3.24:Plotofdouble-pulse˜2
nobtainedfromthetsofGeDSSDsignalsusingalinearcombinationoftwosingledetectorpulses........59Figure3.25:Plotof˜2
nvs.energyofthesecondpulsefortheGeDSSDobtainedfromthedouble-pulsettingmethod..................60Figure3.26:Panels(a)through(c)displayGeDSSDsignals,showninblack,withthedouble-pulset,showninred,overlayedforthreesignaltypesthatfailthedouble-pulsetbutpassthe˜2
ntest.Thevaluesobtainedfromthevarious˜2metricsusedforthisanalysis,describedinthetext,arelabeledoneachpanel.Oneormoreoftheadditional˜2cutsrejecteachsignalin(a)through(c).Agooddouble-pulsetisshownin(d)withthesamesetof˜2metricsas(a)through(c).Thetin(d)passesallmetrics.Inallpanelsthesignalsareshowninblackwhilethebestdouble-pulsettoeachsignalisshowninred.60xviiiFigure3.27:(a)Distributionof˜2
nTvalues.(b)Distributionof˜2
nLEvalues.(c)Distributionof˜2
nLELvalues.Theredverticallinesin(a)through(c)representtheupperlimitofacceptabilityforeachrespective˜2value,withacceptablevaluesbeingbelowtheredlineineachcase.(d)Plotoftheratio(single-pulset/double-pulset)of˜2
nvs.energyofthesecondpulseobtainedfromthedouble-pulsettingmethod.Valuesbelowtheredhorizontallineareacceptabledouble-pulseevents...61Figure3.28:Energyspectrumdisplayingtheenergyofthe(a)rstand(b)secondriseofthedouble-pulsesignals.Theenergieswereobtainedfromtheamplitudesoftheconstituentpulsesofdouble-pulsetssatisfyingthe˜2criteria,andwerecalibratedusingthetechniquesdescribedinSection3.5.4...............................62Figure3.29:PlotoftheenergyofthesecondriseofthedoublepulsesonthexaxisforeachbackstripoftheGeDSSDontheyaxis.........63Figure3.30:ResponseofthePSPMTtoasingleionimplantationeventinthesegmentedplasticscintillator.EachboxshowsthedigitizeddetectorsignalfromapixelofthePSPMT.Theheightofeachboxis16384ADCunits(1Vfullscalerange)andthewidthis500ns......66Figure3.31:Two-dimensionalhistogramshowingtheactiverowvs.activecolumninthePSPMT,determinedinthecenterofgravityalgorithm,forallimplantationeventsrecordedine14057.Projectionsontotheactive-rowandactive-columnaxesareshowntotherightandabovethetwo-dimensionalhistogram,respectively.................68Figure3.32:Two-dimensionalhistogramshowingtheactiverowvs.activecolumninthePSPMT,determinedinthecenterofgravityalgorithm,foralldecayeventsrecordedine14057.Projectionsontotheactive-rowandactive-columnaxesareshowntotherightandabovethetwo-dimensionalhistogram,respectively...................69Figure3.33:(a)Sampledouble-pulseeventrecordedduringe14057.(b)Samedouble-pulseeventasin(a)showninblackwithanoverlayofthescaledtriggerlteralgorithmshowninred.Thezerocrossingpointsofthetriggerlteralgorithmareusedtoidentifysubsequenttriggersandextracttiminginformation.(c)Overlayofthedynamicthreshold,showningreen,discussedinthetext.(d)Scaledresponseoftheenergylteralgorithmusedtoextracttheenergyofeachpulse....70xixFigure3.34:Creationofa\dynamic"thresholdtomitigatesubsequenttriggeringfromtheringingofthescintillatorduringthedouble-pulsesearch.Theredlineisthethresholdandalleventsbelowthresholdarecon-sideredasringingeventswhileeventsabovearefrompotentialdouble-pulseeventsinthePSPMT.......................71Figure3.35:Energyspectrumdisplayingtheenergyofthesecondconstituentpulseofthedouble-pulsesignalsrecordedine14057..........72Figure3.36:SeGAenergycalibrationresidualsforeachofthe16individualde-tectorsfromarepresentativeruntakenduringexperimente14039..74Figure3.37:(a)SeGAenergycalibrationresidualsforall16detectorscombinedoverthesamerepresentativerunusedinFig.3.36.(b)SeGAenergycalibrationresidualsforall16detectorscombinedforallrunsoverthedurationofe14039..........................75Figure3.38:Eciencyratios(Simulation/Experiment)forraysoftheSRMsourcewithSeGAinthe\beta-SeGA"conguration..........77Figure3.39:Eciencyratios(Simulation/Experiment)forraysoftheSRMsourceplaceddownstreamoftheplanarGeDSSDwithSeGAinthenale14039experimentalconguration.................78Figure3.40:Eciencyratios(Simulation/Experiment)forraysoftheSRMsourceplacedupstreamofthesegmentedplasticscintillatorwithSeGAinthenale14057experimentalconguration..........79Figure3.41:SimulatedSeGA-raydetectionecienciesforA=68nucleiinexper-imentse14039(blacksquares)ande14057(redcircles).ThedepthofionsinweretakenfromFigs.3.2and3.4fore14039ande14057,respectively,whiletheimplantxandydistributionsarefromFigs.3.9and3.31fore14039ande14057,respectively.Symbolsrepresentsimulationresultswhilelinesaresixth-orderpolynomialtstothesimulationresultsusedforinterpolation................80Figure3.42:EnergycalibrationresidualsfortheindividualtenLaBr3detectorsoverarepresentativegroupofsixrunsduringe14057.........82Figure3.43:(a)LaBr3energycalibrationresidualsforall10detectorscombinedoverthesamerepresentativegroupofrunsusedinFig.3.42.(b)SeGAenergycalibrationresidualsforall16detectorscombinedforallrunsoverthedurationofe14039..................82Figure3.44:Ratioof-rayeciencies(LaBr3/SeGA)asafunctionofenergy..83xxFigure3.45:(a)Two-dimensionalhistogramofthedynodesignalamplitudeplot-tedagainsttheLaBr3-PSMPTdynodetimedierenceforasingleLaBr3detectorgatedoneitherthe1173.2-or1332.5-keVphoto-peakinthatdetector.(b)Plotofcentroidposition,extractedfromttingtheprojectionofeachbinina)ontothetime-dierenceaxis.Ahigh-orderpolynomial,showninred,wasusedforinterpolationbetweenthedatatoextractthetimewalkasafunctionofdynodesignalamplitude.............................86Figure3.46:(a)Two-dimensionalhistogramoftheLaBr3energyplottedagainsttheLaBr3-PSMPTdynodetimedierenceforasingleLaBr3detec-torgatedondynodeamplitudesbetween20and500ADCunits.(b)PlotofcentroidpositionforeachLaBr3energybin,extractedfromttingtheprojectionofeachbinin(a)ontothetime-dierenceaxis.Ahighorderpolynomial,showninred,wasusedextractthetimewalkasafunctionofLaBr3energy...................88Figure3.47:(a)LaBr3energyspectrumforalltendetectors,gatedondynodeamplitudesof>60and<500ADCunits,intheregionaround1077.4keV.Thepeakandbackgroundregionsusedforthisanalysisaredenotedwithredsolidandreddashedlines,respectively.......89Figure3.48:(a)Background-subtractedtwo-dimensionaldynodesignalamplitudevs.time-dierencespectrumforthe1077.4-keVpeakintheexperi-mentaldata.(b)Thetwo-dimensionaldynodesignalamplitudevs.time-dierencespectrumforthe60Cosourcemeasurementsforthesameenergygateasa)..........................90Figure3.49:(a)Sigma(inns)asafunctionofdynodesignalamplitudeshowninbluecirclesfortheexperimentaldataandasblacksquaresforthesourcedatapresentedinFigs.3.48aand3.48b,respectively.(b)Theratio(experiment/source)ofsigmavaluesfroma)asafunctionofdynodesignalamplitude.ThettothedatarepresentstheDOIcorrectionforthetimeresolution....................91Figure3.50:(a)LaBr3energyvs.timedierenceand(b)vs.LaBr3energydyn-odeamplitude,respectively,forthesameLaBr3energyrangeasinFig.3.47.Thesame1064-to1094-keVpeakand1110-to1140-
keVbackgroundregionsillustratedinFig.3.47areshownagainbyredsolidanddashedlines,respectively.Panels(c)and(d)showtheprojectionsofa)andb)ontothetime-dierenceanddynodeam-plitudeaxesrespectively,forthepeakregionbetweenthesolidredlines.Panels(e)and(f)showtheprojectionsof(a)and(b)ontothetime-dierenceanddynodeamplitudeaxesrespectively,forthebackgroundregionbetweenthedashedredlines............95xxiFigure3.51:DynodesignalamplitudedistributionfortheLaBr3-dynodecoinci-dencesbetween1064and1094keV.ThisdistributionisobtainedbysubtractingthedatainFig.3.50f,scaledbys,fromFig.3.50d.Thecountsateachdynodeenergy,Ep,atthisspecicenergy,E,arePEp;EfromEq.(3.11).........................96Figure3.52:Resultsofthettingtechniqueforthe1077.4-keVstatein68Zn.Thetotaltime-dierencespectrumforthe1064-to1094-keVLaBr3energyregion,alsoshowninFig.3.50c,isshowninblack.Thescaledback-groundtime-dierencespectrumoverthe1110-to1140-keVLaBr3energyregionisshowninblue,whilethetotaltofthedetectorre-sponseforthecountsunderthepeakisshowninredandthetotaltisshownincyan.............................97Figure3.53:LaBr3energyspectrumforalltendetectors,gatedondynodeampli-tudesof>60and<500ADCunits,intheregionaround594.3keV.Thepeakandbackgroundregionsusedfortheanalysisaredenotedwithredsolidandreddashedlines,respectively............98Figure3.54:Distributionof˜2valuesobtainedfromacomparisonofthetotalt,R(t;t0;˝;E;Ep),andtheexperimentaldata,shownascyanandblackinFig.3.55,respectively,forfourteenhalf-lifevaluesequallydistributedabouttheminimum.Thedistributionistwithasecondorderpolynomialshowninred.Thelocationoftheminimumrepre-sentsthehalf-lifeofthestateandthesecondderivativeofthetistheerroronthatvalue.Ahalf-lifeof135(26)psisobtainedforthe915.3-keVstatein69Niwhichagreeswiththepreviouslymeasuredvalueof120(34)ps[53]..........................99Figure3.55:Resultsofthettingtechniqueforthe915.3-keVstatein69Ni.Thetotaltime-dierencespectrumforthe574-to614-keVLaBr3energyregionisshowninblack.Thescaledbackgroundtime-dierencespec-trumoverthe620-to660-keVLaBr3energyregionisshowninblue,whilethetotaltofthedetectorresponseforthecountsunderthepeakisshowninredandthetotaltisshownincyan........100Figure3.56:LaBr3energyspectrumforalltendetectors,gatedondynodeampli-tudesof>60and<500ADCunits,intheregionaround448.5keV.Thepeakandbackgroundregionsusedfortheanalysisaredenotedwithredsolidandreddashedlines,respectively............101xxiiFigure3.57:Distributionof˜2valuesobtainedfromacomparisonofthetotaltandtheexperimentaldata,shownascyanandblackinFig.3.55,respectively,forfourteenhalf-lifevaluesequallydistributedabouttheminimum.Thedistributionistwithasecondorderpolynomialshowninredresultinginalifetimeof1.04(6)nsforthe2677-keVstatein70Ni................................102Figure3.58:Resultsofthettingtechniqueforthe2677-keVstatein70Ni.Thetotaltime-dierencespectrumforthe396-to424-keVLaBr3energyregionisshowninblack.Thescaledbackgroundtime-dierencespec-trumoverthe434-to462-keVLaBr3energyregionisshowninblue,whilethetotaltofthedetectorresponseforthecountsunderthepeakisshowninredandthetotaltisshownincyan........103Figure4.1:Decayscheme,adaptedfromRef.[21],forthedecayofthelow-spin68Coisomerpopulatingstatesin68Nirepresentingtheextentofknowledgepriortothepresentwork.Otherlow-energylevelsin68Ni,notshownhere,areknownfromreactionstudiesanddecayspectroscopyofthehigh-spin68Coisomer.Threespinandparityas-signmentsof(1;+;2;3+)havebeenproposedforthelow-spin68CoisomerbyRefs.[12,21,55].The1.6(3)shalf-lifecomesfromRef.[12],asdoesthe<15nslimitonthehalf-lifeofthe2511-keV0+
3state.A-delayedneutronbranchof>2.6%wasreportedbyRef.[21].The-decayQ-valuewastakenfromRef.[56].Alllogftvaluesand-decayfeedingintensitiesweretakenfromRef.[21].Thehalf-livesof270(5)nsforthe1604-keV0+
2state,0.31(5)psforthe2033-keV2+
1,and0.86(5)msforthe2847-keV5stateweretakenfromRef.[22].105Figure4.2:-delayed-rayspectrumrecordedinSeGAwithin4000msofanimplanted68Feion.Transitionsidentiedinthesubsequentanalysisasaliatedwiththedecayof68Niarelabeledwiththeirenergywhilecontaminatingtransitions,resultingfromspuriouscorrelationsofthedecayofotherimplantednuclei,aredenotedwithsymbols.Thepeaksat1460and2614keVareknownbackground-raysfromthedecayof40K[49]and208Tl[50],respectively.Theinsetin(e)showsthefullheightofthe2032.9-keVpeaktruncatedinthespectrumdisplayedin(e).....................................109Figure4.3:Background-subtractedcoincidencespectragatedonthe1514.3-keV(2+)!0+
3transitionin68Nifocusingaroundthe511-keVre-gion.Thebackgroundwastakenbelowthe1514.3-keVpeaktoavoidthe1521.5-keVsingleescapepeakfromthe2032.9-keVray.TheupperrangeofthegatewasalsoreducedbyacoupleofkeVtoavoidincludingthelow-energytailofthe1521.5-keVescapepeak......115xxiiiFigure4.4:Spectrumofraysrecordedincoincidencewiththedetectionofthe0+
2!0+
1E0transitionin68Ni.Theinsetin(a)showsthefullheightofthe511-keVpeaktruncatedin(a).Theleftandrightinsetsin(c)showthefullheightsofthe1139.2-and2422.0-keVpeakstruncatedinpanels(b)and(c),respectively.Theinsetin(f)showsthe6000-to6400-keVregionofthesamespectrumpresentedin(a)through(f).Inallcasestransitionsarelabeledwiththeirenergiesand,whenapplicable,singleanddouble-escapepeaksaredenotedwithoneortwostars,respectively,inadditiontotheenergyofthepeak.....119Figure4.5:Spectrumofraysrecordedincoincidencewiththedetectionofthe0+
2!0+
1E0transitionin68Nifocusedinonthe1514.3-keVregion.121Figure4.6:Decayschemeforthelong-lived,low-spin,68Coisomerpopulatedthroughthedecayof68Fe.Statesin68NiarelabeledwithanenergyinkeVandthespininparity(ifknown)ontheright.Ontheleft,-decaybranchingratiosandlog10ftvaluesareshown.-decayQ-valuetakenfromRef.[56].The0.31(5)pshalf-lifeofthe2033-keV2+
1stateistakenfromtheevaluationinRef.[22]...........125Figure4.7:Motivationforthedevelopmentoftheexclusiontechnique.Twode-caycurvesfor68Feareshowninblackin(a)and(b)obtainedfromtheanalysisusingthenon-exclusionandexclusioncorrelationtechniques,respectively.Thedecaycurveshavehadtheirspurious-correlationcomponent,determinedusingthetechniquesinSection4.1.2.1,sub-tractedoutandwerenormalizedhaveequivalentintegralnumbersofcounts.Foreachdecaycurveatotalt(red)wasperformedcom-prisedof68Feparent(green),68Codaughter(magenta),and68Nigranddaughter(orange)decays.Thehalf-lifeof68Niwasxedtotheliteraturevalueof29s[22].Fitresiduals,normalizedtothebiner-ror,areshownin(c)and(d)forthetotaltcomparedtothedatain(a)and(b),forthenon-exclusionandexclusiondecaycurvets,respectively................................132xxivFigure4.8:Schematicviewoftheexclusiontechniquehighlightingthedierenceswiththenon-exclusioncorrelationtechniques.Thetimestructureofimplantations(blackverticallines),parentdecays(redverticallines),anddaughterdecay(blueverticallines)fortwoimplantedionsisshown.Solidanddashedlinesareusedtodistinguisheventsaliatedwitheachdierention.Horizontalgreenbarsrepresentthecorrelationsandagrayhorizontalbarrepresentsadecayeventthatisoutsidethecorrelationwindow.In(a)theexclusionwindowoftimeisacrosshatchedrectangleabovethecorrelations.Implantsremovedfromtheanalysisbytheexclusiontechniquearelabeledwithan\X".Timeproceedsforwardlefttorightindicatedbytheblackarrowatthebottomofeachpanel........................134Figure4.9:(a)Decaycurvevs.coincident-rayenergy,recordedinSeGAduringe14039,fortheregionaroundthe161.8-and184.3-keVpeaks.(b)Projectionof(a)ontotheenergyaxis.Setsofsolidredverticallinesanddashedverticallinesidentifythepeakandbackgroundregions,respectively,foreachpeak........................136Figure4.10:Decaycurvesobtainedbyprojecting4.27aontothetime-dierenceaxisovertheregionsof(a)159to165keV,(b)166to172keV,
(c)181to187keV,and(d)185to195keV.Regionsshownin(a)
and(c)representtheencompassthe161.8-keVand184.3-keVpeaks,respectively,while(b)and(d)arerepresentativebackgroundstobescaledandsubtractedforeachrespectivepeak.............137Figure4.11:(a)Background-subtracted-gateddecaycurveforthedecayof68Feinto68Co.Gateswereplacedonthe161.8-keVand184.3-keVtran-sitionsin68Coandthebackground,scaledappropriatelyandsub-tracted,wassampleddirectlyaboveeachpeak.Thebackground-subtracteddataareshowninblackwhilethespuriouscorrelationcomponent,obtainedusingthetechniquesinSection4.1.2.1,isshowninblue.Incyan,attothespuriouscorrelationcomponentisshown,andwasusedtorepresentthespuriouscorrelationsinthetotaltofthedatashowninred.Thecontributionfromthedecayof68Feisshowningreen.Thehalf-lifeof68Fe,extractedfromthet,is175(9)ms.Thiscomparestotheevaluatedvalueof188(4)ms[22].(b)Fitresidualsforthetotaltcomparedtothedatain(a)normalizedtothebinerrorin(a)............................138Figure4.12:Resultsoftheanalysisrunbackwardsintimethroughthedata.(a)Decaycurvevs.coincident-ray,recordedinSeGAduringe14039,fortheregionaroundthe161.8-and184.3-keVpeaks.(b)Projectionof(a)ontotheenergyaxis........................139xxvFigure4.13:(a)Double-pulse-gateddecaycurveforthedecayof68Cointo68Ni.Thedataareshowninblackwhilethespuriouscorrelationcompo-nent,obtainedbyrunningtheanalysisbackwardsintimeandscaledbythet,isshowninblue.Incyan,attothespuriouscorrelationcomponentisshown,andwasusedtorepresentthespuriouscorrela-tionsinthebesttotaltofthedatashowninredusingthehalf-lifeoftheminimumobtainedfromFig.4.14.Thecontributionfromthedecayof68Coisshowninmagenta.(b)Fitresidualsforthetotaltcomparedtothedatain(a)normalizedtothebinerrorin(a)....140Figure4.14:Distributionof˜2valuesasafunctionof68Cohalf-lifeobtainedfromttingthedatashowninblackinFig.4.13withacombinationofspuriouscorrelationsandthe68Codaughtergrow-in,describedbyequation(2.21).Thespurious-correlationcomponentandhalf-lifeof68Fewerexedleavingthe68Cohalf-lifeastheonlyfreeparameter.The˜2distributionwastwithafthorderpolynomial,showninred,forinterpolationbetweenpoints.Avalueof2360(130)mswasextractedforthehalf-lifeofthe68Colow-spinisomer.........141Figure4.15:(a)Decaycurveforthedecayofionsof68Feine14039.Thedataareshowninblackwhilethespuriouscorrelationcomponent,obtainedbyrunningtheanalysisbackwardsintimeandscaledbythet,isshowninblue.Incyan,attothespuriouscorrelationcomponentisshown,andwasusedtorepresentthespuriouscorrelationsinthebesttotaltofthedatashowninredusingthehalf-lifeoftheminimumobtainedfromFig.4.14.Thecontributionfromthedecayof68Fe,68Co,and68Niisshowningreen,magenta,andorange,respectively.Thetotaltisshowninred.(b)Fitresidualsforthetotaltcomparedtothedatain(a)normalizedtothebinerrorin(a)..............143Figure4.16:(a)Decaycurveforthedecayofionsof68Feine14057.Thedataareshowninblackwhilethespuriouscorrelationcomponent,obtainedbyrunningtheanalysisbackwardsintimeandscaledbythet,isshowninblue.Incyan,attothespuriouscorrelationcomponentisshown,andwasusedtorepresentthespuriouscorrelationsinthebesttotaltofthedatashowninredusingthehalf-lifeoftheminimumobtainedfromFig.4.14.Thecontributionfromthedecayof68Fe,68Co,and68Niisshowningreen,magenta,andorange,respectively.Thetotaltisshowninred.(b)Fitresidualsforthetotaltcomparedtothedatain(a)normalizedtothebinerrorin(a)..............144xxviFigure4.17:(a)and(b)Time-dierencedistributionsbetweenthetwoconstituentpulsesofdoublepulsesignalsrecordedine14057ande14039,respec-tively.Thesecondpulsewasrestrictedtoamplitudesbetween400and8000ADCunitsine14057andenergiesof400and2000keVfor
e14039.Aweightedaveragebetweenthetworesultsyieldsavalueof274(4)nsforthehalf-lifeofthe0+
2statein68Ni............148Figure4.18:Spectrumof-raysrecordedintheLaBr3detectorsaroundthe477.7-keVpeakcoincidentwithadecayeventinthesegmentedplasticscintillator.Thesetofsolidredanddashedredbarsrepresenttheenergywindowsusedforthepeakandbackgroundregionsofinterest,respectively................................149Figure4.19:(a)Two-dimensionalspectrumof-raysrecordedintheLaBr3de-tectorscoincidentwithadecayeventinthesegmentedplasticscin-tillatorvs.timedierencebetweentheLaBr3andsegmentedplasticscintillator.Thesolidredanddashedredbarsdenotetheenergywindowsusedforthepeakandbackgroundregionsofinterest(ROI),respectively.(b)and(c)Time-dierencespectra(LaBr3-segmentedplasticscintillator)obtainedbyprojectingthespectrumin(a)ontothetime-dierenceaxisovertheregionsbetweenthesolid(peakROI)anddashed(backgroundROI)redlines,respectively..........150Figure4.20:˜2asafunctionoftrialhalf-lifeusedineachconvolutiont,shownasblacksquares,andquadratict,showninred,forinterpolationbetweenpoints..............................151Figure4.21:Besttresultsforthelifetimeofthe0+
3statein68Ni.Inblackandbluearethetime-dierencespectraforthepeakandbackgroundROIsshowninFigs.4.19band4.19c,respectively.Theconvolutionofthedetectorresponsewiththebest-thalf-lifeisshowninRedandthetotaltofbackgroundplusconvolutionisshownincyan.....151Figure4.22:-delayed-rayspectrumrecordedinSeGAwithin4000msofanimplanted70Coion.Transitionsidentiedinthesubsequentanalysisasaliatedwiththedecayof70Niarelabeledwiththeirenergywhilecontaminatingtransitions,resultingfromspuriouscorrelationsofthedecayofotherimplantednuclei,aredenotedwithsymbols.Theinsetin(c)showsthefullheightofthe1259.1-keVpeakcutoinspectrumshownin(c).Theinsetin(e)showsthefullheightofthe2032.9-keVpeakcutoinspectrumshownin(e)..................154xxviiFigure4.23:(a)Decaycurvevs.coincident-rayenergy,recordedinSeGAduringe14039,fortheregionaroundthe448.5-keVpeak.(b)Projectionof(a)ontotheenergyaxis.Setsofsolidredverticallinesanddashedverticallinesidentifythepeakandbackgroundregions,respectively,foreachpeak...............................158Figure4.24:(a)and(b)Decaycurvesobtainedbyprojecting4.23aontothetime-dierenceaxisovertheregionsof(a)443to453keVand(b)433to443keV.Theregionshownin(a)encompassesthe448.5-keVpeakwhile(b)isarepresentativebackgroundtobescaledandsubtractedfromthepeak..............................158Figure4.25:(a)Background-subtracted,-gateddecaycurveforthedecayoftheshort-lived,high-spin,70Coisomerinto70Ni.Agatewasplacedonthe448.5-keVtransitionsin70Nitoisolatedtheshort-lived,high-spin,isomerexclusively.Thebackground,scaledappropriatelyandsubtracted,wassampleddirectlybelowthepeak.Thebackground-subtracteddataareshowninblackwhilethespuriouscorrelationcomponent,obtainedusingthetechniquesinSection4.1.2.1,isshowninblue.Incyan,attothespuriouscorrelationcomponentisshown,andwasusedtorepresentthespuriouscorrelationsinthetotaltofthedatashowninred.Thecorrelatedcontributionfromthedecayof70Coisshowningreen.Thehalf-lifeofshort-lived,high-spin,70Coisomer,extractedfromthet,is104.5(20)mswhichagreeswiththeevaluatedvalueof114(7)ms[58].(b)Fitresiduals,normalizedtothebinerror,forthetotaltcomparedtothedatain(a).......159Figure4.26:Resultsoftheanalysisrunbackwardsintimethroughthedata.(a)Decaycurvevs.coincident-ray,recordedinSeGAduringe14039,fortheregionaroundthe448.5-keVpeak.(b)Projectionof(a)ontotheenergyaxis..............................160Figure4.27:(a)Decaycurvevs.coincident-rayenergy,recordedinSeGAduringe14039,fortheregionaroundthe607.6-keVpeak.(b)Projectionof(a)ontotheenergyaxis.Setsofsolidredverticallinesanddashedverticallinesidentifythepeakandbackgroundregions,respectively,foreachpeak...............................161Figure4.28:(a)and(b)Decaycurvesobtainedbyprojecting4.27aontothetime-dierenceaxisovertheregionsof(a)605to615keVand(b)635to645keV.Theregionshownin(a)encompassesthe607.6-keVpeakwhile(b)isarepresentativebackgroundtobescaledandsubtractedfromthepeak..............................162xxviiiFigure4.29:(a)Background-subtracted-gateddecaycurveforthedecayoftheshort-lived,high-spin,70Coisomerinto70Ni.Agatewasplacedonthe607.5-keVtransitionsin70Nitoisolatedtheshort-lived,high-spin,isomerexclusively.Thebackground,scaledappropriatelyandsubtracted,wassampleddirectlybelowthepeak.Thebackground-subtracteddataareshowninblackwhilethespuriouscorrelationcomponent,obtainedusingthetechniquesinSection4.1.2.1,isshowninblue.Incyan,attothespuriouscorrelationcomponentisshown,andwasusedtorepresentthespuriouscorrelationsinthetotaltofthedatashowninred.Thecorrelatedcontributionfromthedecayof70Coisshowningreen.Thehalf-lifeofshort-lived,high-spin,70Coisomer,extractedfromthet,is470(20)msforthelong-lived,low-spin,70Coisomerwhichisconsistentwiththepreviouslymeasuredvalueof500(180)ms[12].(b)Fitresiduals,normalizedtothebinerror.163Figure4.30:Resultsoftheanalysisrunbackwardsintimethroughthedata.(a)Decaycurvevs.coincident-ray,recordedinSeGAduringe14039,fortheregionaroundthe607.6-keVpeak.(b)Projectionof(a)ontotheenergyaxis..............................164Figure4.31:(a)Decaycurveshowingthetimedistributionofrecordeddecayeventsfollowingwithin4000msofanimplanted70Coion.A4000ms\exclusionwindow"wassetfollowingtheimplantationofeachionsuchthatallsubsequentionswithinthatwindowwereignored.Thetotaltisshowninred,thedataareshowninblack,andthetimedistributionofspuriouscorrelations,obtainedbyrunningtheanalysisbackwardsintime,isshowninblue.The70Coparent,70Nidaugh-ter,and70Cugranddaughtercontributionsareillustratedasgreen,cyan,andmagentalines,respectively.Theshort-livedisomerdecayisshownassolidlineswhilethelong-livedisomerdecayisshownasadashedline.Thehalf-livesof70Niand70CuwerexedtotheNNDCevaluatedvaluesof6.0(3)sand6.6(3)s[59],respectively.Fromthet,thehalf-lifeoftheshort-lived70Coisomerwasdeterminedtobe104(4)mswhileahalf-lifevalueof450(13)mswasextractedforthelong-lived70Coisomer.(b)Fitresidualsnormalizedtotheerrorineachbin..................................166xxixFigure4.32:(a)Decaycurveshowingthetimedistributionofrecordeddecayeventsfollowingwithin4000msofanimplanted70Coiongatedonthe1259.1-keV(2+
1!0+
1)transition.Thesame4000ms\exclusionwindow"wassetfollowingtheimplantationofeachionsuchthatallsubsequentionswithinthatwindowwereignored.Thetotaltisshowninred,thedataareshowninblack,andthescaledtimedistributionofspuriouscorrelationsusedinFig.4.31,obtainedbyrunningtheanalysisbackwardsintime,isshowninblue.The70Coparentisshowningreenandtheshort-andlong-livedisomerdecaysareshownassolidanddashedlines,respectively.Half-livesof106(5)and446(42)mswereextractedfromthetfortheshort-andlong-lived70Coisomers,respectively.Thesevaluesareconsistentwiththe104.5(20)and470(20)msdeterminedearlierinthissection.(b)Fitresidualsnormalizedtothebinerror..................168Figure4.33:(a)Transformeddecaycurveshowingthenaturallogarithmofthetimedistributionofrecordeddecayeventsfollowingwithin4000msofanimplanted70Coiongatedonthe1259.0-keV(2+
1!0+
1)tran-sition.Thesame4000ms\exclusionwindow"wassetfollowingtheimplantationofeachionsuchthatallsubsequentionswithinthatwindowwereignored.Thetotaltisshowninred,thedataare
showninblack,andthescaledtimedistributionofspuriouscorrela-tionsusedinFig.4.31,obtainedbyrunningtheanalysisbackwardsintime,isshowninblue.The70Coparentisshowningreenandtheshort-andlong-livedisomerdecaysareshownassolidanddashedlines,respectively.Half-livesof104(5)and440(50)msfortheshort-andlong-lived70Coisomers,respectively,wereextractedfromthet.(b)Fitresidualsnormalizedtothebinerror..............170Figure4.34:Naturallogarithmofthetimedierencebetweendecayand70Coionimplantation,shownontheyaxis,ishistogrammedvs.coincident-delayed-rayenergyfrom0to1500keVonthexaxis.ThezaxisiscountsperunittimedierenceperkeV...............171Figure4.35:Resultsofttingtheprojectionsofeachenergybinontothetimeaxisofthetwo-dimensionalhistogramofthenaturallogarithmofthetimedierencebetweendecayand70Coionimplantationvs.coincident-delayed-rayenergy.Theintegralofeachcomponentisshownasahistogram.Theshort-andlong-livedisomercontributionsareshownasgreenandmagenta,respectively,whilethespuriouscorrelationcomponentisshowninblue.Thesumofallcomponentsisshowninredandthetotalprojectionofthetwo-dimensionalspectrumontotheenergyaxisisshowninblack.Theinsetin(d)showsthefullheightofthe1259-keVtransitioncutoin(d).Theinsetin(e)showsthefullheightofthe2033-keVtransitioncutoin(f)...........173xxxFigure4.36:Decayschemefortheshort-lived,high-spin,70Coisomer.Statesin70NiarelabeledwithanenergyinkeVandthespininparity(ifknown)ontheright.Ontheleft,-decaybranchingratiosandlog10ftvaluesareshown.QvaluetakenfromRef.[56]...........179Figure4.37:Backgroundsubtractedcoincidencespectrumgatedonthe1259.1-keV(2+
1!0+
1)transitionwithin4000msofthedecayof70Cofrom(a)0to2500keVand(b)from2500to5000keV.Thebackgroundwastakensymmetricallyeithersideofthe1259.1-keVpeak.Coincidencesaliatedwiththelong-lived,low-spin,70Coisomerarelabeledwithanenergywhilecoincidencesaliatedwiththeshort-lived,high-spin,70Coisomeraredenotedwithblacksquares.Escapepeaksarede-notedwithblackstarsandtransitionsseenincoincidencesbutnotinsinglesaredenotedwithasingleasterisk................184Figure4.38:Backgroundsubtractedcoincidencespectrumgatedonthe607.6-keV(2+
2!2+
1)[panels(a)and(b)]and1866.5-keV(2+
2!0+
1)[panels(c)and(d)]transitionswithin4000msofthedecayof70Co.Thebackgroundwastakensymmetricallyeithersideofeachpeak.Coincidencesaliatedwiththelong-lived,low-spin,70Coisomerarelabeledwithanenergywhilecoincidencesaliatedwiththeshort-lived,high-spin,70Coisomeraredenotedwithblacksquares.Con-taminatingcoincidencesaredenotedwithblackupside-downtrianglesandlabeledwiththeoendingisotope,ifknown............185Figure4.39:Backgroundsubtractedcoincidencespectrumgatedonthe(a)307.6-keVand(b)1943.8-keVtransitionswithin4000msofthedecayof70Co.Thebackgroundwastakensymmetricallyeithersideofthe307.6-keVpeakandbelowthe1943.8-keVpeakduecloselyneighbor-ingtransitions.Coincidencesaliatedwiththelong-lived,low-spin,70Coisomerarelabeledwithanenergy.................186Figure4.40:(a)Backgroundsubtractedcoincidencespectrumgatedonthe1943.8-keVtransitionwithin4000msofthedecayof70Co.(b)Beta-gated-raysinglesspectrumwithin4000msofthedecayof70Co.Bothspectrahighlighttheregionaround1567keVandno1567-keVpeakisobservedineitherspectrum...................186Figure4.41:Decayschemeforthelong-lived,low-spin,70Coisomer.Statesin70NiarelabeledwithanenergyinkeVandthespininparity(ifknown)ontheright.Ontheleft,-decaybranchingratiosandlog10ftvaluesareshown.aQ-valuetakenfromRef.[56]..........190xxxiFigure4.42:(a)and(b)Spectrumof-raysrecordedintheLaBr3andSeGAdetectors,respectively,coincidentwitha70Codecayeventinthesegmentedplasticscintillator.(c)Spectrumof-raysrecordedintheLaBr3coincidentwithadecayeventinthesegmentedplasticscintillator.(d)Spectrumshowninpanel(c)gatedonthe1259.1-keVtransitioninSeGA.Inpanels(c)and(d)thecoincidencewindowbetweentheLaBr3detectorsandPSPMTwas50nsandin(d)theLaBr3-SeGAcoincidencewindowwas600ns.Inallpanelsthesetofsolidredanddashedredbarsrepresenttheenergywindowsusedforthepeakandbackgroundregionsofinterest,respectively.......191Figure4.43:(a)Two-dimensionalspectrumof-raysrecordedintheLaBr3de-tectorscoincidentwithadecayeventinthesegmentedplasticscin-tillatorvs.timedierencebetweentheLaBr3andsegmentedplasticscintillator.Thesolidredanddashedredbarsdenotetheenergywindowsusedforthepeakandbackgroundregionsofinterest(ROI),respectively.(b)and(c)Time-dierencespectra(LaBr3-segmentedplasticscintillator)obtainedbyprojectingthespectrumin(a)ontothetime-dierenceaxisovertheregionsbetweenthesolid(peakROI)anddashed(backgroundROI)redlines,respectively..........192Figure4.44:˜2asafunctionoftrialhalf-lifeusedineachconvolutiont,shownasblacksquares,andquadratict,showninred,forinterpolationbetweenpoints..............................193Figure4.45:Besttresultsforthelifetimeofthe(0+
2)statein70Ni.Inblackandbluearethetime-dierencespectraforthepeakandbackgroundROIsshowninFigs.4.43band4.43c,respectively.Theconvolutionofthedetectorresponsewiththebest-thalf-lifeisshowninRedandthetotaltofbackgroundplusconvolutionisshownincyan.....193Figure5.1:Half-livesandtransitionstrengthsofthelowestfourstatesin68Ni(left)andthelowestthreestatesin70Ni(right)comparedwithpre-dictionsofadvancedshellmodelcalculationsusingtheLNPS[21]andA3DA[68]eectiveinteractions.Half-livesofthestates,whenknown,aregivenontheupperleftsideofeachlevelwiththeassociateden-ergies(inkeV)onthelowerleftside.Unobservedtransitionsareindicatedbydottedlines.ElectricmonopoletransitionstrengthsaregivenfortheE0transitions,whileB(E2)values,inunitsofe2fm4,aregivenforE2transitions.Experimentalvaluesforthe2+
1statehalf-lifeandB(E2)for70NiareadoptedfromRef.[64].Notethat,whileLNPSpredictionsofthe70NiB(E2:0+
2!2+
1)valuehavenotbeenpublishedsofar,Ref.[69]indicatesacalculatedB(E2:2+
1!0+
1)valueof102e2fm4withthisinteraction(notshown)..........198xxxiiFigure5.2:Apparentcumulative-decayintensitiesdeducedfromtheexperi-mentaldecayschemeinFig.4.36(blacklinewithsalmonerrorbars)comparedwithshellmodelcalculations(dasheddarkblueline)....202Figure5.3:Apparentcumulative-decayintensitiesdeducedfromtheexperi-mentaldecayschemeinFig.4.36(blacklinewithturquoiseerrorbars)comparedwithshellmodelcalculations(dasheddarkblueline).203Figure5.4:Apparentcumulative-decayintensitiesdeducedfromtheexperi-mentaldecayschemeinFig.4.41(blacklinewithsalmonerrorbars)comparedwithshellmodelcalculations(dasheddarkblueline)....205Figure5.5:Apparentcumulative-decayintensitiesdeducedfromtheexperi-mentaldecayschemeinFig.4.41(blacklinewithturquoiseerrorbars)comparedwithshellmodelcalculations(dasheddarkblueline).206Figure5.6:Apparentcumulative-decayintensitiesdeducedfromtheexperi-mentaldecayschemeinFig.4.6(blacklinewithsalmonerrorbars)comparedwithshellmodelcalculations(dasheddarkblueline)....208Figure5.7:Apparentcumulative-decayintensitiesdeducedfromtheexperi-mentaldecayschemeinFig.4.6(blacklinewithturquoiseerrorbars)comparedwithshellmodelcalculations(dasheddarkblueline).209FigureA.1:(a)Coincidentrstriseenergiesofdoublepulseswitha92.6-keVsecondriseenergy.(b)GammaraysrecordedinSeGAcoincidentwithdoublepulsesrecordedintheGeDSSDwiththeenergyofthesecondriseinthe92.6-keVpeak....................215FigureA.2:GammaraysrecordedinSeGAcoincidentwithdoublepulsesrecordedintheGeDSSDwiththeenergyofthesecondriseinthe175-keV
peak.The511-and1139.2-keVpeaks,labeledwithtwoasterisks,arecoincidentwiththedecayofthe0+
2statein68Niduringeventswherethetherewasincompleteenergycollectionforthepair-productionorinternalconversiondecayprocesses.The806.2-keVpeakisnewandremainsunidentied...........................216xxxiiiFigureA.3:GammaraysrecordedinSeGAcoincidentwithdoublepulsesrecordedintheGeDSSDwiththeenergyofthesecondriseinthe190-keV
peak.The511-keVpeak,labeledwithtwoasterisks,wascoincidentwiththedecayofthe0+
2statein68Niduringeventswherethetherewasincompleteenergycollectionforthepair-productionorinternalconversiondecayprocesses.The1357-keVpeakwascoincidentwithanunresolvedandunidentiedˇ200keVsecondpulseenergy.The681-and1870-keVtransitionsarefromthe680.6-1872.3-keV-raycascadethatdepopulatesthe2552-keVstatein69Cu[52].......217FigureB.1:Background-subtractedcoincidencespectragatedonthe2032.9-keV2+
1!0+
1transitionin68Ni.Thebackgroundwastakensymmet-ricallyeithersideofthe2032.9-keVpeak.Coincidenttransitionsarelabeledwiththeirenergiesand,whenapplicable,singleanddouble-escapepeaksaredenotedwithoneortwostars,respectively,inad-ditiontotheenergyofthepeak.....................220FigureB.2:Background-subtractedcoincidencespectragatedonthe(a)709.3-keV,(b)1139.2-keV,(c)2742.2-keV,and(d)sumofthe709.3-,1139.2-,and2742.2-keVtransitions.Thebackgroundwastakensym-metricallyeithersideofeachrespectivepeakregion.Coincidenttran-sitionsarelabeledwiththeirenergiesand,whenapplicable,single-escapepeaksaredenotedwithonestarinadditiontotheenergyofthepeak.Theinsetsin(a)and(b)showthefullheightsofthe2032.9-keVand511-keVpeakstruncatedin(a)and(b),respectively.222FigureB.3:Background-subtractedcoincidencespectra.Coincidenttransi-tionsarelabeledwiththeirenergies.Allinsetsdisplayadditionalrangesoftheirrespectivespectra.Theopensquaresymbolusedon(c)representsacontaminating649.2-327.0-keVcoincidencefrom68Co.Asingleasteriskafteranenergylabelsigniesthetransitionwasobservedexclusivelyincoincidence,andtwoasterisksfollowinganenergylabelidentiesacoincidencewithcontaminatingtransition.224FigureB.4:Background-subtractedcoincidencespectragatedonthesumofthe1282.6-keV,1514.3-keV,1992.1-keV,2422.0-keV,and4024.6-keVtransitions.Thebackgroundwastakensymmetricallyeithersideofeachrespectivepeakregion.Coincidenttransitionsarelabeledwiththeirenergies.Theinsetshowsazoomed-inviewofthe1500to1900keVregionofthespectrum........................233xxxivFigureB.5:Background-subtracted-double-pulsecoincidencespectrarecordedincoincidencewiththedetectionofthe0+
2!0+
1E0transitionin68Ni.Thebackgroundwastakensymmetricallyeithersideofthepeakexcept.Theinsetin(a)showsthefullheightofthe511-keVpeakcutointhespectrumdisplayedin(a).Theinsetinpanel(k)showstheregionbetween2510and2550keVforthespectrumin(k).Theinsetsinpanels(l)and(n)showtheregionbetween2400and2440-keVforthesamespectrumineachpanel.Theinsetin(o)showsthefullheightofthe511-keVpeakcutointhespectrumdisplayedin(o)....................................243FigureC.1:Seriesofbackgroundsubtractedcoincidencespectracorrelatedtothedecayoftheshort-lived,high-spin,70Coisomer.Thebackgroundwastakensymmetricallyeithersideofthepeakexceptwhereotherraysinterfered,inwhichcasethebackgroundwastakenaboveascloseaspossibletothepeakofinterest.Transitionsaliatedwiththelong-lived,low-spin,70Coisomeraredenotedwithblacksquares.246FigureD.1:Seriesofbackgroundsubtractedcoincidencespectracorrelatedtothedecayofthelong-lived,low-spin,70Coisomer.Thebackgroundwastakensymmetricallyeithersideofthepeakexceptwhereotherraysinterfered,inwhichcasethebackgroundwastakenaboveascloseaspossibletothepeakofinterest.Transitionsaliatedwiththeshort-lived,high-spin,70Coisomeraredenotedwithblacksquares.Transitionsobservedincoincidencebutnotinsinglesaredenotedwithasterisks.Theinsetsin(l)and(m)showthecoincidencespectragatedonthe1626-keVand771.9-keVtransitions.......251xxxvChapter1
Introduction
Inthischapterthefundamentalforces,whichdictatethestructureoftheatomicnucleus,arediscussed.Theevolutionofnuclearstructure,withbothchangingnumbersofconstituentnucleonsaswellastheredistributionofnucleonswithinasinglenucleus,isexplored.Fi-nally,anoverviewofthecurrentunderstandingoftheregionaroundtheN=40andZ=28neutronsubshellandprotonshellclosuresispresented,establishingthemotivationforthemeasurementsperformedinthiswork.
1.1NuclearShellStructure
SincethediscoveryoftheatomicnucleusbyErnestRutherfordin1911[1],countlessex-perimentalandtheoreticalinvestigationshavebeenperformedtoexploretheunderlyingfundamentalforcesgoverningnuclearproperties.Torstorder,thenucleusisunderstoodasacompositeentitymadeofprotonsandneutronsboundtogetherbythestrongnuclearforce.Thoughnoanalyticexpressionexiststodescribethestrongforce,itiswellestablishedasashortrangeforcewitharepulsivecorethatsaturatesatlongerdistances.Despitethedeciencyintheunderstandingofthenucleon-nucleonforce,varioustheoret-icalconstructshavehadsuccessreproducingtherobustpatternsthatemergewithchangingnumbersofnucleons.Onesuchexampleisthenuclearshellmodel.Intheshellmodelnucleonsareorganizedintocollectionsofnearlydegeneratesingle-particlestatesseparated1DS(MeV)nNeutron Number (N)02468050100150Atomic Number (Z)020601004080First Ionization Energy (eV)05152030
1025(a)(b)20288508212686(Rn)54(Xe)36(Kr)18(Ar)10(Ne)2(He)Figure1.1:(a)Firstionizationenergyplottedasafunctionofatomicnumber.Thenoble-gaselementsandtheiratomicnumbers,correspondingtoclosedelectronshellcongurations,arelabeled.AllionizationenergiesweretakenfromRef.[2].(b)Dierentialneutronseparationenergiesasafunctionofneutronnumberforavarietyofeven-evennucleiadaptedfromRef.[3].Nucleialongthesameisotopicchainsareconnectedwithlines.bylargeenergygaps.Thisisanalogoustoelectronshellstructureinatomicsystems.Theeectsofelectronicshellstructureareillustratedbythetrendsintherstionizationenergyasafunctionofatomicnumber,showninFig.1.1a.Therstionizationenergyreferstotheamountofenergyrequiredtoremoveoneelectronfromanatom.Thelargepeaksinion-izationenergyateachnoblegaselement(atomicnumbers=2,10,18,36,54,86)representthe2completellingofanatomicshell.Inatoms,shellstructureleadstotheenhancedchemicalstabilityofthenoblegases.Inthenuclearcase,radioactivenucleithatpossesscompletelylledprotonand/orneutronshells(ZorN=2,8,20,28,50,82,and126(forN),oftencalledthe\magic"numbers),areobservedtoexhibitenhancedstability.Empiricalevidencefornuclearshellstructureincludesthetrendsinthedierentialone-neutronseparationen-ergy,Sn,asafunctionofneutronnumber,N,showninFig.1.1b.TheneutronseparationenergyisexpressedasSn=BE(N;Z)BE(N1;Z);(1.1)whereZistheatomicnumber,Nistheneutronnumber,andBE(N1;Z)andBE(N;Z)arethebindingenergiesofneighboringnucleialonganisotopicchain.Snrepresentstheenergyrequiredtoremoveasingleneutronfromthenucleus.Thedierentialneutronsepa-rationenergy,Sn,isthedierenceofneutronseparationenergiesbetweennearestneighborisotopes,andiswrittenasSn=BE(N;Z)BE(N1;Z)[BE(N+1;Z)BE(N;Z)];(1.2)whereagainZistheatomicnumber,Nistheneutronnumber,andBE(N1;Z),BE(N;Z),andBE(N+1;Z)arethebindingenergiesofthreeneighboringnucleialonganisotopicchain.SimilartotheelectronionizationenergiesinFig.1.1a,thepeaksattheneutronshellclosuresinFig.1.1bprovideevidenceoftherelativelylargeenergygapbetweensingle-particlestatesataclosedshellandthenextavailablesingle-particlestates.ThesamebehaviorisalsoobservedforprotonseparationenergieswithcorrespondingpeaksinthedierentialprotonseparationenergyfoundatidenticallocationsasinFig.1.1b(exceptforZ=126).31.2NuclearShellEvolution
Shellstructureisobservedtoevolveawayfromthevalleyofstabilitywithchangingnum-bersofbothprotonsandneutronsaswellaswiththeredistributionofnucleonsamongstthesingleparticlestates.Thetensorforcehasbeenidentiedasadrivingforceofthisevolution[4{9].Theeasiestwaytounderstandtheimpactofthetensorforceonnuclearstructureistoexaminetheangle-averaged,or\monopole"component,ofthetensorforce,writtenasVTab=PJ(2J+1)hjajbjVjjajbiJ;TPJ(2J+1);(1.3)[4]wherejaandjbaretheorbitsoccupiedbythetwonucleons,eachwithquantumnumbersn,l,andj(inasphericalpotential),coupledtototalangularmomentum,J,andtotalisospin,T.Themonopolecomponentofthetensorforcecreatesashiftintheenergyoforbitjaproportionaltotheoccupancyoforbitjb.Valuesofjcanbej<=l1=2andj>=l+1=2.Themonopoleinteractionisrepulsiveforj<j<andj>j>andattractiveforj>j<andj<j>.Theeectofthemonopoleinteractiononeectivesingle-particleenergiesisshownschematicallyinFig.1.2.0f7/2(j)>0f5/2(j)<0g(j)9/2>Figure1.2:Schematicrepresentationoftheeectofthemonopolecomponentofthetensorforce.FromFig.1.2itcanbeseenthatthemonopolecomponentofthetensorforcereducestheenergyseparationofspin-orbitpartnersanddirectlyinuencesnuclearstructureinseveral4regionsofthenuclearchart.Nuclearshellevolution,asdiscussedherein,referstotwosituations.Therstisthemigrationofeectivesingle-particleenergiesacrossanisotopicorisotonicchainduetochangesinthemonopoleinteractionofthetensorforcewithchangingprotonorneutronnumber.Thistypeofshellevolutionislinkedtothedisappearanceoftraditionalmagicnumbersandtheappearanceofnewones[9].OnesuchexampleistheappearanceofN=32andN=34semi-magicnumbersintheCaisotopes.IntheCaisotopes,theˇ0f7=2orbit(whereˇdenotestheprotonorbitalanddenotesaneutronorbital)isunoccupiedwhileintheNiisotopestheˇ0f7=2orbitisfullyoccupied.Thestrongattractiveˇ0f7=2-0f5=2monopoleinteractionplacesthe0f5=2orbitbetweenthe1p3=2and1p1=2orbitsbutintheabsenceofthemonopoleinteractionthe0f5=2islessboundandhigherinenergythanthe1p1=2orbit,givingrisetotherelativelylargeenergyspacingbetweenthe1p3=2and1p1=2and1p1=2and0f5=2orbitscreatingtheN=32andN=34semi-magicnumbers[9].AdditionalconsequencesofthiswillbediscussedinSec.1.4.Thesecondisthechangeineectivesingle-particleenergiesfromthemonopoleinterac-tionofthetensorforceduetoparticle-holeexcitations.Thistypeofshellevolutiongivesrisetolow-energyintruderstatecongurationsandaphenomenoncalledshapecoexistence,discussedfurtherinSec.1.3.OneexampleofshellevolutiongivingrisetoshapecoexistenceisprovidedbytheHgisotopes.Hereparticle-holeexcitationsaltertheoccupancyofspecicsingleparticlestates.Theresultingproton-neutroninteractions,includingthemonopolein-teraction,drivethemigrationofintruderstatesdowninexcitationenergy[10].Afteryearsofdetailedspectroscopyexperiments,alow-lyingintruderstatebandwasobservedacrossmid-shellforneutronsalongtheHgisotopicchain.Figure1.3,adaptedfromRef.[11],showstheenergyofyraststates(black,lledcircles)andprolate-deformedintruderstates(red,5opencircles)asafunctionofneutronnumber.Thecoexistenceofthenear-sphericalyraststateswiththeprolate-deformedintruderstatesisaprimeexampleofshapecoexistence.92Energy (keV)0100015002000250030005002+0+6+4+10+8+6+4+2+0+2+2+12+10+0+2+4+6+8+12+96100104108116112120124128Neutron Number (N)Figure1.3:ShellevolutionalongtheHgisotopicchain1.3NuclearShapeCoexistence
Asalludedtointheprevioussection,shapecoexistenceoccurswhenmultiplestateswithcongurationspossessingdierentintrinsicshapescoexistatsimilarexcitationenergy.Fre-quentlyobservednearshellclosures,thesecoexistingintruder-statecongurationsbornofparticle-holeexcitationsowetheirexistencetoadelicatebalancebetweenthecostofpro-motingparticlesacrossashellgapandthestabilizingeectofresidualinteractionssuchasthemonopolecomponentofthetensorforce.Whenthesecompetingfactorsaresimilarinmagnitudetheenergyofnormal-orderedandintrudercongurationscanbesimilarandaresaidto\coexist".6Multiplelow-lying0+statesareoftenahallmarkofshapecoexistenceineven-evennucleiandthus,spectroscopyof0+statesisavaluabletoolforinvestigatingshapecoexistence.Ofparticularinterestaretransitionsbetweentwo0+stateswhichoccursexclusivelythroughelectricmonopole,E0,transitions,discussedfurtherinSection2.5.Half-livesofexcited0+statesanddecaybranchesarerequiredtocharacterizeE0transitions.AlsoofinterestaretheB(E2)valuesfor2+!0+transitions.Section2.5discusseshowratiosofB(E2)valuescanbeusedtoinferthedegreeofmixingbetween0+states.1.4NuclearStructureNearN=40andZ=28Theneutron-richnucleineartheN=40neutronsubshellandZ=28protonshellclosureshavebeenstudiedextensivelybynumeroustheoreticalandexperimentalinvestigations.Thegoalofthisworkhasbeentounderstandtherapidchangesinnuclearstructurewithchangingprotonandneutronnumber,whichappeartogiverisetoshapecoexistenceinthisregion.68NihasbeencentraltothisexplorationlocatedattheZ=28protonshellclosure,denedbyenergygapbetweentheˇ0f7=2andˇ1p3=2singleparticlesates,andtheN=40neutronsubshellclosure,denedbytheenergygapbetweentheneutron1p1=2and0g9=2singleparticlestates.Originally,theN=40neutronsubshellclosurewasconsideredrobustand68Niwasseenasasemi-magicnucleusbasedontherelativelylargeenergyofthe2+
1stateandlowB(E2;0+
1!2+
1)[12].Howeverin66Fe,withtheremovalofjusttwoprotons,evidencesupportingaN=40neutronsubshellclosurequicklyvanishes.InFig.1.4the(a)2+
1stateenergiesand(b)B(E2;0+
1!2+
1)values,takenfromRef.[13],arepresentedasafunctionofneutronnumberfortheCr,Fe,andNiisotopes.Theprecipitousdropin2+
1stateenergies7suggestsasuddenonsetofdeformationbeyond68Ni.Further,massmeasurements[14]ndnodipinthetwoneutronseparationenergy,acharacteristicofshellclosures,atN=40foranyneighboringisotopesaboveNi.303234363840424405001000150020002500Chromium (Z = 24)Iron (Z = 26)Nickel (Z = 28)2  Energy (keV)+
105001000150020002500B(E2; 0     2 )  (efm)24+
1+
1Neutron Number ()N(b)(a)Figure1.4:Systematicsof(a)2+
1stateenergiesand(b)B(E2;0+
1!2+
1)valuesasafunctionofneutronnumberfortheCr,Fe,andNiisotopes.DatatakenfromRef.[13].Theoretically,therapidonsetofcollectivityisexplainedbythemigrationofsingle-particlestatesunderthechanginginuenceofthemonopoleinteractionofthetensorforcewithchangingprotonandneutronnumber[5,9].Asprotonsareremovedfromtheˇ0f7=28orbit,movingfromNitoCa,theattractiveˇ0f7=20f5=2monopoleinteractiondecreasesresultinginthemigrationofthe0f5=2upwardinenergytowardstheFermisurface,andexcitationsofneutronsintothe0g9=2orbitbecomeincreasinglyprobable.Theadmixtureofthe0g9=2orbitintotheground-statewavefunctionleadstodeformationintheCrandFeisotopes,whilealackofitin68Nipreservesthesphericalshapeforthegroundstate[5,9].ThesamephysicsthatdestroysthemagicityoftheN=40subshellclosureanddrivesnucleitodeformedshapesalsogivesrisetoshapecoexistenceintheregion.Twosuchexamplesaretheodd-ACoisotopesandtheeven-evenNiisotopes.In67Co,a496-msisomeric(1/2)statehasbeenidentiedat491.6keV.Thisstatecanonlybeexplainedbyexcitationsofprotonsintothe[321]1=2orbit(originatingfromthesphericalˇp3=2orbit)atprolate(>0:2)deformation[15].Lowerinmassalongtheisotopicchain,thecorresponding(1/2)statein65Coislocatedat1095keV[16].Itisbelievedthatstrongproton-neutroncorrelationsinducedeformationandlowertheenergyofthe(1/2)statewithaddedneutrons[15].Thegroundstateof67Coispresumedsphericalwitha7=2spinandparityfromaˇ0f17=2conguration[15].Therefore,67Coprovidesanexampleofspherical-prolateshapecoexistence.Transitioningtotheeven-evenNiisotopes,evidenceofshapecoexistenceisbuilding.Experimentally,three0+stateshavebeenidentiedin68Niatenergiesof0,1604[17{19],and2511keV[12,20].Advancedshell-modelcalculationsusingtheA3DA[7]andLNPS[5,8]interactionsoverthe(0f1p0g9=21d5=2)ˇand(0f1p)ˇ(0f1p0g9=21d5=2)modelspaces,respectively,predictthethree68Ni0+statestobeassociatedwithspherical,oblate,andprolatecongurations,respectively.AccordingtotheA3DAcalculations,thespherical68Ni0+
1groundstatecontainsveryfewparticle-holeexcitationsacrossZ=28orN=40with,onaverage,onlyoneneutron9inthe0g9=2.Theoblate-deformed0+
2statecontainsadditionalexcitationsacrosstheshellandsubshellgapswithˇ0.7protonsandˇ2.4neutronsexcited.TheworkofRef.[18]directlyobservedthe0+
2!0+
1E0transition,andusingmaximalmixingwithinthetwo-levelmixingmodelobtainedadierenceinmeansquarechargeradiiofhr2i=0:15fm2andanabsolutevalueof102efm2fortheintrinsicquadrupolemoment,whichagreeswellwiththe-95efm2[18]andjQ0j=93efm2[8]fromtheshell-modelcalculations.TheA3DAcalculationsalsopredictthatthe2+
1stateisamemberofadeformedrotationalbandbuiltonthe0+
2state.Investigationofthisclaimrequiresobservationofthe2+
1!0+
2transition,andameasurementofthebranchingratioisnecessarytodeducetheB(E2).Limitsof<1%[18]and<0.7%[21]havebeenplacedonthebranchingratioofthistransitionbasedonpreviousmeasurements.Ameasuredhalf-lifeof0.31(5)psalreadyexistsforthe2+
1statein68Ni[22].Thepresumedprolate-deformed0+
3stateispredictedtocontainfarmoreexcitationswith˘3protonsacrossZ=28and˘4neutronsacrossN=40[9].Thecalculationssuggestthattheneutronsaretakenequallyfromthe0f5=2and1p1=2orbits,bothj<orbits,andplacedintothe0g9=2orbit,whichisaj>orbit[9].Theresultisa˘33%reductioninthedierenceineectivesingle-particleenergiesbetweentheˇ0f7=2andˇ0f5=2orbitsandisresponsiblefortheincreasedoccupancyoftheˇ0f5=2orbit.Thepredictedquadrupolemomentofthe0+
3isˇ250efm2[9].Half-lifepredictionsforthe0+
3stateexistbutvarysignicantlybetweentheA3DAandLNPScalculationswithvaluesof108nsand1.5ns,respectively[21].Experimentally,alimitof<15nswasplacedonthehalf-lifeofthe0+
3state[12].Additionally,the0+
3!0+
2and0+
3!0+
1E0transitionsin68Nihavenotbeenobserved,butbranchingratiolimitsof<2%ontheformerand<4%onthetotalhavebeenplaced[21].10In70Ni,theA3DAcalculationssuggestadecreaseofthe2511-keVprolatestatein68Nidownto1525keVin70Ni.Thisisexplainedbythefurtherdecreaseinthedierenceineectivesingleparticleenergiesbetweentheˇ0f7=2andˇ0f5=2orbits,withtheadditionoftwoneutronsintothe0g9=2orbit.Priortothiswork,acandidate0+
2statein70Niat1484keVwasproposedbasedonuplacedraysobservedinsingles[23].Additionallythecorresponding2+and4+rotationalbandmembersweretentativelyidentied[23].1.5GoalsoftheExperiment
ThepurposeofthepresentworkistoinvestigatethepredictionsofshapecoexistenceintheNiisotopesnearN=40.Tothatend,twocomplimentary-decayspectroscopyexperimentswereperformed.Therstexperimentwasdesignedtoobservethe2+
1!0+
2transitionin68NiandmeasureitsbranchingratioinordertodeducetheB(E2:2+
1!0+
2).Searchesforother0+statesandE0transitionswerealsoperformed.Thesecondexperimentwasdesingedtomeasurehalf-livesofexcitednulcearstatesin68;70NitodetermineabsoluteB(E2)values.Thecomparisonoftransitionprobabilitiesextractedfromexperimentwiththeoreticalpredicitionswouldprovetobeasensitiveprobeofnuclearwavefunctions.11Chapter2
NuclearDecayModes
Inthischapter,decaymodesrelevanttothenucleiofinterestarediscussed.Thefundamentalnuclearphysicsgoverningeachdecaymode,aswellasimportantexperimentalobservables,aredescribed.
2.1DecayNucleardecayisaprocessbywhichanucleusofmassnumberAundergoestransmutationbyconvertinganeutrontoaprotonorvice-versa.Threedistinct-decayprocessesareconsidered:,+,andelectroncapture(EC).ThesethreeprocessestransmutemoreexoticparentnucleitolessexoticdaughternucleiwhilekeepingAconstantwithsuccessivedecayspropagatingalonganisobaricchaintowardsthevalleyofstability.Theseprocessesarewrittenas::A
ZXN!AZ+1Y+N1++e+Q;(2.1)+:A
ZXN!AZ1YN+1+++e+Q+;(2.2)andEC:A
ZXN+e!AZ1YN+1+e+QEC;(2.3)12whereisanelectron()orpositron(+),eisanelectronneutrino,eisanelectronanti-neutrino,eisanorbitalelectron,andQ,Q+,andQECarethe-decayQ-values.TheQ-valuescanbecalculatedusingQ=[M(A;Z)M(A;Z+1)]c2;(2.4)Q+=[M(A;Z)M(A;Z1)2me]c2;(2.5)andQEC=[M(A;Z)M(A;Z1)]c2;(2.6)whereM(A;Z)isthemassofnucleuswithAnucleonsandZprotons,meisthemassoftheelectron,andcisthespeedoflight.Often,decaypopulatessomenumberofexcitedstatesinthedaughternucleus.ThetotalenergyreleasedbydecayinthatcaseisthedierencebetweentheQ-valueandtheexcitationenergyofthenalstate.Nucleirelevanttothepresentexperimentsareneutron-richanddecaybydecay.decayispossiblewheneverQ>0.Thedecayenergyfromdecayissharedbetweenthee,thee,andtherecoilingdaughternucleus.Theenergyofthe-decayelectronisacontinuousdistributionrangingfromzerouptoQ(neglectingthesmallcontributionsfromtheeanddaughterenergies).Theeemittedfromdecayleavesundetected,whiletheemitted-decayelectronlossesenergyinthesurroundingmaterials.Inthepresentexperiments,describedinthefollowingchapter,decayingnucleiaredepositedintoanactivedetectorvolumeandtheenergylossfromtheemittedelectronsisrecorded.Whilethenucleiinthepresentstudydonotdecayby+orEC,theseprocessesare13brieydiscussedhereforcompleteness.In+decay,aproton-richnucleusconvertsaprotontoaneutron,emittingapositronandanelectronneutrino.+decayispossiblewheneverQ+>0.Thedecayenergyfrom+decayissharedbetweenthee+,thee,andtherecoilingdaughternucleus.Theemittede+interactswithitssurroundingslosingenergyuntilitannihilateswithanelectron,creatingtwo511-keV-raysemittedoppositeindirection.ECdecayisanalternativeto+decay.InECdecay,aprotoncapturesanatomicelectron,typicallyfromtheinner-mostshells,leavingadaughternucleuswithonefewerprotonthantheparentandavacancyinaparticularelectronorbital.ElectronsfromouterorbitsllthevacancyemittingXraysorAugerelectrons.Unlike+decay,mono-energeticelectronneutrinosareemitted.decayisgovernedbythe-decayselectionrules.Alloweddecayemitstheeandewitharelativeorbitalangularmomentum,l,equaltozero.Highervaluesoflarereferredtoasforbiddentransitionsandarehinderedcomparedtoallowedtransitions.Typically,thehindranceis˘3104foreachadditionalunitofangularmomentum[24].Inaddition,the-decayelectronandtheelectronanti-neutrinobothhaveintrinsicspin,s,equalto1/2.Theparallel(S=0)andanti-parallel(S=1)alignmentsofthetwospinsofthesetwoparticlesgiverisetotheFermiandGamow-Tellerdecaymodes,respectively.TheselectionrulesforbothFermiandGamow-TellerdecayareshowninTable2.1adaptedfromRef.[25].Table2.1:-decayselectionrules,adaptedfromRef.[25]TransitionTypeJ=jJfJijˇiˇfFermi0+1Gamow-Teller1(Ji=0orJf=0)+1Gamow-Teller0,1(Ji>0orJf>0)+1Often,agreatdealabouttheunderlyingphysicscanbelearnedfrommeasurementofthe-decayhalf-life.Denotedast1=2,thehalf-lifeistheaveragetimerequiredforhalfof14theradioactivenucleiinasampletodecayaway,andcanbeexpressedintermsofthedecayconstant,,ast1=2=ln(2):(2.7)Often,severaldierenttransitionsbetweentheinitialstateandnalstatesinthedaugh-tercontributetodecay.Thedecayconstant,,inEq.(2.7)isthesumofthedecayconstantsofall-decaytransitions,suchthat=Xf(if);(2.8)where(if)isthetransitionprobabilityforaparticulartransitionbetweentheinitialparentstate,i,andsomenalstateinthedaughternucleus,f.Thepartialhalf-lifeofaparticulartransition,t(if)1=2,isthent(if)1=2=ln(2)(if);(2.9)whichcanalsobewrittenast(if)1=2=t1=2BR(if);(2.10)wheret1=2isthehalf-lifeoftheinitialstate,i,andBR(if)isthebranchingratiotonalstatef.Thepartialhalf-lifecanalsobeexpressedintermsoftheFermiandGamow-Tellerreducedtransitionprobabilities,B(F)andB(GT),respectively,ast(if)1=2=2ˇ3h7ln2f0(m5
ec4G2
F)(BF+BGT);(2.11)wherehisPlanksconstantdividedby2ˇ,meistheelectronmass,cisthespeedoflight,GFistheFermicouplingconstant,andf0istheFermiintegral[25].TheFermiintegral15accountsfortheCoulombinteractionbetweentheemittedewiththedaughternucleusandcanbewritten(usingthenon-relativisticPrimako-Rosenapproximation)asf0ˇ130(E5010E20+15E06)2ˇZf1e2ˇZf;(2.12)whereisthenestructureconstant,Zfistheatomicnumberofthedaughternucleus,andE0istheendpointenergy.TheendpointenergycanbewrittenasE0=EiEfmec2;(2.13)wheremeistheelectronmass,cisthespeedoflight,andEiandEfarethetotalenergiesoftheinitialandnalstates,respectively[25].Thereducedtransitionprobabilities,BFandBGT,arerelatedtothematrixelements,MFandMGTbyBFg2V2Ji+1jMFj2(2.14)andBGTg2A2Ji+1jMGTj2;(2.15)wheregAandgVaretheaxial-vectorandvectorcouplingconstants.ThereducedmatrixelementsaredenedasMF=(˘fJfjj˝jj˘iJi)(2.16)andMGT=(˘fJfjj˝˙jj˘iJi);(2.17)16where˝and˙arethePauliisospinandspinoperators[25],respectively.Thematrixelementscontainallthenuclearphysicsinformation,andareinverselypro-portionaltothepartialhalf-life.Fromthepartialhalf-lifethecomparativehalf-lifeftcanbecalculated.Thecomparativehalf-lifeisameasureofhowprobableaparticulardecaytransitionis.Typicallytherangeinftvaluesislarge,andthustheyareexpressedinlog10scale.Asummaryoftherangeoflog10(f0t)valuesassociatedwithallowedandvarioustypesofforbiddendecayispresentedinTable2.2.Itisworthmentioningthattherangesforlog10(f0t)valuesinTable2.2areguidelinesandsomeoverlapexistsbetweentransitiontypes.
Table2.2:Classicationof-decaytransitionsandassociatedlog10(f0t)values,adaptedfromRef.[24].TransitionTypelJˇlogf0tSuperallowed00No2.9-3.7Allowed00,1No4.4-6.0Firstforbidden10,1,2Yes6-10Secondforbidden21,2,3No10-13Thirdforbidden32,3,4Yes15Experimentally,thedecayhalf-lifeisoftendeterminedbyttingtheactivityofasample-decayingnucleiasafunctionoftime.Sincedecayfollowsrstorderkinetics,thedecayrateisproportionaltothenumberofradioactivenucleipresentandcanbewrittenasdNdt=N;(2.18)whereisthedecayconstant,relatedtothehalf-lifeasgiveninEq.(2.7).Thenumberof-decayingnuclei,N,attime,t,isgivenbyN(t)=N0et;(2.19)17whereN0isthenumberofnucleiattimet=0.Inachainof-decayingnucleithequantityofparent,daughter,andgranddaughternucleiasafunctionoftimecanbedeterminedusingN1(t)=N1;t=0e1t;(2.20)N2(t)=f121N1;t=0ge1t;N2;t=00;(2.21)andN2(t)=f231121N1;t=0ge1tf232121N1;t=0ge2t+f232131N1;t=0ge3t;N2;t=0N3;t=00;(2.22)[26]wherethenotationN2;t=00andN3;t=00signiesthatnodaughterorgrand-daughternucleiarepresentattimezero.
2.1.1-DelayedParticleEmissionIfthe-decayQ-valueislargeenoughsuchthatstatesaboveparticleseparationenergiesarepopulated,thedaughternucleuscanemitnucleonsorclustersofnucleons.Thenucleiofinterestinthisstudyareneutron-rich,withQ-valuesnear12MeV.Theaverageneutronseparationenergyofthedaughternucleusis˘7.5MeV,andthus-delayedneutronemission(n)isenergeticallypossible.The(n)processinvolves-decayingtoneutron-unboundstatesinthedaughternucleus,whichthenspontaneouslyemitsaneutron.-delayedneutron18emissioncanbewrittenasA
ZXN!A1
ZXN1+n+Qn;(2.23)whereQnrepresentsthedierenceintotalenergybetweenthenalandinitialstates.Fol-lowing-delayedneutrondecay,excitedstatesmaybepopulatedintheA1XN1-delayedneutrondaughter,whichthendecaybyemittingelectromagneticradiation.Typically,delayedneutronemissiondominatesoverelectromagneticdecaysforstatesabovetheneutronseparationenergy.However,neutronemissioncanbehinderedifemissionofahighl-valueneutronisrequired,orifthenuclearstructureoftheneutron-unboundexcitedstateinthedaughterisdierentthanthatofthebeta-delayedneutrondaughter.Inthesecircumstances,electromagneticdecayscancompetewithneutronemission[27{29].2.2DecayTypically,decaypopulatesoneormoreexcitedstatesinthedaughternucleus,belowthenucleonseparationenergies,whichthendecaypredominatelyby-rayemission.Theseraysarecommonlyreferredtoas-delayedrays.A-raytransitionconnectsaninitialstate,i,toanalstate,f,andcarrieswithitanintegeramountofangularmomentum,calledthemultipolarity,,whichcanhavevaluesofj(JiJf)j(Ji+Jf);(2.24)with1.-rayshaveanintrinsicspinofone,therefore=0transitionsareforbidden.Thetransitionrateforagivenmultipolarity,,oftype,˙(electricormagnetic),canbe19expressedasT(˙)fi=Xmimf20h+1[(2+1)!!]2 Ehc!(2+1)B(˙;˘iJi!˘fJf);(2.25)where0ispermittivityoffreespace,hisPlank'sconstantdividedby2ˇ,cisthespeedoflight,Eistheenergyofthetransition,andB˙arethereducedelectromagnetictransitionprobabilities.Thereducedelectromagnetictransitionprobabilitiesarerelatedtothematrixelementscontainingthemagneticandelectrictensoroperators,M˙,byB(˙;˘iJi!˘fJf)=12Ji+1
(˘fJfjjM˙jj˘iJi)
2:(2.26)Thetransitionprobabilityisrelatedtothehalf-lifeofthetransitionbyt1=2=ln2T(˙)fi:(2.27)Sincethehalf-lifeofthedecayingstateisinverselyproportionaltothetransitionprob-ability,andthusthematrixelements,whichcontainalloftheinformationregardingthewavefunctionsoftheinitialandnalstates,measurementsofexcitedstatelifetimescandi-rectlyprobenuclearstructure.Forexample,thereducedtransitionprobabilityforanE2transition,inunitsofe2b2,canbedeterminedfromthehalf-lifeusingB(E2";˘iJi!˘fJf)=28:31013(BR)(t1=2)(E)5(1+);(2.28)fromRef.[30],whereBRisthebranchingratiooftheE2transitionofinterest,t1=2isthehalf-lifeofthedecayingstateinps,EisthetransitionenergyinkeV,andisthe20internalconversioncoecient,discussedinthenextsection.Thedirectionofthetransition(i.e.0+!2+or2+!0+)isimportantfordeterminingB(E2)values.Inthepresent,worktheB(E2#)valueswillbededucedfromlifetimemeasurements.B(E2")valuesarerelatedtoB(E2#)byB(E2")=2Jf+12Ji+1B(E2#):(2.29)Thereducedtransitionprobabilitycanbesimpliedusingasingle-particlelimit,referredtoasWeisskopflimits,whereall-raytransitionsarepresumedtoresultfromtheredistri-butionofasinglenucleonwithinthenucleus.Inthesingle-particlelimit,theexpressionsforthereducedtransitionprobabilitiesbecomeBW(E)=1:224ˇ3(+3)2A2=3e2;(fm)2(2.30)andBW(M)=10ˇ(1:2)(22)3(+3)2A(22)=3h2mpc2e2(fm)22;(2.31)whereAisthemassnumberofthenucleus,hisPlank'sconstantdividedby2ˇ,cisthespeedoflight,mpisthemassoftheproton,Eistheenergyofthetransition.TheresultingreducedtransitionprobabilitiesareknownasWeisskopfsingle-particleestimates.TheWeisskopfsingle-particleestimatesforthereducedtransitionprobabilitiesaretypicallygoodtowithinafactorof10forsphericalnuclei[24].Asummaryof-raytransitionselectionrules,withWeisskopfestimates,areshowninTable2.3fortherstfourmultipolaritiesofelectricandmagnetictransitiontypes.21Table2.3:Selectionrulesandelectromagnetictransitionrates,assumingasingle-particletransitionfromaninitialstatetoanalstate,fortherstfourmultipolaritiesofelectricandmagnetictransitions.isthemultipolarityofthetransition,ˇisthechangeinparitybetweentheinitialandnalstates,Eisthe-rayenergyinMeV,andAisthemassnumberofthenucleus.[24].NameRadiationTypeˇTW(˙)(s1)ElectricdipoleE11Yes1:031014A2=3E3MagneticdipoleM11No3:151013E3ElectricquadrupoleE22No7:28107A4=3E5MagneticquadrupoleM22Yes2:24107A2=3E5ElectricoctupoleE33Yes3:39101A2E7MagneticoctupoleM33No1:04101A4=3E7ElectrichexadecapoleE44No1:07105A8=3E9MagnetichexadecapoleM44Yes3:27106A2E9ThetransitionratespresentedinTable2.3decreaseasmultipolarityincreases.Therefore,-raysoflowermultipolaritiesaregenerallymoreprobablefortransitionsofagivenenergy.Inaddition,ifanexcitedstatecandecaytomultiplenalstateswiththesamespinandparitythehighestenergytransitionwillhavethelargesttransitionprobability,providedthatnostrongdierencesinthematrixelementsexist.
2.3InternalConversion
Anotherdecayprocessavailabletoexcitednuclearstates,whichcompeteswith-raydecay,isinternalconversion.Inthisprocess,theexcitednucleusinteractselectromagneticallywithanorbitalelectronandejectstheelectron.Thevacancycreatedbytheejectedelectronislledbytheouterorbitalelectrons,whichresultsinX-rayorAugerelectronemission.Internalconversionelectronsemittedfromagiventransitionaremono-energeticwithanenergy,EIC,ofEIC=(EiEf)EBE;(2.32)22whereEBEisthebindingenergyoftheejectedorbitalelectronandEiandEfaretheenergiesoftheinitialandnalstates,respectively.Thecompetitionbetweeninternalconversionand-rayemissionischaracterizedbytheinternalconversioncoecient,,denedas=numberofinternal-conversiondecaysnumberof-raydecays:(2.33)ConversionelectronscanoriginatefromanyoftheK,L,M...electronshellsbutaK-shellelectronismostprobablesincetheseelectronshavethehighestprobabilitytobefoundatthenucleus.Thetotalinternalconversioncoecient,total,isthesumoftheconversioncoecientsofallavailableelectronshellssuchthattotal=K+L+M+::::(2.34)Expressionsforinternalconversioncoecientshavebeenderivedfromatomicphysicsandapproximatevaluescanbeobtainedfrom(E)=Z3n3+1e24ˇ0hc42mec2E+5=2(2.35)and(M)=Z3n3e24ˇ0hc42mec2E+3=2;(2.36)[24]whereisthemultipolarityofthetransition,Zistheatomicnumberofthenucleus,nistheprincipalquantumnumberoftheejectedorbitalelectron,meisthemassoftheelectron,cisthespeedoflight,0ispermittivityoffreespace,hisPlank'sconstantdivided23by2ˇ,eistheelementarycharge,andEistheenergyofthetransition[24].Fromequations(2.35)and(2.36),onecanconcludethatinternalconversionismostprobableinheavynucleiforlowerenergytransitionswithhighermultipolarities.
2.4InternalPairFormation
Athirdelectromagnetic-decayprocessthatcompeteswithboth-rayemissionaswellasinternalconversionisinternalpairformation.Internalpairformationisaprocessbywhichanelectron-positronpairisdirectlycreated.Thetransitionenergymustbeabove1.022MeVtoproducetheelectron-positronpair,andanyadditionalenergyissharedequallyamongtheelectronandpositronaskineticenergy.Theemittedelectronandpositroninteractwiththesurroundingmaterials,losingenergyuntilthepositronannihilateswithanelectron,creatingtwo511-keVphotonsemittedinoppositedirections.Typically,theprobabilityofinternalpairproductionisseveralordersofmagnitudere-ducedwhencomparedwith-raydecay.However,internalpairproductionisimportantwhen-raydecayisforbidden,suchasfortransitionsbetweentwo0+states.2.5E0TransitionsElectromagnetictransitionsthatconnecttwostateswithidenticalspinandparitiescandecayviaelectricmonopole(E0)transitions.E0transitionstakeplaceviainternalconversionorinternalpairproduction.TypicallyE0transitionsareonlyobservedinthedecaybetweentwo0+statessincehighermultipolarity-raydecaysoftendominatewhentheinitialandnalstateshave,equal,nuclearspinsgreaterthanzero.Thestrengthofanelectricmonopole24transitionischaracterizedbyadimensionlessquantity,ˆ2(E0),whichcanbewrittenasˆ2(E0)=



h fj^T(E0)j iieR2



2;(2.37)where iand faretheinitialandnalstates,eisthefundamentalunitofcharge,Risthemeannuclearradius(Rˇ1:2A1=3fm),and^T(E0)istheelectricmonopoleoperatordenedby^T(E0)=Xkekr2k;(2.38)whereekistheeectivechargeforthekthnucleonandrkisthepositionofthekthnucleonrelativetothecenterofmassofthenucleus[31].ˆ2(E0)containsalltheinformationaboutthenalandinitialstates.Becausethevalueofˆ2(E0)isoftenbetween103and101,itiscommonlyreportedas103ˆ2(E0).Databasesofˆ2(E0)valuesbetween0+statesacrossthechartofthenuclidesareavailable[32].ThetransitionprobabilityforanE0transition,(E0),canbewrittenas(E0)=IC(E0)+ˇ(E0)=ln2T1=2(E0)=ˆ2(E0)[IC(E0)+ˇ(E0)];(2.39)whereIC(E0)andˇ(E0)arethepartialtransitionprobabilitiesforinternalconversionandinternalpairproduction,respectively.ˆ2(E0)istheelectricmonopoletransitionstrength.ThequantitiesIC(E0)andˇ(E0)arethe\electronicfactors"[33]forinternalconversionandpairproduction,respectively,andT1=2(E0)isthepartialhalf-lifeoftheE0transition.Electronicfactorsdependontheatomicnumberofthenucleusandthetransitionenergybutareindependentofnuclearproperties.TabulationsoftheelectronicfactorscanbefoundintheBrIccdatabase[34].25Inthelimitsofasimpletwo-levelmixingmodel,ˆ2(E0)canberelatedtothedierenceindeformationbetweenthetwo0+states.Inthisapproach,eachofthe0+statesisdescribedasalinearcombinationoftwodierentcongurationsofnucleonseachwitha0+spinandparitybutwithadierentintrinsicquadrupolemoment.Inthetwo-levelmixingmodelthetwo0+statesj0+
iiandj0+
ficanbeexpressedasj0+
ii=cos()j0+
sisin()j0+
di(2.40)andj0+
fi=sin()j0+
si+cos()j0+
di;(2.41)whereisthemixingangle,andj0+
siandj0+
diaretwodierentcongurationsofnucleonsassociatedwithsphericalanddeformedshapes,respectively[31].Inthelimitofmaximalmixingsin()=cos()=1=p2.Inthismodel,Eq.(2.37)canbewrittenasˆ2(E0)=1eR2[cos2()sin2()]h0+
dj^T(E0)j0+
si+cos()sin()(h0+
sj^T(E0)j0+
sih0+
dj^T(E0)j0+
di)2:(2.42)InEq.(2.42),ifnomixingoccursthesecondtermiszero,sincecos(0)sin(0)=0andthematrixelementh0+
dj^T(E0)j0+
sifromthersttermwillbesmallduetothesmallradialover-lapofthesphericalanddeformedcongurationwavefunctions.Therefore,ˆ2(E0)becomesverysmallintheabsenceofmixing.Ontheotherhand,inthecaseofmaximalmixingthersttermbecomeszero,since26sin2()=cos2(),leavingˆ2(E0)ˇhcos()sin()(h0+
sj^T(E0)j0+
sih0+
dj^T(E0)j0+
di)i2:(2.43)UsingEqs.(2.43)and(2.38),ˆ2(E0)canbeexpressedasadierenceinmean-squarechargeradii,hr2i,usingˆ2(E0)=Z2e2R4cos2()sin2()hhr2ii2:(2.44)Thelargerthedierenceinthehr2ithelargerthevalueofˆ2(E0).Whilemaximalmixingisanusefulapproximation,themixingangle,,canbededucedfromelectricquadrupole(E2)transitionprobabilities[35].TheE2transitionbetweenthe2+and0+statesinvolvesonlythedeformedadmixturetoeachwavefunction,andassuch,itfollowsfromEqs.(2.40)and(2.41)thatB(E2;2+!0+
i)=B(E2;2d!0d)cos2()(2.45)andB(E2;2+!0+
f)=B(E2;2d!0d)sin2():(2.46)Therefore,withinthetwo-levelmixingmodeltan2()=B(E2;2+!0+
f)B(E2;2+!0+
i);(2.47)suchthatthemixingbetweentwo0+statescanbededucedentirelyfromspectroscopicinformation[35],butthe2+!0+transitionsmustbeaccessible.27Chapter3
ExperimentalDescription
Inthischapter,twocomplimentaryexperimentsperformedattheNationalSuperconductingCyclotronLaboratory(NSCL)aredescribed.Therstexperimentwase14039,forwhichtheprimarygoalsweretherstobservationofthe2+
1!0+
2transitionin68Ni,andasearchforthe0+
2statein70Ni.Thesecondexperiment,e14057,wasperformedtomeasurelevellifetimesofexcitedstates,particularlythe0+
3state,in68Ni.Thecombinedresultsofthesetwoexperimentsyieldacomprehensiveinvestigationofshapecoexistencein68Niand70Niandprovideextensiveknowledgeaboutthelow-energylevelstructureof68Niandneighboringnuclei.Thischapterisdividedintoseveralsections.Section3.1explainsthebeamproductionanddeliverytechniquesattheNationalSuperconductingLaboratory(NSCL).Theexper-imentalendstationsusedfore14039ande14057arepresentedinsections3.2and3.3,respectively.Section3.4describestheNSCLDigitalAcquisitionSystem(DDAS)usedtoin-strumentalldetectors.DetaileddescriptionsofalldetectorsystemsincludingthenecessarycalibrationandanalysistechniquesarepresentedinSections3.5through3.8.283.1IsotopeProduction,Identication,andDeliveryattheNationalSuperconductingCyclotronLabora-
tory(NSCL)TheNationalSuperconductingCyclotronLaboratory(NSCL)producesexoticisotopesthroughprojectilefragmentation.AschematicrepresentationoftheCoupledCyclotronFacility(CCF)atNSCLisshowninFig.3.1.Astableprimaryionbeamisproducedandac-celeratedbythecoupledcyclotrons[36]toanenergyoforderof100MeV/nucleon.Theprimarybeamisthenimpingedonastationarystabletarget,typicallyBe,creatingawidevarietyofbothstableandradioactivenuclei.K500CyclotronK1200CyclotronProductionTargetA1900DispersiveImageA1900Focal
PlaneFigure3.1:SchematicrepresentationoftheCoupledCyclotronFacility(CCF)[36]andA1900fragmentseparator[37]atNSCLIsotopesofinterest,producedinthefragmentationreaction,areselectedfortransmission29totheexperimentalendstationbytheA1900fragmentseparator[37]basedontheirmagneticrigidity,Bˆ,denedastheratioofmomentum,p,toatomiccharge,q.Duetothekinematicsoffragmentationreactions,productsenteringtheA1900allpossessnearlythesamevelocity,slightlybelowthatoftheprimarybeamvelocity[24],whichmeansseparationbyBˆselectsspecieswithsimilarmasstochargeratio.Toenhanceselectivity,awedge-shapeddegraderwasplacedatthedispersiveimageoftheA1900fragmentseparator.Energylossthroughthedegraderisproportionaltothesquareoftheatomicnumberoftheion,Z2,sothationswithdierentnumbersofprotonsexperiencedierentenergyloss.Followingthedegrader,ionswithsimilarmass-to-chargeratiosbutdierentZwillhavedierentmomentaandasecondBˆselection,coupledwithslitslocatedattheA1900focalplane,isusedtoremoveunwantedfragments.SlitslocatedateachintermediateimagepositionoftheA1900servetocontroltheoverallmomentumacceptance,p=p,whichhasamaximumvalueof5%.IdenticationofionsproducedbytheCCFisperformedusingstandardE-TOFtech-niques.Thesetechniquesinvolvemeasuringtheenergyloss(E)ofionstravelingthroughoneormoresiliconPINdetectorsalongwiththeTime-Of-Flight(TOF)betweenascintil-latorintheA1900fragmentseparatorandtherstSiPINdetectoratexperimentalendstation.TheTOFisproportionaltoA=qwhile(E)isproportionaltoZ2suchthatiso-topicinformationcanbeobtainedbyplottingEvs.TOF.EachofthetwoexperimentsemployedthreesiliconPINdetectorsupstreamofthecentralimplantationdetectorforpar-ticleidentication.305006007008009001000Normalized Number of Ions (Arb Units)0246810Implantation Depth (m)m70
68Co
FeFigure3.2:Normalizedimplantationdepthdistributionsfor68Feand70CoionsdepositedinsidetheGeDSSDcrystalduringe14039.
3.2NSCLe14039ExperimentalSetup
ThesetupforNSCLexperimente14039consistedoftheGermaniumDoubleSidedStripDetector(GeDSSD),describedinSection3.5,surroundedbysixteendetectorsfromtheSegmentedGermaniumArray(SeGA),describedinSection3.7.TheSeGAdetectorswerearrangedintotwoconcentricringsofeightdetectorssurroundingtheGeDSSD,withthefaceofeachdetectorincloseproximity(˘1cm)tothesideoftheGeDSSDcryostat.Approximately1mupstreamoftheGeDSSDwasasetofthreesiliconPINdetectorswiththicknessesof996,488,and503m.Ionsofinterestwerecreatedbyfragmentinga76Geprimarybeamat130MeV/Aona282g/cm29Betarget.ThebeamdeliveredtotheexperimentalendstationpassedthroughthesiliconPINdetectors,athinkaptonwindow,onetotwocmofair,andthecryostatoftheGeDSSD.Ionswereimplantedintothe1-cmthickGeDSSDcrystaltoadepthofroughly750microns.Thedepthdistributionsoftheimplanted68Feand70CoionsinsidetheGeDSSDcrystal,ascalculatedusingLISE++[38],arepresentedinFig.3.2.LISE++calculations31wereperformedusingtheA1900magnetsettings(Segment1and2Bˆ=4:16Tm,Segment3and4Bˆ=3:92Tm)andknowledgeofthematerialsupstreamofthedetector.1600017000180001900016000180002000022000110210310410Time-of-Flight (Arb. Units)Energy Loss (Arb. Units)68Fe70Co69Co72Ni71Ni67Fe67Mn66Mn65CrFigure3.3:ParticleidenticationplotforionsdepositedintheGeDSSDcrystalduringe14039.ThedatashownwereobtainedfromtheenergylossinformationprovidedbytherstPINdetectorandtheTOFmeasuredbetweentheextendedfocalplanescintillatorintheA1900andtherstPINdetector.Asaconditionontheplot,theGeDSSDhadtorecordcoincidentimplantenergydepositioninatleastonefrontandonebackstrip.UsingthetechniquesdiscussedinSection3.1,theparticleidenticationplotfore14039,obtainedfromtheenergylossinformationprovidedbytherstPINdetectorandtheTOFmeasuredbetweentheextendedfocalplanescintillatorintheA1900andtherstPINdetectorattheexperimentalendstation,wascreated,andisshowninFig.3.3.EnergyfromtheimplantedionmustberecordedonboththefrontandbackstripsoftheplanarGeDSSDfortheiontoberecordedintheparticleidenticationplotinFig.3.3.GraphicalcutsweremadeoneachisotopespotinFig.3.3andintegratedtoprovidethequantityofeachisotopedepositedinsidetheGeDSSDcrystalduringe14039,showninTable3.1.32Table3.1:NumberofionsofeachisotopeimplantedintotheGeDSSDcrystalovertheninedaysofbeamtimeduringe14039.IsotopeNumberofImplants65Cr3.67(19)10366Mn2.84(14)10467Mn5.75(29)10467Fe5.55(28)10468Fe6.10(30)10669Co3.21(16)10670Co3.93(20)10671Ni3.91(19)10472Ni1.30(6)1043.3NSCLe14057ExperimentalSetup2000220024002600280030000123Implantation Depth (m)m70
68Co
FeNormalized Number of Ions (Arb Units)Figure3.4:Normalizedimplantationdepthdistributionsfor68Feand70Coionsdepositedinsidethesegmentedplasticscintillatorduringe14057.InNSCLexperimente14057,asegmentedplasticscintillatorcoupledtoaposition-sensitivephotomultipliertube(PSPMT),describedinSection3.6,wasusedasthecentralimplantationdetectorinplaceoftheGeDSSDtoimprovetheintrinsictimeresolutionfordetectionof-decayelectrons.Thisimplantationdetectorassemblywasplacedintoalight-tight,thin-walled,cylindricalaluminumchamber.TenLaBr3detectors,describedinSection334000600080001000012000100001200014000110210310410Time-of-Flight (Arb. Units)Energy Loss (Arb. Units)68Fe70Co69Co72Ni71Ni67Fe67Mn66Mn65CrFigure3.5:Particleidenticationplotforionsdepositedinthesegmentedplasticscintillatorduringe14057.ThedatashownwereobtainedfromtheenergylossinformationprovidedbytherstPINdetectorandtheTOFmeasuredbetweenthescintillatoratthedispersiveimageoftheA1900andtherstPINdetector.Asaconditionontheplot,thesegmentedplasticscintillatorhadtorecordimplantenergydeposition.3.8,werepositionedradiallysurroundingthechamberwiththefaceofeachLaBr3detectorlocated˘1mmawayfromtheoutsideofthechamber.TheLaBr3detectorswerearrangedintotworings,onewitheightdetectorscenteredonthesegmentedplasticscintillator,andonewiththeremainingtwodetectorslocatedslightlydownstreamofthesegmentedplasticscintillator.Thealuminumchamber,withitsencloseddetectors,andtheframeholdingthesurround-ingtenLaBr3detectorsweredesignedsuchthatsixteenSeGAdetectorscouldbeutilizedinthesamecongurationase14039.ThethreePINdetectorsusedine14039wereplacedinthesamelocation˘1mupstreamofthesegmentedplasticscintillator.Ionsofinterestwerecreatedbyfragmentinga76Geprimarybeamat130MeV/Aona282g/cm29Betarget.ThebeamdeliveredtotheexperimentalendstationpassedthroughthesiliconPINdetectorsfollowedbyathinkaptonwindowbeforeenteringthealuminumchamber.Thechamberwasatatmosphericpressuremeaningthebeamencountered˘1034Table3.2:Numberofionsofeachisotopeimplantedintothesegmentedplasticscintillatoroverthesixdaysofbeamtimeduringe14057.IsotopeNumberofImplants65Cr4.59(24)10366Mn1.32(6)10567Mn1.41(7)10467Fe2.55(13)10468Fe7.94(40)10669Co4.22(21)10670Co4.65(23)10571Ni3.65(18)10472Ni5.81(30)103cmofairbeforepassingthroughthesiliconDSSDanddepositingintothesegmentedplasticscintillator.Ionswereimplantedtoadepthofroughly2500micronsintothe1-cmthickplasticscintillator.Thedepthdistributionsoftheimplanted68Feand70CoionsinsidetheGeDSSDcrystal,ascalculatedusingLISE++[38],arepresentedinFig.3.4.LISE++calculationswereperformedusingtheA1900magnetsettings(Segment1and2Bˆ=4:16Tm,Segment3and4Bˆ=3:86Tm)andknowledgeofthematerialsupstreamofthedetector.UsingthetechniquesdiscussedinSection3.1,theparticleidenticationplotfore14057,obtainedfromtheenergylossinformationprovidedbytherstPINdetectorandtheTOFmeasuredbetweenascintillatorlocatedatdispersiveimageoftheA1900andtherstPINdetector,wascreated,andisshowninFig.3.5.EnergyfromtheimplantedionmustberecordedinthesegmentedplasticscintillatorfortheiontoberecordedintheparticleidenticationplotinFig.3.5.GraphicalcutsweremadeoneachisotopeinFig.3.5andintegratedtoprovidethenumberofionsofeachisotopedepositedinsidethesegmentedplasticscintillatorduringe14057,showninTable3.2.353.4NSCLDigitalDataAcquisitionSystem(DDAS)
Inbothexperiments,theNSCLDigitalDataAcquisitionSystem(DDAS)[39]wasusedtoinstrumentalldetectorsandthesystem'scapabilitiesplayedacriticalroleinaccomplishingtheexperimentalobjectives.DDASisamodularsystemcomprisedof16-channel,FPGA-programmablemodules,existinginthreevarieties:12-bit,100Mega-SamplePerSecond(MSPS),14-bit,250MSPS,and12-bit,500MSPS.Eachmoduletypehastwohardwaregainsettings.The(low-,hi-)gainsettingshavedynamicrangesof(0.5V,1.2V),(1V,2V),and(1V,4V)forthe100-,250-,and500-MSPSmodules,respectively.DDASmodulesofanyvarietycancoexistinthesamecratewithupto13modulespercrate,andupto8cratescanbesynchronizedtogether.ThereareseveralbenetsofDDAS,realizedsimultaneously,overanalogelectronics,includinglower-energythresholds,uniquetriggeringconditions,largedynamicrangefromdigitalltering,nearlyzeroacquisitiondeadtime,andtheabilitytorecordthedetectorsignalasafunctionoftime(referredtoas\tracecapture").3.4.1Triggering
Triggeringinthemodulesisperformedusingaleading-edgetriggerontheresponseofasymmetrictrapezoidallteralgorithm,whichisreferredtoasthe\triggerlter".Thetrigger-lterresponse,TF,iscalculatedfromthedigitizeddetectorsignal,Tr,usingEq.(3.1)bytakingthedierenceoftwosummingregions,bothoflengthL,andseparatedbyagapG.TF[i]=tXi=tL+1Tr[i]tLGXi=t2LG+1Tr[i](3.1)36Theresponseofthetrigger-lteralgorithm,shownindarkred,whenappliedtoadigitizedsignalfromtheGeDSSD,showninblack,ispresentedinFig.3.6.Superimposedisablackdashedlinerepresentingtheuser-denedtrigger-lterthreshold.0246810Time (ms)200040006000800010000AmplitudeLeading-EdgeTriggerPointEnergy SamplingPointDetector SignalTrigger Filter/25             Energy Filter/2Trigger FilterThresholdFigure3.6:ExampleofDDASdigitallteringalgorithms.AsampledetectorsignalacquiredfromtheplanarGeDSSDbya14-bit250MSPSisshowninblack.TheresponseoftheDDAStrigger-lteralgorithmisshownindarkredalongwiththeuser-denedtriggerlterthresholdillustratedasablackdashedline.ShownindarkblueistheresponseoftheDDASenergylteralgorithm.Keypointsintimerelatedtotriggeringandenergyextractionarelabeled.Whentheamplitudeofthetriggerltercrossestheuser-denedthreshold,thesystemtriggers,and,uponvalidationofthetrigger,recordstheevent.Inleading-edgetriggering,thetimeassociatedwitheacheventwillhaveanativeprecisionof10ns,8ns,and10nsforthe100MSPS,250MSPS,and500MSPSmodules,respectively.Thesevaluesdierfromthenaivepredictionofthedigitizer'sclockperiodduetoparallelprocessingnecessitatedbyFPGAbandwidthlimitations.Triggervalidationcanbeconguredinavarietyofwaystosuittheneedsoftheexper-iment.Theleastcomplicatedmethodisafree-runningchannel-by-channelmode,whereall37eventswithatrigger-lterresponseabovethresholdarevalidatedwithoutanyadditionalrequirements.DDAScanalsorequireanexternalvalidation,whereanexternalgate,ofuser-denedlengthanddelay,ispresentedtothemoduleanddenesawindowoftimeinwhichtriggerscanbevalidated.
3.4.2EnergyExtraction
EnergyextractioninDDASisaccomplishedbyemployingasecond,simultaneous,symmet-ric,trapezoidal-lteralgorithmthatisreferredtoasthe\energylter".Theresponseoftheenergylter,EF,isgivenbyEq.(3.2)andformulatedinRef.[40].Incontrastwiththetriggerlter,theenergyltercorrectsfortheexponentialdecayofthepreamplier,yieldingatrapezoidal-shapedresponse.Theenergylterisdescribedby:EF[i]=a0tXi=tL+1Tr[i]+agtLXi=tLG+1Tr[i]+a1tLGXi=t2LG+1Tr[i]kB;(3.2)wherea0=(b1)L(b1)L1;(3.3)ag=1;(3.4)anda1=1(b1)L1;(3.5)withb1=Expt˝:(3.6)InEqs.(3.2)through(3.5),thedigitizeddetectorwaveform,ortrace,isdenotedasTrwhilethecharacteristiclengthandgapoftheenergylterareLandG,respectively.Thecoecientsa0,ag,anda1thatmultiplytherunningsumsinEq.(3.2)arefunctionsofLandaparameterb1,denedinEq.(3.6),whichdependsonthesamplingperiod,t,38andthepreamplierdecayconstant˝.Thebackgroundisaccountedforintheresponseofthealgorithmbysubtractingothebaselinevalue,B,multipliedbyaconstant,k,whichdependsonthevaluesofa0,ag,anda1.TheresponseoftheenergylterisshownindarkblueinFig.3.6.TherisetimeandlengthoftheattoparexedbyLandG,respectively,andtheamplitudeofthetrapezoidalresponseisproportionaltotheamplitudeofthedetectorsignal.WhenDDAStriggers,denotedbythe\Leading-EdgeTriggerPoint"inFig.3.6,thesystemwaitsaperiodoftime,denedas2L+G1,tosampletheresponseoftheenergylter,shownasthe\EnergySamplingPoint"inFig.3.6.Theamplitudeoftheenergylteratthe\EnergySamplingPoint"isrecordedastheextractedenergy.Thismethodsamplestheenergylterinthe\at-top"regionwherethereisminimalvariation,yieldingenhancedenergyresolution.3.4.3FastTimingCapabilitiesofDDAS
Inadditiontoextractinghigh-resolutionenergyinformationfromdetectorsignals,DDAScanbeusedtoperformsimultaneous,high-resolution,timingmeasurements.Adigitalconstantfractiondiscriminator(CFD)isusedtoextracttimeinformationwithprecisiongreaterthantheADCclockperiod.ThedigitalCFDemployedinDDASisformulatedinRef.[41]anddescribedbyEq.(3.7).CFD[i]=fkLXi=kTr[i]kLGXi=k2L+GTr[i]kDXi=kDLTr[i]kDLGXi=kD2LGTr[i](3.7)InEq.(3.7),theCFDischaracterizedbyfourparameters.Therearetworunningsumsbothcharacterizedbyalength,L,separatedbyagap,G.TheCFDfractionisfandthe39CFDdelayisD.TheresponseofthedigitalCFDalgorithm,showninred,toaLaBr3detectorsignal,showninblack,acquiredusinga500-MSPSmodule,ispresentedinFigure3.7.Atthepresenttime,the500-MSPSmodulermwarexestheCFDparameterstobef=1,D=5,L=5,andG=1.Thesevalueswerechosenbythemanufacturertooptimizethealgorithmforfastscintillatordetectors.DetailsofamethoddesignedtooptimizethetimingpropertiesofthedigitalCFDinthe100-and250-MSPSmodulescanbefoundinRef.[42].02004006008001000600800100012001400Detector SignalDigital CFD / 2Digital CFDThresholdDigital CFDZero CrossingPointAmplitudeTime (ns)Figure3.7:ExampleoftheDDASdigitalconstantfractiondiscriminator(CFD)algorithm.AsampledetectorsignalacquiredfromaLaBr3detectorbya12-bit500MSPSisshowninblack.TheresponseoftheDDASCFDalgorithmisshowninredalongwiththeuser-denedCFDthresholdillustratedasablackdashedline.Keypointsintimerelatedtoprecisiontimeextractionarelabeled.TheCFDtimeisextractedfromtheCFDresponse,showninredinFig.3.7,usingalinearinterpolationacrossthepointsdirectlybeforeandaftertheCFDzerocrossingpoint.IftheCFDresponseeitherdoesnotcrosstheCFDthresholdordoesnotzerocrosswithin32ADCclockperiods(64nsinthepresentexample)ofcrossingtheCFDthreshold,a0valueisreportedfortheCFDtime.TheCFDalgorithmsemployedbyDDASresultinanearly40negligiblecontributiontothedetectorsystemtimeresolution,providedsignalamplitudesoccupy>10%oftheADCdynamicrange.Figure3.8showstheDDAStimeresolutionforsimulatedLaBr3detectortypesignals,generatedbyaAgilent33522Aarbitrarywaveformgenerator,asafunctionofinputsignalamplitude.FurtherdetailscanbefoundinRef.[42].Voltage (%ADC Dynamic Range)110100DDAS ElectronicTime Resolution (ps)101001000100 MSPS
250 MSPSFigure3.8:DDASElectronicstimeresolutionforLaBr3detectortypesignals,generatedbyaAgilent33522Aarbitrarywaveformgenerator,asafunctionofinputsignalamplituderelativetothedynamicrangeoftheADC.Forsignalamplitudesoccupying>10%oftheADCdynamicrangetheelectronicscontributiontothedetectorsystemtimeresolutionisessentiallynegligible.TheimprovementinelectronicstimeresolutiononecanobtainbothfromfasterdigitizersandlargersignalamplitudesisdemonstratedinFig.3.8.Theelectronicscontributionaddsinquadraturewiththedetectorcontribution.Ingeneral,thebesttimeresolutionisachievedbythefastestdigitizer.413.5PlanarGermaniumDouble-SidedStripDetector(GeDSSD)Aplanargermaniumdoublesidedstripdetector(GeDSSD)servedasthecentralimplantationdetectorfore14039.TheGeDSSDiscomprisedofa1-cmthickby9-cmdiameterGecrystalthatiselectricallysegmentedintosixteen5-mmstripsonthefrontandsixteenorthogonal5-mmstripsontheback.Thecrystaliscontainedinastainlesssteelcryostatwith0.1143-mmthickaluminumwindowsonbothfacesandmechanicallycooledtoatemperatureof66KbyaStirlingcooler.EachstripoftheGeDSSDisinstrumentedwithtwopreampliers.Thelow-gainpreamplierhasa0to30GeVdynamicrange,suitablefordetectingionsimplantedintothecrystal,whilethehigh-gainpreamplierhasa0to15MeVdynamicrangecapableofdetecting-decayelectronsand-rays.AdditionaldetailsabouttheGeDSSDcanbefoundinRef.[43].
3.5.1InstrumentationandTriggeringConditions
Thehigh-gainpreampliersoftheGeDSSDwereinstrumentedwith14-bit250-MSPSmod-ules,whilethelow-gainpreamplierswhereinstrumentedwith12-bit100-MSPSmodules.Thelow-gainstripswerenotrequiredforhigh-resolutionspectroscopyorsophisticatedpulse-shapeanalysisroutinesandtheimplementationoflowerfrequencydigitizersreducedtheoveralldatarate.TheGeDSSDwasoperatedina\freerunning"acquisitionmode.Inthismode,DDASrecordsdataforeachstripeverytimethetriggerltercrossesanuser-setthreshold.TracecapturewasenabledforboththefrontandbackoftheGeDSSD,forboththehigh-andlow-gainelectronics,andthetracelengthwassetto6switha2sdelayforallchannels.423.5.2EventLocalizationandCorrelation
Asmentionedabove,theGeDSSDhastwosetsoforthogonalstrips,oneseteithersideofthecrystal,whichyieldsaneectivegridof2565x5x10mm3pixels.Bothhigh-gainandlow-gaineventsarelocalizedintheGeDSSDbyidentifyingtheintersectionofthestripswiththemostenergydepositedoneachsideofthedetector.decays,alongwithanycoincidentradiationdetectedinancillarydetectors,arecorrelatedtopreviouslyimplantedionsbylocatingthemostrecentionimplantationwithinthesamepixelorrangeofpixels.Thecoincidencewindowwassetinsoftwareto10s.Thespatialdistributionofimplantedionsfore14039isshownFig.3.9asatwo-dimensionalhistogramofthelow-gainmaximumstriponthefrontvs.thelow-gainmaximumstriponthebackforalllowgaineventsrecordedduringe14039.ImmediatelyobviousinFig.3.9isaregionofthedetectorwheretherearemissingevents.Theproleofthedistributionalongeitherstripaxisisexpectedtobeasmooth,roughlyGaussian,shapewithnojaggedfeatureslikewhatisseentheFig.3.9.TheregionoftheGeDSSDwheretherearemissingeventsisthesameregionwherethebeamhasbeenimplantedatvariousintensitiesanddepthsforseveralexperiments.Therefore,alikelyexplanationforthisbehaviorisseverechargetrappingduetodamageofthecrystal.Thesamebehaviorisobservedforthedecayevents.Figure3.10presentsthesametwo-dimensionalhistogramshowninFig.3.9,butforthehigh-gainstrips.InFig.3.10,thecharge-trappingregionofthedetectorislessobviousuntiloneprojectsthetwo-dimensionalhistogramontothefront-andback-stripaxes.Thehigh-gainbehaviorisslightlydierentthanthelow-gainbehavior.Heavyionsdepositalloftheirenergyinaverylocalizedregionofthedetectorwhilethe-decayelectrons,onaverage,travelmuch4304812160481216110210310410510610024Maximum Low-Gain Back ChannelCounts (x10)6102Maximum Low-Gain Front ChannelCounts (x10)6Figure3.9:Two-dimensionalhistogramshowingthemaximumlow-gainfrontchannelvs.themaximumlow-gainbackchannelforalllow-gaineventsine14039.Projectionsontothefront-andback-stripaxesareshowntotherightandabovethetwo-dimensionalhistogram,respectively.Thereisaclearregionofmissingeventsduetochargetrappingasaresultofcrystaldamage.
furtherinveryerratictrajectoriesdepositingenergyacrossalldepthsofthedamagedregion.Asaresult,someelectronswilldepositenergyacrossarangeofdepths,someofwhicharenotdamaged,andarerecorded.Severalattemptsweremadeduringtheanalysistolocatethemissingimplantedions,butnomethodwassuccessfulinrecoveringthedata.Intheseattemptsthenumberofeventswithafront(back)energybutnoback(front)energywereexamined.Arelativelylargenumberofthesewereobservedsuggestingthatoftenonesideortheotherrecordsnocharge.Ultimately,thisproblemdidnotsignicantlyimpacttheanalysis,butdidincreasethenumberofspuriouscorrelationsandreducetheoverallstatistics4431004812160481216410510610061201020Maximum High-Gain Back ChannelCounts (x10)6Maximum High-Gain Front ChannelCounts (x10)6Figure3.10:Two-dimensionalhistogramshowingthemaximumhigh-gainfrontchannelvs.themaximumhigh-gainbackchannelforallhigh-gaineventsine14039.Projectionsontothefront-andback-stripaxesareshowntotherightandabovethetwo-dimensionalhistogram,respectively.Theregionofmissingeventsduetochargetrappingasaresultofcrystaldamageislessevidentduetothefactthattheelectronsandrayscantraveloutsidethelocalizeddamagedregionandcandepositenergyacrossthedepthofthedetector.inthe-gatedandcorrelatedspectra.453.5.3CrosstalkCalibration
ThepreamplierchannelsoftheGeDSSDexhibitelectroniccrosstalk.Crosstalkmanifestsitselfassmallamplitudesignalsinducedontheneighboringchannelsofastripthathaschargedeposition.Inanenergyspectrum,thisresultsinlow-energypeaksthatareartifacts,andthusmustbecalibratedout.Electroniccrosstalkisroughlysymmetriconeithersideofthestripthatcollectstherealchargefromtheevent.Figure3.11showsanexampleofelectroniccrosstalkacrossthreestripsobservedwhenmeasuringa137Cssource.170018001900200020002500300035000500100015002100220023002400Time (ADC Clock Cycles)Amplitude (ADC Units)Strip 11
662 keVStrip 10
27 keV
Strip 12
26 keVa)
b)
c)Figure3.11:RepresentativecrosstalkexamplefortheGeDSSDshowing(b)afullenergydepositionofa662-keVrayinstrip11.Panels(a)and(c)showinducedsignalsinstrips10and12respectively.Theseinducedsignalsyieldlow-energypeaksintheGeDSSDstripenergyspectraandmustbecalibratedout.Thecrosstalkcorrectionwasdeterminedbeforetheexperimentusinga137Cssourcebyexaminingtheratioofsignalamplitudesincoincidentadjacentstripsforeventswhere46atleastthreeconsecutivestripsredanda662-keVphotopeakeventwasdetectedinthecentralstripofthegroupofthree.Figure3.12presentsarepresentativesampleofcrosstalkcalibrationsusingstrip10onthebackoftheGeDSSD.Figures3.12aand3.12bshowtheratioofthesignalinducedonstrips9and11,respectively,bythesignalpresentonstrip10.Amplitude Ratio (Back Strip 9 / Back Strip 10)0.020.030.040.050.060.07Counts0500100015002000DataGaussian Fit0.020.030.040.050.060.07050010001500Amplitude Ratio (Back Strip 11 / Back Strip 10)Gaussian FitDataGaussian Fita)b)Figure3.12:Representativesampleofcrosstalkcalibrationsusingstrip10onthebackoftheGeDSSD.Panels(a)and(b)showtheratioofthesignalinducedonstrips9and11,respectively,byasignalpresentonstrip10.ThecentroidoftheGaussiantinFigs.3.12aand3.12b,multipliedbytheamplitudeofanysignalonstrip10,isthecrosstalkcorrectionandtheamountthatmustbesubtractedfromasignalonstrips9and11,respectively.Thiscalibrationisperformedforeachstripinthedetectorforboththefrontandback.Table3.3presentsthesummaryofthecrosstalkcorrectionsfortheGeDSSDusedinallsubsequentanalysis.Theresultsofthecrosstalkcorrectionforstrip10isshowninFig.3.13.TheuncorrectedspectrumisshowninFig.3.13awithaninsetshowingthelow-energyregionwherecrosstalkpeaksinducedbyadjacentstripsarepresent.Figure3.13bshowstheresultsofthecrosstalkcalibrationwithaninsetexpandingthesamelow-energyregionasinFig.3.13a.ThecrosstalkpeakshavebeenremovedandtheKx-raysaround32keVareclearlyobserved.47Table3.3:RatiosofinducedsignalsintheGeDSSDbystripnonadjacentstrips(n+1)or(n1).Whenmultipliedbythesignalamplitudeofstripnthesevaluescorrecttheamplitudeofthesignalpresentonstripsn+1orn1.StripFront(n+1)/nFront(n-1)/nBack(n+1)/nBack(n-1)/n10.0215-0.0261618-20.02880.02150.03350.026730.03210.02900.03570.032840.03960.03210.04040.034450.07080.03820.04700.042660.07180.06980.03780.042770.07100.07170.03900.038680.06800.06910.03870.037390.05520.07020.04670.0450100.03870.05710.04160.0431110.04080.04010.04170.0423120.03590.04010.04200.0413130.03280.03530.03970.0415140.02730.03310.03160.0401150.02150.02750.02660.033616-0.0226-0.0254480500010000150002000025000020040060080005000020406080100050001000001000020000020406080100Energy (keV)Counts / keVCounts / keVEnergy (keV)Energy (keV)Counts / keVCounts / keVa)
b)Figure3.13:ResultsofthecrosstalkcalibrationforarepresentativestripofthebackoftheGeDSSD.Theuncorrectedandcorrectedspectrafor137Csareshownin(a)and(b),respectively.Foreachspectrumaninsetexpandsthelowenergyregionanddemonstratestheexistenceandsubsequentremovalofthecrosstalkinducedpeaks.493.5.4EnergyCalibration
SeveralmethodswereusedthroughouttheanalysistoextracttheenergyofeventsintheGeDSSD.TheseincludetheDDASenergylter,describedinSection3.4.2,aswellaspulseamplitude,pulsearea,andpulsetting,discussedlaterinSection3.5.5.Inallcasestheenergycalibrationprocedureswereidentical.Theuncalibrated,crosstalkcorrected,energyspectraforthebackstripsoftheGeDSSDacquiredusinga137CssourceareshowninFig.3.14.10100100011000200000300040000010002000300040001000200030004000100020003000400050001
11010010100110100Pixie Energy (Arb. Units)CountsCountsCountsCountsStrip 1Strip 2Strip 3Strip 4Strip 5Strip 6Strip 7Strip 8Strip 9Strip 10Strip 11Strip 12Strip 13Strip 14Strip 15Strip 16Pixie Energy (Arb. Units)Pixie Energy (Arb. Units)Pixie Energy (Arb. Units)Figure3.14:Uncalibrated,crosstalkcorrected,energyspectraforall16backstripsoftheGeDSSDfora137Cssource.Strips4through9clearlyexhibitmultiplepeakswhichresultfromdierencesinchargecollectionalongthedamagedregionsofthosestrips.EnergieswereobtainedfromtheDDASdigitallter.InFig.3.14,strips4through9exhibitmultiplepeaksforamonoenergeticsource.ThesestripshavebeenbombardedwithheavyionsatthehighestratesduringallexperimentsforwhichtheGeDSSDwasused.Theenergyspectraforbackstrip7atdierentpositions,50basedonthelocationofthecoincidentsignalonthefrontoftheGeDSSD,areshowninFig.3.15.Basedontheseenergyspectraasimplestrip-by-stripenergycalibrationwouldbeinsucient.Instead,theenergycalibrationfortheGeDSSDwasdoneindividuallyforeachofthe256eectivepixelsforboththefrontandbackoftheGeDSSD,andisreferredtoasthetwo-dimensionalenergycalibration.0100020003000400050001101001000Front Strip 1
Front Strip 4
Front Strip 7Front Strip 10
Front Strip 13
Front Strip 16Energy (Arb. Units)CountsGeDSSD Front Interaction LocationFigure3.15:EnergyspectraofGeDSSDbackstrip7takenwitha137Cssourceandhis-togrammedbyinteractionlocationfromthefrontoftheGeDSSD.Theblack,green,cyan,magenta,red,andbluespectracorrespondtopositionsalongthelengthofbackstrip7basedonthecoincidentsignalinfrontstrips1,4,7,10,13,and16,respectively.Thelocationofthe662-keVphotopeakisidenticalforstrips1,13,and16butislowerinenergyforstrip4.Eventsoccurringinbackstrip7localizedtostrips7and10onthefrontdonotdisplayaphotopeak.Thetwo-dimensionalenergycalibrationisalinearonepointcalibrationwithaxed0-keVosetforeachofthe256eectivepixels.Datawasrecordedwitha137Cssourceandtheenergyspectraforeacheectivepixel,forboththefrontandbackoftheGeDSSD,werecreated.Thecentroidofthe662-keVphotopeakisthenextractedforeachpixel,andtheratioof662.6-keVtotheextractedcentroidprovidestheslopefortheenergycalibrationofeachpixel.Forpixelsthatdonotprovidea662-keVphotopeak,theenergycalibration51wasperformedusingtheComptonedge.Theapplicationofthetwo-dimensionalenergycalibrationtothedatashowninFig.3.14ispresentedinFig.3.16.Thetwo-dimensionalenergycalibrationremovesthemultipeakingpresentinFig.3.14andallstripsgivethesamephotopeakenergyfor137Cs.2004000600Pixie Energy (keV)60060060020040002004000200400080010100100001
1
1
1Counts / keV1000101001000101001000101001000Counts / keVCounts / keVCounts / keVStrip 1Strip 2Strip 3Strip 4Strip 5Strip 6Strip 7Strip 8Strip 9Strip 10Strip 11Strip 12Strip 13Strip 14Strip 15Strip 16Pixie Energy (keV)Pixie Energy (keV)Pixie Energy (keV)Figure3.16:Calibrated,crosstalkcorrected,energyspectraforall16backstripsoftheGeDSSDfora137Cssource.3.5.5PulseShapeAnalysis
Apulse-shapettingalgorithmwasemployedtoanalyzeGeDSSDsignalstosearchforthe0+
2!0+
1E0transitionfromthedecayofthe0+
2statein68Ni.Aschematiclevelschemefor68Ni,depictingthersttwostates,ispresentedinFig.3.17.Populatedinthedecayof68Co,the0+
2statehasbeenstudiedextensively,andthreehalf-lifemeasurementshaveyieldedvaluesof270(5)ns[44],268(12)ns[18],and235(23)ns[21].DuetothehighelectrondetectioneciencyoftheplanarGeDSSDandthe˘270ns52Figure3.17:Selectedlevelschemefor68NishowingthersttwolevelsandtheE0transitionthatconnectsthem.
half-lifeofthe0+
2statein68Ni,itsdecayleavesacharacteristic\double-pulse"signatureintheGeDSSD.AnexampleofadoublepulserecordedintheGeDSSDduringe14039isshowninFig.3.18.Figure3.18:Exampledouble-pulsesignalrecordedintheGeDSSDduringe14039.Thedouble-pulsesignalshapeiswellunderstood.Therstconstituentpulseistheelectronfromthedecayof68Co,whichdirectlyorindirectlypopulatesthe0+
2statein68Ni.Sometimelater,asecondelectroneventduetothedecayofthe0+
2stateisrecorded,53whichproducesthesecondriseofthedouble-pulsesignal.Sincethedecaytimeofthepreamplier(ˇ30s)islongcomparedtothehalf-lifeofthe0+
2state,thepulsespileupononeanother.Oinepulse-shapeanalysisofthisdouble-pulsesignalisrequiredtoextracttheamplitudesofeachpulseaswellasthetimedierencebetweenthem.ThetechniquesdescribedhereinareverysimilartothoseofRef.[18],adaptedfromRef.[45].Beforettingcommenced,traceswerecheckedforoverows,underows,transients,andnoise,allofwhichwouldprecludeagoodtresult.Thesepreliminarychecksreducedthenumbersignalstobettedandthustheamountofanalysistimerequired.Anoverowedorunderowedtraceissimplyoneforwhichtheamplitudeofthedetectorsignalextendsaboveorbelow,respectively,thedynamicrangeoftheADCatsomepointinthetracewindow.Transientswereidentiedusingthetriggerlteralgorithm,describedinSection3.4.1,settoa40nslengthwitha0nsgap.TheresponseofthetriggerltertovarioustypesofsignalsdetectedintheplanarGeDSSDisshowninFig.3.19.Therelativelylong(˝ˇ30s)decaytimeoftheGeDSSDpreampliersresultsinanearsteplikepulseonthe10'sofnstimescaleofthetriggerlter.Thereforenormalsingle-pulsesignalsgiveasingletriangularshapedresponse,showninFigs.3.19aand3.19b.Apositive(negative)transientsignalleadstoatriggerlterresponsewhichrapidlyincreases(decreases)thenabruptlycrosseszero,furtherdecreasing(increasing)beforereturn-ingtobaseline.ExamplesofnegativeandpositivetransientsareshowninFigs.3.19cand3.19d,respectively.Thetrigger-lterresponsewascomparedtotherootmeansquareofthebaselineofthedetectorsignal.Ifthetrigger-lterresponsedroppedbelowafactoroftenofthebaselineRMS,thesignalwasrejectedasatransient.Sometransientsdomakeitthroughthisinitiallter,butwererejectedlaterinthettingprocedure.Additionally,ifthesignalhadalargebaselineRMS(>20ADCUnits)thesignalwas54Figure3.19:Responseofthetriggerlteralgorithmusedfortransientrejectionintheanalysisto(a)large-amplitudesinglepulse,(b)low-amplitudesinglepulse,(c)negativetransient,and(d)positivetransientGeDSSDsignals.Detectorsignalsareshowninblackwhilethetriggerlterresponsesareshowninred.Triggerlterresponseshavebeenreducedbyafactoroftenandthebaselineofthesignalhasbeenadded.
rejectedaswell.Typically,suchsignalshavestrangeshapesorslopingbaselinesandwouldfailthettingprocedureifallowedtopass.Uponpassingallchecks,tracescontinuedontopulsetting.Therstiterationofthetracettingprocedureattemptedtotalldetectorsignalswiththeresponseofthedetectortoasingleenergydepositionreferredtoasa\single-pulse"t.AsampleGeDSSDsignalassociatedwithasingleenergydepositionisshowninFig.3.20.Atemplatesinglepulsewascreatedforeachofthe256eectiveGeDSSDpixelsfromtheaverageof1000signalslikethatofFig.3.20.Ineacht,theheightandrelativetimeosetwerefreeparameters.The˜2fromthetdividedbyamplitudeofthetrace,denotedfromhereonoutas˜2
n,wasusedtoassessthequalityofthet.Thedistributionof˜2
nvalues,obtainedfromthesingle-pulsetstoallGeDSSDsignals,ispresentedinFig.3.21.Therearethreedistinctregionsofnormalized˜2valuesinFig.3.21.Therstpeak55Figure3.20:SampleresponseoftheGeDSSDtoasingleeventrecordedusinga137Cssource.01234560500100015003x10Log[/ PulseAmplitude]c2CountsFigure3.21:Distributionof˜2dividedbysignalamplitude(˜2
n)forthetofhigh-gainGeDSSDsignalswithasingledetectorpulse.Alltsabovethereddashedlinearetwiththelinearcombinationoftwosingledetectorpulseswhilealltsbelowtheredsolidlineareconsideredgoodsingle-pulseevents.
around100isfromgoodtsofsingle-pulsedetectorsignals.Thesecondpeakisfromlow-amplitudesignals,someofwhicharetransientsthatmadeitthroughthetransientrejectionalgorithm.Thethirdpeakaredouble-pulsesignalevents.Exampletsfromeachregionare56showninFig.3.22.0200040006000050001000015000Time (s)mAmplitude (ADC Units)c= 418902
n17001800190020000200040006000Time (s)mc= 2692
n170017501800185019000200040006000c= 2882
n15002000250030000200040006000Amplitude (ADC Units)c= 362
n(a)(b)(c)(d)Figure3.22:Single-pulsetresultsforavarietyofdierentsignaltypesintheGeDSSD.(a)Goodtofasinglepulsebyasingle-pulset.(b)Fitofatransientwithasinglepulse.(c)Fitofalowamplitudesignalwithasingle-pulset.(d)Fitofadouble-pulseeventwithasinglepulse.Detectorsignalsareshowninblackwhilethetsareshowninred.The˜2
nislabeledoneacht.TheenergiesofallGeDSSDeventsthathaveasingle-pulset˜2
noflessthan250arehistogrammedtogeneratetheenergyspectrumforallsingleradioactivedecaysrecordedintheplanarGeDSSDduringe14039,showninFig.3.23.ThespectrumofsingleradioactivedecayenergiesintheGeDSSDisdominatedby-decayelectronscomingfromthedecayofunstablenucleiimplantedwithinthedetector.Sincedecayisathree-bodyprocess,theelectronenergydistributioniscontinuouswithamaximumenergyuptotheQ-value,whichisbetween500keVand12.5MeVfornucleidecayinginsidetheGeDSSD.Thereisalsoacontributionfromlow-energyraysandComptonscattering.ThepeakslabeledinFig.3.23originatefromknownsourcesandarefurtherdiscussedinAppendixAGeDSSDeventsthatyieldeda˜2
ngreaterthan100forthesingle-pulset,denotedby57020004000600080000204060801000100200300400010020030092.6141.4185.0239.2352.1Energy (keV)x103Counts / 2 keVFigure3.23:EnergyspectrumobtainedfromthetofGeDSSDsignalsbyasingletemplatedetectorsignalwhere˜2
n<250.MostofthecountsarefromthecontinuouselectronenergydistributionsfromdecayandfromCompton-scatteredrays.Thepeakat92.6-keVisfromthedecayofthe93.3-keV1=2statein67Znand141.4-keVtransitioncomesfromthedecayofthe242.6-keVisomericstatein70Cu.The185.0-keV,239.2-keV,and352.1-keVareroombackgroundlinesfrom226Ra,212Pb,and214Pb,respectively.thereddashedlineinFig.3.21,continuedontothedouble-pulsettingprocedure.Inthisapproach,alinearcombinationoftwosingledetectorpulses,osetbysomeamountoftime,isattempted.Theamplitudesandtimeosetsofeachpulsewerefreeparametersinthet.Theresultingdistributionof˜2
nvalues,obtainedinthedouble-pulseanalysis,isshowninFig.3.24.The˜2
ndistributionisbroadandrelativelyfeatureless,suchthatfurtheranalysiswasrequired.ThesignalsofinterestintheGeDSSDoriginatingfromthe0+
2!0+
1E0transitionin68Nishouldhavesecondpulseenergiesofroughly581and1603keVfortheinternalpairformationandinternalconversiondecayprocesses,respectively.Fromexaminationofthe˜2
ndistributionvs.theextractedenergyofthesecondpulse,showninFig.3.25,thelimitontheacceptable˜2
nvalueswasdetermined.Avalueof600(2.78inlogscale)waschosen580123456020406080100Counts3x10Log[/ PulseAmplitude]c2Figure3.24:Plotofdouble-pulse˜2
nobtainedfromthetsofGeDSSDsignalsusingalinearcombinationoftwosingledetectorpulses.
astheupperlimiton˜2
n,shownasaredlineinFig.3.25.Traceswithdouble-pulset˜2
nvaluesabovetheredlinehavepoorshapes,oftenfromballisticdecit,and,assucharepoorlyt.Belowtheredlineahighpercentageofthetsaregooddouble-pulsetsandpeakscorrespondingtoknowntransitionenergiesarepresent.Afterexaminationofseveraladditionalrecordeddetectortraces,threemore˜2
ncutsusingspecicregionsonthetraceweremadetoremoveadditionalpoorqualitydouble-pulsetsnoteliminatedbythe˜2
ncut.Therstoftheseisthe˜2
nT,whichlooksalongthetailofthepulsefrom4440nsto5040ns.Thesecond,denotedas˜2
nLEexaminestheleadingedgeofthepulsefrom1920to2160ns.Thethird,labeled˜2
nLELisaslightlydelayedlongertimeregionontheleadingedgefrom2040nsto2400ns.Exampletraces,overlayedwiththeirdouble-pulset,andlabeledwithassociated˜2values,areshowninFig.3.26.The˜2
nT,˜2
nLE,and˜2
nLELdistributionsobtainedfromtheanalysisarepresentedinFigs.3.27a,3.27b,and3.27c,respectively.InFig.3.27dthesingle-pulset˜2
ndivided590500100015002000012345110210310410Second Pulse Energy (keV)Log[/ PulseAmplitude]c2Figure3.25:Plotof˜2
nvs.energyofthesecondpulsefortheGeDSSDobtainedfromthedouble-pulsettingmethod.020004000600018002000220024002600Amplitude (ADC Units)c= 382.52
ncRatio = 0.252
nc= 56.92
nTc= 99.82
nLEc= 74.92
nLEL180020002200240026002800Amplitude (ADC Units)0200040006000c= 316.82
ncRatio = 0.222
nc= 10.32
nTc= 153.32
nLEc= 119.02
nLEL0200040006000800010000120000200040006000Time (s)mAmplitude (ADC Units)c= 402.92
ncRatio = 0.032
nc= 0.632
nTc= 212.52
nLEc= 334.52
nLEL020004000600080001000012000c= 98.62
ncRatio = 0.0012
nc= 0.312
nTc= 2.52
nLEc= 56.32
nLEL0200040006000Time (s)mAmplitude (ADC Units)(a)
(c)(b)(d)SignalFitFigure3.26:Panels(a)through(c)displayGeDSSDsignals,showninblack,withthedouble-pulset,showninred,overlayedforthreesignaltypesthatfailthedouble-pulsetbutpassthe˜2
ntest.Thevaluesobtainedfromthevarious˜2metricsusedforthisanalysis,describedinthetext,arelabeledoneachpanel.Oneormoreoftheadditional˜2cutsrejecteachsignalin(a)through(c).Agooddouble-pulsetisshownin(d)withthesamesetof˜2metricsas(a)through(c).Thetin(d)passesallmetrics.Inallpanelsthesignalsareshowninblackwhilethebestdouble-pulsettoeachsignalisshowninred.60bydouble-pulset˜2
nasafunctionoftheextractedenergyofthesecondpulsefromthedouble-pulsetisshown.Cutsplacedoneachdistribution,shownasredlinesonFig.3.27,weremotivatedbyexaminationofseveraltstopoor-qualitytracesofthetypepresentedinFigs.3.26athrough3.26caswellaststorealdouble-pulsetraceslikethatofFig.3.26d.050010001500200000.10.20.30.40.5110210310Second Pulse Energy (keV)Log[c/ PulseAmplitude]Ratio (Single / Double)2
n02004006008001000010203040503x103Log[c/ PulseAmplitude]2
nLECounts0200400600800100001020304050x103CountsLog[c/ PulseAmplitude]2
nLEL0501001502000200040006000CountsLog[c/ PulseAmplitude]2
nT(a)(b)(c)(d)Figure3.27:(a)Distributionof˜2
nTvalues.(b)Distributionof˜2
nLEvalues.(c)Distributionof˜2
nLELvalues.Theredverticallinesin(a)through(c)representtheupperlimitofacceptabilityforeachrespective˜2value,withacceptablevaluesbeingbelowtheredlineineachcase.(d)Plotoftheratio(single-pulset/double-pulset)of˜2
nvs.energyofthesecondpulseobtainedfromthedouble-pulsettingmethod.Valuesbelowtheredhorizontallineareacceptabledouble-pulseevents.Afteralldouble-pulsesignalsweretted,applyingtheselected˜2cuts,thespectrashowninFigs.3.28aand3.28bwereobtainedfortheenergyoftherstandsecondrises,respectively.Theenergyspectrafromtherstriseofthedouble-pulsesignals,showninFig.3.28a,isdominatedbythe-decayelectronenergydistribution.However,twopeaksareobservedat100.2and308.3keVbothcoincidentwiththe92.6-keVsecondriseenergy,exclusively.61020004000600080000100200300400500600010020030040002004000500100015002000010002000300040005000100.2308.3100.2308.3Energy (keV)Counts / 2 keVCounts / 2 keV92.6581175, 1901603(a)(b)Figure3.28:Energyspectrumdisplayingtheenergyofthe(a)rstand(b)secondriseofthedouble-pulsesignals.Theenergieswereobtainedfromtheamplitudesoftheconstituentpulsesofdouble-pulsetssatisfyingthe˜2criteria,andwerecalibratedusingthetechniquesdescribedinSection3.5.4.
ThesearediscussedfurtherinAppendixA.ThetwolargestpeaksinFig.3.28b,locatedat581keVand1603keV,arefromthepair-productionandinternalconversiondecaymodesofthe0+
2statein68Ni.Therayscoincidentwiththesetwosecondpulseenergiesarepresentedandanalyzedindetailinthenextchapter.Thefeaturespresent,tosomedegree,abovethe581-keVpeakand,toagreaterextent,abovethe1603-keVpeakarefromdierencesinindividualstrips.Figure3.29presentstheenergyofthesecondriseofthedoublepulsesonthexaxisforeachback62stripoftheGeDSSDontheyaxis.05001000150020000246810121416181101001000Second Pulse Energy (keV)GeDSSD Back Strip NumberFigure3.29:PlotoftheenergyofthesecondriseofthedoublepulsesonthexaxisforeachbackstripoftheGeDSSDontheyaxis.Overthetendayexperiment,damagetothedetectorcrystalfromheavyionimplantationresultedinachangetothetwo-dimensionalenergycalibrationinthestripsexposedtobeam.Therefore,thecalibrationusedforthisanalysis,generatedaftertheexperimentusingthetechniquesdescribedinSection3.5.4,performspoorlyfordataearlyintheexperimentandtheenergyspectraexhibitdouble-peakingintheregionwhereionswereimplantedatahighrate.Datatakenlaterintheexperimentfallintoonepeak,withdegradedresolution,andthecentroidisrelativelyuniformacrossthedierentGeDSSDstrips.However,sincethepurposeofthedouble-pulsedetectionalgorithminthisanalysisistoprovideasensitivetagforthe0+
2!0+
1E0transitionin68Ni,noattemptwasmadetomorepreciselycalibratetheGeDSSD.633.6SegmentedPlasticScintillatorandPosition-SensitivePhoto-MultiplierTube(PSPMT)Thesegmentedplasticscintillator,madeofELJENEJ-204,was525210mm3insizeandopticallysegmentedinto2563.253.2510mm3pixels.ThescintillatorwascoupledtoaHamamatsuH8500seriesmulti-anodePosition-SensitivePhoto-MultiplierTube(PSPMT)with64truepixels.TheoutputofthePSPMTwas65channels,whereonechannelwasthecommondynodesignalandtheremaining64weretheindividualanodereadouts.AdditionalinformationabouttheconstructionandcharacterizationofthisdetectorcanbefoundinRef.[46].TheremainderofthissectiondescribesindetailtheinstrumentationandoperationofthePSPMT.
3.6.1InstrumentationandTriggeringConditions
ThedynodeofthePSPMTwasinstrumentedbythe12-bit,500-MSPSmodule,whileeachofthe64anodesignalswerereadoutbythe14-bit,250-MSPSmoduleswithonechanneldedicatedtoeachanode.Thefasterdigitizeremployedforthedynodesignalmaximizesthetime-resolvingcapabilitiesofthesystem.TheanodesignalsareusedforpositionlocalizationofeventsinthePSPMTratherthantimingand,assuch,theincreasedbitdepthofthe14-bitdigitizerisidealforthisapplication.TracecapturewasenabledinDDASforthedynodeandallanodesignals.Thedynodetraceswere2slongwitha400nsdelayandanodetraceswere500nslongwitha160nsdelay.Theacquisitionforthedynodesignalwasleftina\free-running"mode,wheredatawererecordedeachtimethedynodetriggeredbasedonthealgorithmsdescribedinSection3.4.1.64ThedigitalCFD,discussedinSection3.4.3,wasemployedtoextractprecisiontimingbelowthenativeclockperiodofthedigitizer.Theanodesignalswerecollectedusinganexternalvalidationtriggermodewhere,upontriggering,theystillrequiredthepresenceofanexternalinputsignal,generatedwhenthedynodetriggers,torecorddata.TheCFDalgorithmwasalsoenabledfortheanodesignals.3.6.2EventLocalizationandCorrelation
Thelocationofbothimplantanddecayeventsinsidetheplasticscintillatorwasdeterminedusinga\center-of-gravity"algorithm[46],presentedinEqs.(3.8)and(3.9).Onecanthinkofthegridofpixelsasrows(i)andcolumns(j)suchthattheenergyofeachofthe64pixelscanbelabeledasEijwereiandjrunfrom1to8.ActiveRow=2ET64Xi=1iEij(3.8)ActiveColumn=2ET64Xi=1jEij(3.9)TheresponseofthePSPMTtoasingleimplantationeventisshowninFig.3.30.Eachofthe64digitizedPSPMTanodesignalsareshowninaboxinFig.3.30.Theheightofeachboxis16384ADCunits(1Vfullscalerange)andthewidthis500ns.Theenergyofeachsignalwasobtainedfromtheareaunderthepulse,determinedoineusingpulse-shapeanalysis.Theresultsofthecenter-of-gravityalgorithmreturnanon-integervaluefortheactiverowandcolumnoftheeventforthe88gridofpixels.Thesevaluesweremultipliedbytwoandtruncatedtogivea1616pixeleld.65j=1j=8i=1
i=8Figure3.30:ResponseofthePSPMTtoasingleionimplantationeventinthesegmentedplasticscintillator.EachboxshowsthedigitizeddetectorsignalfromapixelofthePSPMT.Theheightofeachboxis16384ADCunits(1Vfullscalerange)andthewidthis500nsUnliketheGeDSSDdescribedin,Section3.5,thePSPMTdoesnothavetwogainrangesfordetecting˘GeVimplantedionsandsubsequent˘MeV-decayelectrons.Therefore,thesmallergainrange(1.0V)waschosentomaintainsensitivitytolow-energyelectrons,butasaconsequencetheimplantpixelandthosesurroundingareoverowed,asdepictedinFig.3.30.Theseoverowsarethereasonforusingthepulseareasinsteadoftheamplitudes,sincetheformerretainssomeproportionalitytotheenergy,whilethelaterdoesnot.Additionally,allpixelsinFig.3.30exhibitaringingbehaviorduringanimplant.Theareaoftheringingpulseswasoftenverysmallcomparedtotheareaofsignalscentraltotheimplantlocation,andthereforetheringingpulseslittleeectonthecenter-of-gravityalgorithm.TheidenticationofanimplantwasbasedonthepresenceoftheEandTOFsignals,intheSiPINdetectorsandTACs,respectively,withinthesameevent.Implantationevents66mustcoincidewithPINdetectorsignalsaswellasatime-to-amplitudeconvertersignal,whiledecayeventscannothaveeitherincoincidence.Thecoincidencewindowwassetto10s.Thelocationdistributionofimplantedionsfore14057isshownFig.3.31asatwo-dimensionalhistogramoftheactiverowvs.activecolumninthePSPMTforallimplantationeventsrecordedduringe14057.Projectionsontotheactive-rowandactive-columnaxesareshowntotherightandabovethetwo-dimensionalhistogram,respectively.Thesametwo-dimensionalactiverowvs.activecolumnhistogramforalldecayeventsrecordedduringe14057ispresentedinFig.3.32.Withthepositioninformationextractedandidenticationofeventscomplete,thecor-relationtechniquesusedforthePSPMTwereidenticaltothatoftheGeDSSD,detailedinSection3.5.2,wherethedecays,alongwithanycoincidentradiationdetectedinancillary-raydetectorarrays,werecorrelatedtopreviously-implantedionsbylocatingthemostrecentionimplantationwithinthesamepixelorrangeofpixels.TheanalysispresentedinChapter4utilizedanine-pixeleld,consistingofthecentralpixel,identiedasthelocationoftheevent,alongwiththeimmediate8neighboringpixelsforthePSPMT.670481216048121610210310410510Implant X Position CentroidImplantYPosition Centroid120Counts (x10)61012Counts (x10)6Figure3.31:Two-dimensionalhistogramshowingtheactiverowvs.activecolumninthePSPMT,determinedinthecenterofgravityalgorithm,forallimplantationeventsrecordedine14057.Projectionsontotheactive-rowandactive-columnaxesareshowntotherightandabovethetwo-dimensionalhistogram,respectively.6811021031041051061004812160481216DecayYPosition Centroid480Counts (x10)6Decay X Position Centroid048Counts (x10)6Figure3.32:Two-dimensionalhistogramshowingtheactiverowvs.activecolumninthePSPMT,determinedinthecenterofgravityalgorithm,foralldecayeventsrecordedine14057.Projectionsontotheactive-rowandactive-columnaxesareshowntotherightandabovethetwo-dimensionalhistogram,respectively.693.6.3PulseShapeAnalysis
ThePSPMT,liketheGeDSSD,issensitivetothecharacteristicdouble-pulsesignaturefromtheinternalconversionandinternalpairformationdecaysfollowingthedecayofimplantednuclei.Anexampledouble-pulseeventrecordedinthePSPMTisshowninFig.3.33a.800900100011001200Amplitude (ADC Units)Detector SignalTrigger Filter / 4DynamicThreshold040080080090010001100Time (ns)Amplitude (ADC Units)04008001200Time (ns)Energy Filter / 10(a)(b)
(d)(c)Figure3.33:(a)Sampledouble-pulseeventrecordedduringe14057.(b)Samedouble-pulseeventasin(a)showninblackwithanoverlayofthescaledtriggerlteralgorithmshowninred.Thezerocrossingpointsofthetriggerlteralgorithmareusedtoidentifysubsequenttriggersandextracttiminginformation.(c)Overlayofthedynamicthreshold,showningreen,discussedinthetext.(d)Scaledresponseoftheenergylteralgorithmusedtoextracttheenergyofeachpulse.Double-pulseeventswereidentiedusingashorttimescale(Length=10ns,Gap=0ns)trigger-lteralgorithm,describedinSection3.4.1.Theapplicationofthisalgorithmtothedouble-pulsesignalshowninFig.3.33aisshowninredinFigs.3.33band3.33c.Thecharacteristiczero-crossingbehaviorassociatedwitheachdetectorpulsewasusedtoidentifymultiplesignalsfallinginasingletracewindow.ThePSPMTexhibitsringingbehaviorfollowingeachsignal,showninFig.3.33.Aconstantthresholdwouldhavetobeplacedhigh(ˇ25%oftheoriginalsignalheight)in70amplitudetopreventtheringingfromtriggeringthedouble-pulsesearchalgorithm.Assuch,atime-andamplitude-dependentthresholdwasdevelopedandusedtosearchforthesecondconstituentpulseinadouble-pulseevent.Theamplitudeoftheringingisdependentupontheprecedingpulseamplitudeaswellasthetimedierencebetweenthatrstpulseandthesubsequentring.TheratiooftheamplitudeofeachringdividedbythecorrespondingpulseheightasafunctionoftimedierencebetweenthepulseandsubsequentringispresentedinFig.3.34Theamplitudesweretakenfromthetriggerlteralgorithm6nsbeforethezerocrossingtime(ZCT)ofthetriggerlterandthetimedierencewascalculatedfromthedierencebetweenthetwoZCTvalues.TheringingbehaviormanifestsitselfasbrightregionsinthebottomleftcornerinFig.3.34.AfunctionoftheformAn=A0=Exp(B+Cx)+D,shownasthesolidredline,wasdenedasthetime-dependentor\dynamic"threshold.Whenmultipliedbytheheightofthecorrespondingpulse,A0,thethresholdwascalculatedasafunctionoftimefollowingthepulse.Eventsbelowthresholdwerecategorizedasringingevents,whileeventsabovewereidentiedaspotentialdouble-pulseeventsinthePSPMT.010020030040000.10.20.30.40.51101001000Time Difference (ns) {ZCT(n) - ZCT(0)}Amplitude Ratio{TF[ZCT(n)-6] /TF[ZCT(0)-6]}Figure3.34:Creationofa\dynamic"thresholdtomitigatesubsequenttriggeringfromtheringingofthescintillatorduringthedouble-pulsesearch.Theredlineisthethresholdandalleventsbelowthresholdareconsideredasringingeventswhileeventsabovearefrompotentialdouble-pulseeventsinthePSPMT.71TheapplicationofthedynamicthresholdisshowninFig.3.33casthegreenline.Beforethearrivaloftherstpulse,thethresholdisaconstantvalueabovebaseline.Afterthearrivaloftherstpulsethethresholdimmediatelyrisesandthendecaysbacktotheconstantosetabovebaseline.Sometimelater,asecondpulseisrecordedabovethresholdandthedynamicthresholdadjuststoahighvalueandagaindecaysbacktotheconstantvalueabovebaseline.Thismethodallowsforaslowofathresholdaspossiblewhilemitigatingcontaminationfromringing.Theenergyofeachpulseinadouble-pulseeventisobtainedusingtheenergylteralgorithmdescribedinSection3.4.2.ThescaledresponseoftheenergylteralgorithmisshowninblueinFig.3.33d.Theattopregionofthelterfollowingeachpulseistherecordedenergyofeachpulse.Figure3.35showsthedistributionofsecondpulseenergiesfrome14057.0200040006000800005001000150020002500InternalPair FormationInternalConversionSecond Pulse Energy (Arb. Units)67ZnIsomerCountsFigure3.35:Energyspectrumdisplayingtheenergyofthesecondconstituentpulseofthedouble-pulsesignalsrecordedine14057.Thesamefeaturespresentinthesecond-pulseenergyspectrumfrome14039,shown72inFig.3.28b,arepresentinFig.3.35.TheenergyresolutionoftheplasticscintillatorwasexpectedtobefarworsethanthatoftheGeDSSDandexperimentbearsthisout.Thepeakscorrespondingtotheinternalpairformationandinternalconversionprocessesofthe0+
2!0+
1E0transitionin68Niarebroadfeatures.Atthelowenergyregionofthespectrumthe67Znisomerisalsovisible.However,thedouble-pulsetechniquewiththeplasticscintillatorisprimarilyusefulasaselectiveidenticationofthe0+
2!0+
1E0transitionin68Ni.3.7SegmentedGermaniumArray(SeGA)
TheSegmentedGermaniumArray(SeGA)[47]wasusedforthedetectionofprompt,iso-meric,and-delayedraysforbothexperimentse14039ande14057.Inbothexperiments,SeGAwasusedina\beta-SeGA"conguration,whichconsistsoftwoconcentricringsof8detectorseachplacedataradialdistanceof8.65cmfromthecenteroftheimplantationdetector.ToallowplacementoftheGeDSSDduringe14039andtheLaBr3arrayduringe14057,aspacerwasaddedtoexpandthedistancebetweenthedetectorfacesto11.5cm.3.7.1SeGAInstrumentationandTriggeringConditions
Inbothexperiments,thecentralcontactofeachofthesixteenSeGAdetectorswasinstru-mentedbythe14-bit,250-MSPSdigitizers.The32individualsegmentsignalsformtheSeGAGecrystalswerenotinstrumented.TheSeGAcentralcontactswereleftinafree-runningtriggeringmodewhere,uponenergydepositionabovethreshold,datawascollected.TraceswerenotrecordedforSeGA.733.7.2SeGAEnergyCalibrations
SeGAwascalibratedroughlyeverythreehoursthroughouttheexperimentusingroomback-groundlines.TheSeGAenergycalibrationislinearandperformedusingfourbackgroundlineswithenergiesof351.932(2)keVfrom214Pbdecay[48],609.320(5)from214Bidecay[48],1460.822(6)from40Kdecay[49],and2614.51(1)keVfrom208Tldecay[50].Theenergycal-ibrationresidualsforeachofthe16detectorsforarepresentativeruntakenduringe14039arepresentedinFig.3.36.Theresidualsforall16detectorscombinedareshowninFig.3.37aforthatsamerun,whileFig.3.37bshowstheresidualsforall16detectorsforallrunsoverthedurationofe14039.2000100000001000100010002000200020003000SeGAEnergy (keV)SeGAEnergy (keV)SeGAEnergy (keV)SeGAEnergy (keV)0.5
0.5
0.5
0.5-0.5
-0.5
-0.5
-0.50000Residual (keV)Residual (keV)Residual (keV)Residual (keV)SeGA1SeGA2SeGA3SeGA4SeGA4SeGA5SeGA6SeGA7SeGA8SeGA9SeGA10SeGA11SeGA13SeGA14SeGA15SeGA16Figure3.36:SeGAenergycalibrationresidualsforeachofthe16individualdetectorsfromarepresentativeruntakenduringexperimente14039.Theresidualsobtainedfromthedatafromalldetectorsinallrunsarebelow0.1keVandaredistributedrandomly,suggestingnosystematicorenergy-dependentproblemswiththecalibrationprocedure.Basedonthesecalibrationresiduals,a0.2-keVuncertaintywas74010002000-0.4-0.200.20.40100020003000SeGAEnergy (keV)SeGAEnergy (keV)Residual (keV)Single RunTotalAll RunsTotala)b)Figure3.37:(a)SeGAenergycalibrationresidualsforall16detectorscombinedoverthesamerepresentativerunusedinFig.3.36.(b)SeGAenergycalibrationresidualsforall16detectorscombinedforallrunsoverthedurationofe14039.
ascribedtoall-rayenergiesdeducedfromSeGAdatacollectedine14039.Thesame-rayenergycalibrationprocedurewasusedfore14057,yieldingsimilarresults.Asimilar0.2-keVenergycalibrationuncertaintywasappliedto-raysdetectedinSeGAine14057.
3.7.3SeGAAbsoluteEciencyCalibrations
Extractionofbothrelativeandabsolute-rayintensitiesrequiresanabsoluteeciencycalibrationbeperformedonSeGA.Theuseofthickimplantationdetectorssuchasthepla-narGeDSSDandsegmentedplasticscintillatorprohibittheplacementofNISTcalibratedsourcesattheimplantposition.Therefore,datawastakenwithaNIST-calibratedmulti-componentstandardreferencematerial(SRM)comprisedof125Sb,154Eu,and155Eulocatedinwell-denedlocationsacrosstheexperimentalsetupandusedtobenchmarkaGEANT4simulation.ThersttestofthesimulationwasmatchingSeGAaloneinthestandard\betaSeGA"conguration.TheSRMwasplacedinawell-denedlocationbetweenthetworingsofSeGAdetectorsanddatawerecollectedfortwohours.TwelvelinesfromtheSRM,ranging75from42.8keVto1596.5keV,werettedandeciencieswerecalculatedandcorrectedfordetectordeadtime.WithDDAS,deadtimeisminimal(<2%forthisapplication)butwasincludedregardless.Thedead-timecorrectionwascalculatedfromthelive-timedatafromtheinternalscalers,whichkeeptrackoftheratioofacceptedtriggerstototaltriggersforeachchannelofDDAS.Inadditiontocorrectionsfordead-time,summingcorrectionsarerequiredformulti-linesourceswhereraysofinterestarepartof,orparallelto,a-raycascade.ThetreatmentofsummingcorrectionswasprescribedintheSRMdatasheetprovidedbyNIST.ThesummingcorrectionsappliedtotheeciencycalibrationsusingtheSRMareshowninTable3.4.Themagnitudeofthesecorrectionswasbelow5%relativeforall-rayenergies.Afterapplicationofdead-timeandsummingcorrections,theGEANT4simulationwasrunusingonemillionmonoenergetic,isotropically-emitted,raysforeachofthe12linesfromtheSRMandtheresultofthesimulationwascomparedtoexperiment.Thebestwaytovisualizethiscomparisonisaplotoftheratioofthesimulatedtodeducedeciencyasafunctionof-rayenergy.Ifthesimulationwereperfect,theratiowouldbeone.ResultsareshowninFig.3.38.TheagreementbetweensimulationandexperimentdemonstratesthatthesimulationcanmodelSeGA.However,thesimulationmustmatchtheSRMeciencydatatakenwiththefullcomplimentofdetectorsforbothe14039ande14057.Fore14039,thetransmissionofraysthroughtheplanarGeDSSDindicateswhetherornottheGeDSSDisbeingeectivelymodeledbythesimulation.Forthismeasurement,datawerecollectedwiththeSRMsourcepositioneddownstreamoftheplanarGeDSSDinawell-denedlocation.Thesimulationwasmodiedtore-positionSeGAandincludetheplanarGeDSSDandonemillionmonoenergetic,isotropically-emitted,raysweresimulatedforeachofthe12linesfromtheSRM.76Table3.4:SummingcorrectionsusedforabsoluteeciencycalibrationwithSRMsource.TotalecienciesatagivenenergyEaredenotedas[E]whilephoto-peakecienciesaredenotedasfEg.Thecorrectedeciencyisobtainedbydividingtheexperimentaleciencybythevalueofthesummingcorrection.Energy(keV)SummingCorrections42.81.086.61.0105.31.0123.11.0-0.072[248.0]-0.055[591.7]-0.019[692.4]-0.120[723.3]-0.049[756.9]-0.130[873.2]-0.201[1004.8]-0.010[1246.2]-0.401[1274.4]-0.021[1596.5]248.01.0-0.287[42.8]-0.455[123.1]-0.072[444.4]-0.022[582.0]-0.134[591.7]-0.015[612.2]-0.043[625.2]-0.022[676.6]-0.039[723.3]-0.613[756.9]-0.059[892.7]-0.022[904.1]-0.130[1246.2]591.71.0-0.297[42.8]-0.455[123.1]-0.178[248.0]-0.196[756.9]-0.800[1004.8]723.31.0-0.154[42.8]-0.243[123.1]-0.013[248.0]-0.014[625.2]-0.518[873.2]-0.465[996.4]873.2(1.0+0.024f248.0gf625.2g/f873.2g)(1.0-0.282[42.8]-0.455[123.1]-0.894[723.3])996.4(1.0-0.894[723.3])(1.0+0.507f123.1]gf873.2g/f996.4g1004.8(1.0+0.221f248.0]gf756.9g/f1004.8g)(1.0-0.282[42.8]-0.455[123.1]-0.217[591.7])1274.4(1.0+0.014f692.4]gf582.0g/f1274.4g)(1.0-0.281[42.8]-0.455[123.1])1596.5(1.0-0.281[42.8]-0.455[123.1])(1.0+5.568f873.2gf723.3g/f1596.5g+2.094f1004.8gf591.7g/f1596.5g+0.052f1118.5gf478.3g/f1596.5g+0.275f692.4gf904.1g/f1596.5g)1600120080040001.151.101.051.000.950.900.85Efficiency Ratio (Sim. / Exp.)Energy (keV)Figure3.38:Eciencyratios(Simulation/Experiment)forraysoftheSRMsourcewithSeGAinthe\beta-SeGA"conguration.77Duringtheanalysisofthedata,deadtimeandsummingcorrectionswereperformedinthesamemannerdescribedaboveforthe\beta-SeGA"congurationeciencyverication.Thesimulatedeciencywasthencomparedtothededucedeciencyusingtheratiosofsimulatedeciencytoexperimentaleciencyateachmeasuredenergy.ResultsareshowninFig.3.39.1600120080040001.151.101.051.000.950.900.85Efficiency Ratio (Sim. / Exp.)Energy (keV)Figure3.39:Eciencyratios(Simulation/Experiment)forraysoftheSRMsourceplaceddownstreamoftheplanarGeDSSDwithSeGAinthenale14039experimentalconguration.Theagreementbetweensimulationandexperimentisexcellent,suggestingthatallde-tectorsusedintheexperimentarebeingcorrectlymodeledinthesimulation.Thesamebenchmarkingprocedurewasusedforthee14057simulationtoinvestigatetheabilityofthesimulationtomodelthePSPMT,siliconDSSD,andbeampipe.Similartothee14039results,theagreementbetweenthesimulationandcollecteddata,showninFig.3.40,isexcellent.Thevalidatedsimulationswereusedtoobtaintheabsolute-rayecienciesfortherespectiveexperimentaldetectorgeometries.Thebeamisdenedastravelinginthe+zdirection,thexandyproleofthebeamwasapproximatedasatwo-dimensionalGaussian781600120080040001.151.101.051.000.950.900.85Efficiency Ratio (Sim. / Exp.)Energy (keV)Figure3.40:Eciencyratios(Simulation/Experiment)forraysoftheSRMsourceplacedupstreamofthesegmentedplasticscintillatorwithSeGAinthenale14057experimentalconguration.
withwidthsdeterminedfromthexandyproleoftheimplantdistributionsshowninFigs.3.9and3.31fore14039ande14057,respectively.IondepthdistributionsweretakenfromFig.3.2fore14039andfromFig.3.4fore14057.Theeciencysimulationwasrunforonemillionmonoenergeticisotropically-emittedgammaraysfor12dierentenergiesspanninganenergyrangeof50to8000keVforeachisotopeineachexperiment.Thesimulated-raydetectioneciencesfor-raysthatwouldberecordedinSeGAemanatingfromimplantedA=68nucleiduringe14039(blacksquares)ande14057(redcircles)isshowninFig.3.41.ThesimulationresultsinFig.3.41areplottedonlog-logscaletofacilitateeasyttingofasixthorderpolynomialusedforinterpolation.The-raydetectioneciencyinSeGAforA=68nucleiine14039canbecalculatedusingafunctionoftheformE[E](%)=10010[a(x)6+b(x)5+c(x)4+d(x)3+e(x)2+f(x)+g];(3.10)wherex=log10(E)andEisthe-rayenergyinkeV.Thevaluesusedforparametersa79Log[Energy (keV)]101.52.02.53.03.54.0Log[SeGAEfficiency]10-2.0-1.5-1.0e14039
e14057Figure3.41:SimulatedSeGA-raydetectionecienciesforA=68nucleiinexperimentse14039(blacksquares)ande14057(redcircles).ThedepthofionsinweretakenfromFigs.3.2and3.4fore14039ande14057,respectively,whiletheimplantxandydistributionsarefromFigs.3.9and3.31fore14039ande14057,respectively.Symbolsrepresentsimu-lationresultswhilelinesaresixth-orderpolynomialtstothesimulationresultsusedforinterpolation.
throughgarepresentedinTable3.5forbothe14039ande14057.Table3.5:ValuesusedinEq.3.10toparameterizethe-raydetectioneciencyofSeGAfore14039and14057.ParameterValueine14039Valueine14057a-0.22728380.09806254b4.2325952-1.49857809c-32.81203508.88693213d135.3245904-25.1129315e-312.902420331.55816037f383.9575499-7.70484349g-196.0154575-11.50983194A5%uncertaintywasassignedtoallecienciesuniformlyacrossenergyforbothex-perimentsbasedonthecomparisonoftheSRMdatawithsimulationinFigs.3.39and3.40.SincetheimplantdistributionsforA=68andA=70nucleiaresimilar,thesimulated-raydetectionecienciesinSeGAarealsosimilardieringwithintheascribed5%error.803.8LanthanumBromideArray
ThePSPMTwassurroundedwithanarrayoftenSaintGobainBrilLanCeR380LanthunumBromide(LaBr3)detectorsarrangedasdescribedinSection3.3.Thecrystalsofeachdetectorwerecylindricalwithadiameterof38mmandalengthof38mm,andeachcrystalwascoupledtoaHamamatsuR6231photomultipliertube(PMT).
3.8.1InstrumentationandTriggeringConditions
AlltenLaBr3detectorsinthearraywereinstrumentedusingthe12-bit,500-MSPSdigitizers.Theywereoperatedina\free-running"triggermodedescribedinSection3.4.1.Tracecapturewasenabledandtraceswere2slongwitha400nsdelay.ThedigitalCFD,discussedinSection3.4.3,wasemployedtoextractprecisiontimingbelowthenative2nsclockperiodofthedigitizer.
3.8.2LaBr3EnergyCalibrationsEnergycalibrationsfortheLaBr3detectorswereperformedapproximatelyevery12to15hoursthroughouttheexperiment.However,thepoorenergyresolutionofLaBr3comparedtoGe,coupledwiththelargeinternalactivityfrom138La,precludesusingthesameroombackgroundlinesfromtheSeGAcalibrationprocedure.Instead,theenergycalibrationwasperformedusingvewell-knownraysfromthedecayofvariousimplantedisotopes.The161.8(2)-keVand184.3(2)-keVtransitionsin68Co,the594.3(2)-keVtransitionin69Ni,the1077.4(2)-keVtransitionin68Zn,andthe2032.9(2)-keVtransitionin68NiwereusedtocalibratetheLaBr3detectors.Theenergycalibrationtfunctionwasasecond-orderpolynomial,anddatafromsixsequentialrunsweregroupedtogetherforthet.Figure3.4281showstheLaBr3energycalibrationresidualsforarepresentativegroupofsixruns.LaBr1310
10
1010
10
10000Residual (keV)Residual (keV)Residual (keV)20
20
20-20200010000000100010001000200020002000LaBr3Energy (keV)LaBr23LaBr33LaBr43LaBr53LaBr63LaBr73LaBr83LaBr93LaBr103LaBrEnergy (keV)3LaBrEnergy (keV)3LaBrEnergy (keV)3Figure3.42:EnergycalibrationresidualsfortheindividualtenLaBr3detectorsoverarepresentativegroupofsixrunsduringe14057.Mostoftheresidualsarebelow5keV.Detector7hadaverynonlinearcalibration,yieldinglargerresidualsanderrorbars.Theresidualsfromatoftheenergyspectrumofall10detectorscombinedoverthesamegroupofsixrunsareshowninFig.3.43a.Theresidualsforall10detectorsforallrunsoverthedurationofe14057combinedarepresentedinFig.3.43bshows010002000-505010002000LaBrEnergy (keV)3Residual (keV)Single Run GroupTotalAll RunsTotala)b)LaBrEnergy (keV)3Figure3.43:(a)LaBr3energycalibrationresidualsforall10detectorscombinedoverthesamerepresentativegroupofrunsusedinFig.3.42.(b)SeGAenergycalibrationresidualsforall16detectorscombinedforallrunsoverthedurationofe14039.82Basedonthesecalibrationresiduals,a5-keVuncertaintywasascribedtoall-rayenergiesmeasuredinLaBr3ine14057.3.8.3AbsoluteLaBr3EciencyCalibrationsLiketheenergycalibrations,theLaBr3detectoreciencycalibrationswerealsoperformedrelativetoSeGA.Thesameve161.8(2)-,184.3(2)-,594.3(2)-,1077.4(2)-,and2032.9(2)-keVtransitonsusedintheenergycalibrationandanadditional1259.0-keVtransitionfrom70Niwereused.Theratioofpeakareas(LaBr3/SeGA)forthesesixrays,plottedasafunctionof-rayenergy,isshowninFig.3.44.050010001500200025000.20.40.60.81.01.2Ratio = (-1.00513x10)E-103g+ (5.50325x10)E- (1.05167x10)E+ 1.1406-72-3ggEfficiency Ratio (LaBr/ SeGA)3Energy (keV)Figure3.44:Ratioof-rayeciencies(LaBr3/SeGA)asafunctionofenergy.Athird-orderpolynomialttotheseratioswasusedtointerpolatebetweenthe161-to2033-keVenergyregion.TheinterpolatedratioatagivenenergymultipliedbythesimulatedSeGAeciencyatthatenergywasusedfortheLaBr3eciency.833.9LevelLifetimeMeasurementTechniques
Levellifetimemeasurementsinthisworkwereperformedusingthelifetimemeasurementtechnique.Thelifetimemeasurementtechniqueinvolvesmeasuringthetimedierencebetweenthedetectionofthedecayandtherayemittedbythedecayofanisomericstatepopulatedbythedecay.Inthepresentwork,decaysweredetectedinthesegmentedplasticscintillator,describedinSection3.6,andraysweredetectedintheLaBr3detectors.Bothdetectorsystemshaveintrinsictimeresolutionsofhundredsofpsandthusthetechniquesdescribedhereinaresensitivetohalflivesof100pstohundredsofns.Thedistributionoftime-dierencesbetweenraysandtheirprecedingdecaysisaconvolutionoftheGaussiandetectorresponseswiththeexponentialdecayoftheisomericstate.Thedetectortimingresponseisenergydependent,inboththesegmentedplasticscintillatorandLaBr3detectors.Typicallythin(˘3mm)scintillatorsarechosentomitigatetheenergydependenceinthetimeandenergyresponse[35].However,inthepresentworkathick(10mm)plasticscintillatorwasusedtoenhance-decayelectrondetection.Thethickscintillatorampliestheenergydependenceinthetimeresponseandintroducesanadditionaldependenceonthedepthofinteractionwithinthescintillator[51].Thenexttwosectionsdescribethetechniquesdevelopedtoproperlycalibratethetime-responseofthedetectionsystem.3.9.1TimeWalkCorrections
Therststepintheanalysisoftimingexperimentsinvolvescorrectingthetimeresponseofeachdetectorforthepulse-amplitudedependenttimewalk.Thoughthedeploymentofa84digitalConstantFractionDiscriminator(CFD)[41]minimizesthetimewalk,itstillpersistsatthehundredsofpicosecondslevelacrossthedynamicrangeandmustberemoved.Thewalkcorrectiontechniquemadeuseofa60Cosource,whichdecaysmainly(99.9%branch)tothe2505.7-keVstatein60Ni.Thisstatethenyieldsacascadeoftworayswithenergiesof1173.2and1332.5keV.The0.9pshalf-lifeoftheintermediate1332.5-keVstatein60Niisbelowthesensitivityofthetechniquesinthepresentworkandcanbeconsideredasprompt.Datawerecollectedwiththefullexperimentalarrayandthetime-dierencebetweentheLaBr3detectorsandtheplasticscintillatordynodewascalculatedforeacheventandstoredwiththeLaBr3andplasticscintillatorenergyinten,three-dimensionalhistograms;oneforeachLaBr3detector.Apreliminarytime-dierencecorrectionwasappliedtothetimedierencesuniformlyacrosstheLaBr3andplasticscintillatordynodedynamicrangestoaccountfordierencesincablelengthsanddigitizersynchronizationforeachLaBr3detector.Anarticialtime-dierenceosetof1000nswasintroducedtoavoidnegativetimedierences.Next,theplasticscintillatortimeresponsewascalibrated.Inthisprocess,atwo-dimensionalprojectionofeachthree-dimensionalhistogramdescribedabovewastakenoverthe1173.2-and1332.5-keVphotopeakenergyregionineachLaBr3detector.ThisprovidesaregionintheLaBr3detectorswithlowtimewalkvariability,highstatistics,andgoodtimeresolutionforinvestigatingthedynodetimewalk.Eachprojectionshowedthedynodeamplitudevs.timedierencebetweeneachLaBr3detectorandthedynode.Thesumofalltentwo-dimensionalhistogramsispresentedinFig.3.45a.ForeachdynodeamplitudebininFig.3.45a,thecentroidoftheprojectionontothe8510102103996998100010021004010020030040001101021Centroid (ns)999.810001000.2100200300400500a)a)d)c)b)Time Difference (ns)DynodeAmplitude (ADC Units)DynodeAmplitude (ADC Units)Figure3.45:(a)Two-dimensionalhistogramofthedynodesignalamplitudeplottedagainsttheLaBr3-PSMPTdynodetimedierenceforasingleLaBr3detectorgatedoneitherthe1173.2-or1332.5-keVphotopeakinthatdetector.(b)Plotofcentroidposition,extractedfromttingtheprojectionofeachbinina)ontothetime-dierenceaxis.Ahigh-orderpolynomial,showninred,wasusedforinterpolationbetweenthedatatoextractthetimewalkasafunctionofdynodesignalamplitude.
time-dierenceaxis,obtainedfromaGaussiant,isdisplayedinFig.3.45b.Thesecentroidvalueswerettedwithahigh-orderpolynomial,shownasaredlineinFig.3.45b,toextractthewalkcorrectionasafunctionofthedynodesignalamplitude.TheresultofthedynodewalkcorrectionisshowninFigs.3.45cand3.45d.Thecorrectedtwo-dimensionaldynodeamplitudevs.time-dierencespectrumisshownintheformer,whilethedynodewalk-correctedtime-dierencecentroidvaluesforeachbinofFig.3.45cis86presentedinthelatter.Thewalkcorrectionisvalidfordynode-amplituderangesof20to500ADCunits.Theresultingcentroidvaluesareallwithin10psofthe1000nsoset.ThenextstepfocusedoncorrectingtheindividualLaBr3detectorresponses.ToobtainthetimewalkasafunctionofLaBr3detectorenergy,eachbinofthedynodewalk-correctedtwo-dimensionalLaBr3energyvs.time-dierencehistogram,showninFig.3.46aforoneofthetenLaBr3detectors,wasprojectedontothetime-dierenceaxisandttedwithaGaussian.SpecicregionscorrespondingtotheComptonedgesandbackscatterpeaksofboththe1173.2-and1332.5-keVphotopeakswereremovedfromthespectrumshowninFig.3.46aduetoanomalousbehaviorobservedinthetimeresponseovertheseregions.ThecentroidpositionextractedfromthetoftheprojectionofeachLaBr3detectorenergybinshowninFig.3.46aispresentedinFig.3.46b.Thesecentroidvalueswerettedwithahigh-orderpolynomial,shownasaredlineinFig.3.46b,toextractthewalkcorrectionasafunctionofLaBr3energy.TheresultoftheLaBr3walkcorrectionisshowninFigs.3.46cand3.46d.ThewalkcorrectionisvalidforLaBr3energyrangesof30to1400keVandtheresultingcentroidvaluesareallwithin50psofthe1000nsosetacrosstheentiredynodedynamicrange.871101021039951000100505001000110102Centroid (ns)999.510001000.5Time Difference (ns)05001000LaBrEnergy (keV)3LaBrEnergy (keV)3a)d)c)b)Figure3.46:(a)Two-dimensionalhistogramoftheLaBr3energyplottedagainsttheLaBr3-PSMPTdynodetimedierenceforasingleLaBr3detectorgatedondynodeamplitudesbetween20and500ADCunits.(b)PlotofcentroidpositionforeachLaBr3energybin,extractedfromttingtheprojectionofeachbinin(a)ontothetime-dierenceaxis.Ahighorderpolynomial,showninred,wasusedextractthetimewalkasafunctionofLaBr3energy.
3.9.2DepthofInteractionCorrections
Withthewalkcorrectionprocesscomplete,attentionfocusedonaccountingforthedierenceinplasticscintillatortimeresolutionbetweentheexternalsourcedataandtheinternaldecaydataduetodepthofinteraction(DOI)eects.Thelifetimeextractiontechnique,presentedlaterinthissection,utilizedthe60Cosourcedatatomodelthedetectorresponse.Therefore,anunderstandingofthedierenceindetectorresponsesbetweentheexperimentalandsource88dataisrequired.DOIeectsarestudiedheavilyinthemedicalimagingcommunityandcanaltertimeresolutionssignicantly[51].ToquantifytheDOIeectsinthepresentsystem,thedecayofthe1077.4-keVstatein68Znwasstudied.Populatedbythedecayof68Cu,thisstatein68Zndecaystothegroundstatewithahalf-lifeof1.61ps[22].The1.61pshalf-lifeisbelowthesensitivityoftimingmethodspresentedhereandthereforewasconsideredprompt.TheLaBr3energyspectrumforalltendetectors,gatedondynodeamplitudesof>60and<500ADCunits,intheregionaround1077.4keVisshowninFig.3.47.Thepeakregionspansfrom1064to1094keV(solidredlines)whileabackgroundregionwaschosenfrom1110to1140keV(dashedredlines).LaBrEnergy (keV)31000105011001150Counts / 2 keV0100020003000Figure3.47:(a)LaBr3energyspectrumforalltendetectors,gatedondynodeamplitudesof>60and<500ADCunits,intheregionaround1077.4keV.Thepeakandbackgroundregionsusedforthisanalysisaredenotedwithredsolidandreddashedlines,respectively.Thesamepeakandbackgroundregionswereusedtogatethetwo-dimensionaldynodesig-nalamplitudevs.time-dierencespectrumforboththeexperimentalandsourcedata.Inthecaseoftheexperimentaldata,thebackground-gatedtwo-dimensionalspectrumwasscaledtomatchthebackgroundcountsinthepeakregionandsubtractedfromthetwo-dimensional89spectruminthepeakregion.Thisremovesanyresponsefrompotentiallynon-promptcontri-butionsfromComptonscatteringofhigher-energytransitions.Thebackground-subtractedtwo-dimensionaldynodesignalamplitudevs.time-dierencespectrumfortheexperimentaldatainthepeakregionshowninFig.3.47isshowninFig.3.48a.Thetwo-dimensionalspectrumforthesourcedataoverthesameLaBr3energyregionasFig.3.48aisshowninFig.3.48b.Time Difference (ns)9961000DynodeAmplitude (ADC Units)10020030040050010001004110102996Time Difference (ns)b)a)Figure3.48:(a)Background-subtractedtwo-dimensionaldynodesignalamplitudevs.time-dierencespectrumforthe1077.4-keVpeakintheexperimentaldata.(b)Thetwo-dimensionaldynodesignalamplitudevs.time-dierencespectrumforthe60Cosourcemea-surementsforthesameenergygateasa).Thetimeresolutionasafunctionofdynodesignalamplitudewasdeterminedforboththeexperimentalandsourcedatabyprojectingeachbinofthetwo-dimensionalspectrashowninFigs.3.48aand3.48b,respectively,ontothetime-dierenceaxisandttingaGaussianfunctiontoeachprojection.The˙values(inns)obtainedfromtheseprojectiontsareshownasafunctionofdynodesignalamplitudeinFig.3.49a.Thedatafortheexperimentaltimeresponseareshownasblacksquareswhilethesourceresultsareshownasbluecircles.Eachofthetworesponsecurveswerettedwithapowerlaw,whichisdrawn90initsrespectivecolorinFig.3.49a.1002003004005000.40.60.81.01.20.20.30.40.5b)a)Sigma Ratio (Experiment / Source)Sigma (ns)ExperimentSource DataFigure3.49:(a)Sigma(inns)asafunctionofdynodesignalamplitudeshowninbluecirclesfortheexperimentaldataandasblacksquaresforthesourcedatapresentedinFigs.3.48aand3.48b,respectively.(b)Theratio(experiment/source)ofsigmavaluesfroma)asafunctionofdynodesignalamplitude.ThettothedatarepresentstheDOIcorrectionforthetimeresolution.TheratiooftheexperimentaldatatothesourcedataasafunctionofdynodesignalamplitudeisshowninFig.3.49b.Thedistributionofratioswasttedwithapowerlaw,whichisdrawnasasolidblacklinein3.49b.Thettotheratiosrepresentsthedynode-amplitude-dependentcorrectionfactorthatmustmultiplythesigmavalueforthesource91datainthemethoddescribedinthenextsection.
3.9.3NewAnalysisMethodforLifetimeTechniquesAsdemonstratedintheprevioussections,theuseofathickplasticscintillatorintroducesahostoffeaturesthatmustbeaccountedforintheanalysisforlifetimemeasurements.TheamplitudedependenceoftheplasticscintillatorresponseremovestheabilitytoaccuratelytthelifetimedatawiththeconvolutionofasingleGaussianresponseandanexponentialdecaycurve.Instead,theconvolutionofacontinuumofGaussianresponsefunctionswithanexponentialdecayweightedbythenumberofcountsateachenergyinthecontinuummustbeemployed.Inreality,thecontinuousdistributionsarediscretizedintobinsandthetechniquetodescribethedetectorsystemtimeresponse,R(t;t0;˝;Ep;E),canbesummarizedbyEq.(3.11).R(t;t0;˝;Ep;E)=sB(t)+nXi=1EFXEp=E0Li;Ep;EPEp;E[f(t;t0;i;Ep;E)g(t;t0;˝)](3.11)withf(t;t0;i;Ep;E)=Exp12(tt0)D(Ep)˙i(Ep;E)2andg(t;t0;˝)=Exp(tt0)˝92InEq.(3.11),B(t)representsthebackgroundunderneaththepeak.TypicallyB(t)issampledfromnearbyregionswithminimalspectralinterference.Inmostcases,B(t)isroughlyconstantovertheenergyrangeoneneedstosampleandthebackgroundscalefactor,s,isclosetoone.TheGaussianresponsefunction,f(t;t0;i;Ep;E),ischaracterizedbyacentroidt0andatimeresponsewidth˙i(Ep;E).Thevalueof˙i(Ep;E)foraparticularLaBr3detector,i,dependsonthephotopeakenergy,E,andtheplasticscintillatorenergy,Ep,hastobedeterminedforeachlifetimemeasurement.TheDOIcorrectionisrepresentedbyD(Ep).Thewalkcorrectionspresentedabovehaveremovedtheenergyanddetectordependenciesfromt0.Theexponentialdecayoftheexcitedstate,g(t;t0;˝),dependsonlyonthecentroid,t0,andthelifetime,˝,ofthedecayingstate.InEq.(3.11),g(t;t0;˝)isconvolvedwiththedetectorresponse,f(t;t0;i;Ep;E),foreachLaBr3detector,i,andplasticscintillatordynodeamplitude,Ep,ataspecicphotopeakenergyE.TheresultingconvolutionisscaledbytherelativecontributionofeachLaBr3detector,denotedasLi;Ep;E,andthedynodeamplitudedistribution,PEp;E,tocreatethetotalconvolution.Thelinearcombinationofconvolutionfunctionsdescribestheshapeofthetimedistri-butionforthedecayofaparticularstateofinterest.ThatdistributionfunctionissampledmanytimesusingMonteCarlomethodsandtheresultsarehistogrammed.Theresultinghistogramisscaledtothenumberofcountsinthepeakovertheregionofinterest,addedtothescaledbackground,sB(t),andcomparedwiththeexperimentaldata.A˜2minimizationisperformedusingtriallifetimesandtheresultisobtainedfromthetofa˜2distribution.933.9.4DemonstrationoftheTechniqueonaPromptTransition
Throughouttheremainderofthissectionthenewlifetimetechniqueisdemonstratedonthreedierentexcitedstates,allwithknownlifetimes.Therstofthesestatesisthe1077.4-keVstatein68Zn,whichwasusedtoobtaintheDOIcorrection.Thisisasimplecasebecause,withapromptdecay,thereisnoconvolutionandonlytheenergy-dependentGaussiandetectorresponseremains.Inparticular,thistestprobesourabilitytoreproducethetimespectrumwithnofreeparameters.TheLaBr3energyvs.timedierenceandvs.dynodeamplitudeareshowninFigs.3.50aand3.50b,respectively,forthesameLaBr3energyrangeasinFig.3.47.Thesame1064-to1094-keVpeakand1110-to1140-keVbackgroundregions,illustratedinFig.3.47,wereusedhereandareonceagaindepictedbyredsolidanddashedlines,respectively.Figures3.50cand3.50earetheprojectionofFig.3.50aontothetime-dierenceaxisforthepeakandbackgroundregions,respectively.Figure3.50crepresentsthetotaltime-dierencespectrum,whileFig.3.50eistheunscaledbackground,whichisB(t)fromEq.(3.11).Thescalefactor,s,wasobtainedbyttingtheone-dimensionalLaBr3energyspec-trumandcomparingtheintegratedcountsinthepeakovertheregionofinterestwithboththetotalnumberofcountsinthepeakregionandinthebackgroundregion.Forthiscase,s=1:05.Figures3.50dand3.50faretheprojectionofFig.3.50bontothedynodesignalamplitudeaxisforthepeakandbackgroundregions,respectively.ThedatainFig.3.50f,scaledappropriately,aresubtractedfromthedatainFig.3.50d.Thisprovidesthenaldynodeamplitudedistribution,showninFig.3.51,forthecountsunderthepeakintheregionofinterestandalsocorrespondstoPEp;EfromEq.(3.11).9410001050110005010015020025011502000010001000100101LaBEnergy (keV)3DynodeAmplitude (ADC Units)100200300400500Counts / 20ADC UnitsCounts / 50 ps12000600Counts / 20ADC UnitsTime Difference (ns)995100010051000100101Counts / 50 psc)d)
f)e)b)a)Figure3.50:(a)LaBr3energyvs.timedierenceand(b)vs.LaBr3energydynodeam-plitude,respectively,forthesameLaBr3energyrangeasinFig.3.47.Thesame1064-to1094-keVpeakand1110-to1140-keVbackgroundregionsillustratedinFig.3.47areshownagainbyredsolidanddashedlines,respectively.Panels(c)and(d)showtheprojectionsofa)andb)ontothetime-dierenceanddynodeamplitudeaxesrespectively,forthepeakregionbetweenthesolidredlines.Panels(e)and(f)showtheprojectionsof(a)and(b)ontothetime-dierenceanddynodeamplitudeaxesrespectively,forthebackgroundregionbetweenthedashedredlines.95DynodeAmplitude (ADC Units)100200300400500Counts / 20ADC Units050010001500Figure3.51:DynodesignalamplitudedistributionfortheLaBr3-dynodecoincidencesbetween1064and1094keV.ThisdistributionisobtainedbysubtractingthedatainFig.3.50f,scaledbys,fromFig.3.50d.Thecountsateachdynodeenergy,Ep,atthisspecicenergy,E,arePEp;EfromEq.(3.11).ThevaluesofLi;Ep;EwereobtainedfromtheindividualLaBr3coincidencespectra.Thecountsforeachdetectorforthebackgroundenergyregion,scaledbys,aresubtractedfromthecountsofeachrespectivedetectorinthepeakenergyregion.Sigmavalues,˙i(Ep;E),wereobtainedfromthe60Cosourcedataasafunctionofdynodesignalamplitude,EpforthespecicLaBr3energyregion,EinthesamemethoddescribedabovetoobtaintheplotsshowninFig.3.49a.TheDOIcorrection,D(Ep),showninFig.3.49b,wasthenapplied.Withthis,allquantitiesneededtotthedatahavebeenextractedandtheresultsoftheprocedureforthe1077.4-keVstatein68ZnareshowninFig.3.52.InFig.3.52,thetotaltime-dierencespectrumforthe1064-to1094-keVLaBr3energyregionisshowninblack.ThisisthesamespectrumthatisshowninFig.3.50c.Thescaledbackgroundtime-dierencespectrumoverthe1110-to1140-keVLaBr3energyregionisshowninblue.Thetotaltofthedetectorresponseforthecountsunderthepeakis96Time Difference (ns)99510001005110102103104Counts / 100 psDataTotal FitBackgroundConvolutionFigure3.52:Resultsofthettingtechniqueforthe1077.4-keVstatein68Zn.Thetotaltime-dierencespectrumforthe1064-to1094-keVLaBr3energyregion,alsoshowninFig.3.50c,isshowninblack.Thescaledbackgroundtime-dierencespectrumoverthe1110-to1140-keVLaBr3energyregionisshowninblue,whilethetotaltofthedetectorresponseforthecountsunderthepeakisshowninredandthetotaltisshownincyan.showninredandthetotaltisshownincyan.Thistestdemonstratestheabilitytocompletelydescribethetimeresponseofthedetectorsystem.Thestochasticbackgroundisaccountedforbythescaledbackgroundcontributionandthemethodtakesintoaccountthevarioushigher-orderamplitudedependentdetectorresponseeectstoreproducetheexperimentalspectrumtoahighdegree.3.9.5BenchmarkingtheTechniqueonaTwoExcitedStateswithKnownLifetimesWiththelifetime-extractiontechniquedemonstratedforaprompttransition,eortsfocusedtowardsdeducinglifetimesofexcitedstateswithknownlifetimes.Therstofthesewasthe915.3-keVstatein69Ni.Thisstatehasapreviouslymeasuredhalf-lifeof120(34)psandthereisstrong,directfeedingfollowingthedecayof69Co[52].Thestateisdepopulated97exclusivelybya594.3-keVray.TheLaBr3spectrumcoincidentwithcountsinthedynodebetween60and500ADCunitsintheregionaround594.3-keVisshowninFig.3.53.Thepeakandbackgroundenergyregionsofinterestaredenotedwithsolidanddashedredlines,respectively.50055060065070001000200030004000LaBrEnergy (keV)3Counts / 2 keVFigure3.53:LaBr3energyspectrumforalltendetectors,gatedondynodeamplitudesof>60and<500ADCunits,intheregionaround594.3keV.Thepeakandbackgroundregionsusedfortheanalysisaredenotedwithredsolidandreddashedlines,respectively.Thesameprocedureusedforthe68Znanalysisforobtainingthepeak-andbackground-gatedtime-dierenceanddynodedistributionspectra,analogoustothoseinFig.3.50,wasusedhere.Fromthoseresultsthealongwiththecalculatedbackgroundscalefactor,s,thedynodeamplitudedistributionforthecountsinthepeak,analogoustoFig.3.51,wasobtained.ThetotaldetectorresponsefunctiondescribedinEq.(3.11)wasconstructedforfourteentrialhalf-livesandthe˜2betweenR(t;t0;˝;E;Ep)andtheexperimentaldatawascalcu-latedforeachtrialhalf-life.Thedistributionof˜2valuesasblacksquaresforthesetoftrialhalf-livesisshowninFig.3.54.Asecondorderpolynomial,presentedin(3.12),wasusedto98tthe˜2distributionandisshownasasolidredlineinFig.3.54.˜2=a˝2+b˝+c(3.12)260280300320340120130140150Half-Life (ps)c2Figure3.54:Distributionof˜2valuesobtainedfromacomparisonofthetotalt,R(t;t0;˝;E;Ep),andtheexperimentaldata,shownascyanandblackinFig.3.55,respec-tively,forfourteenhalf-lifevaluesequallydistributedabouttheminimum.Thedistributionistwithasecondorderpolynomialshowninred.Thelocationoftheminimumrepre-sentsthehalf-lifeofthestateandthesecondderivativeofthetistheerroronthatvalue.Ahalf-lifeof135(26)psisobtainedforthe915.3-keVstatein69Niwhichagreeswiththepreviouslymeasuredvalueof120(34)ps[53].Thetwasusedtoextractthehalf-lifeanditserrorfromthe˜2distributionusingEq.(3.13)andEq.(3.14),respectively[54].˝=b2a(3.13)˙2˝=22˜2˝21(3.14)Avalueof135(26)pswasobtainedforthe915.3-keVstatein69Ni,whichagreeswiththepreviouslymeasuredvalueof120(34)ps[53].Thestatisticalerrorwasdeterminedfrom99thehalf-lifevaluesone˜2unitfromtheminimum.Systematicerrorswereinvestigatedbyvaryingquantitiessuchastheratioofcountsinthepeaktocountsinthebackground,thecentroidoftheunderlyingGaussiancomponentoftheconvolution,andthemagnitudeoftheDOIcorrection.Allerrorswereaddedinquadrature.Thebesttresultforthe915.3-keVstatein69NiispresentedinFig.3.55.99510001005110102103104Time Difference (ns)Counts / 100 psDataTotal FitBackgroundConvolutionFigure3.55:Resultsofthettingtechniqueforthe915.3-keVstatein69Ni.Thetotaltime-dierencespectrumforthe574-to614-keVLaBr3energyregionisshowninblack.Thescaledbackgroundtime-dierencespectrumoverthe620-to660-keVLaBr3energyregionisshowninblue,whilethetotaltofthedetectorresponseforthecountsunderthepeakisshowninredandthetotaltisshownincyan.Thetotaltime-dierencespectrumforthe574-to614-keVLaBr3energyregionisshowninblack.Thescaledbackgroundtime-dierencespectrumoverthe620-to660-keVLaBr3energyregionisshowninblue,whilethebesttconvolutionforthecountsunderthepeakisshowninredandtheresultingtotalbest-ttothedataisshownincyan.Onceagain,thetechniquedoesagoodjobofreproducingallthefeaturesofthedata.Thesecondstateusedtobenchmarkthetechniqueisthe2677-keVstatein70Ni.Thisstatehasapreviouslymeasuredhalf-lifeof1.05(3)ns[53].TheLaBr3spectrumcoincidentwithcountsinthedynodebetween60and500ADCunitsintheregionaround448.5-keV100isshowninFig.3.56.Thepeakandbackgroundenergyregionsofinterestaredenotedwithsolidanddashedredlines,respectively.Forthisregion,thebackgroundmustbesampledbelowthepeaktoavoidanycontaminationfromthe478-keVtransitionin68Ni.3504004505000100200300LaBrEnergy (keV)3Counts / 2 keVFigure3.56:LaBr3energyspectrumforalltendetectors,gatedondynodeamplitudesof>60and<500ADCunits,intheregionaround448.5keV.Thepeakandbackgroundregionsusedfortheanalysisaredenotedwithredsolidandreddashedlines,respectively.Theanalysisforthe2677-keV6+
1statein70Ni,whichdecaysbyemittinga448.5-keV-ray,isidenticaltothetechniquesdescribedforthe915.3-keVstatein69Ni.Theresulting˜2distributionforthefourteentrialhalflivesdistributedevenlyabouttheminimumispresentedinFig.3.57.Thesamettingprocedureforthe˜2distributionusingtheEq.(3.12)wascarriedoutandtheresultisshownasasolidredlineinFig.3.57.Fromthetofthe˜2distributioninFig.3.57andEqs.(3.13)and(3.14),avalueof1.04(6)nswasobtainedforthehalf-lifeofthe2677-keVstatein70Ni.Thestatisticalerrorwasdeterminedfromthehalf-lifevaluesone˜2unitfromtheminimum.Systematicerrorswereinvestigatedbyvaryingquantitiessuchastheratioofcountsinthepeaktocountsinthebackground,thecentroidoftheunderlyingGaussiancomponentoftheconvolution,and1013234363840420.90.971.041.111.18Half-Life (ns)c2Figure3.57:Distributionof˜2valuesobtainedfromacomparisonofthetotaltandtheexperimentaldata,shownascyanandblackinFig.3.55,respectively,forfourteenhalf-lifevaluesequallydistributedabouttheminimum.Thedistributionistwithasecondorderpolynomialshowninredresultinginalifetimeof1.04(6)nsforthe2677-keVstatein70Ni.themagnitudeoftheDOIcorrection.Allerrorswereaddedinquadrature.Theresultagreesverywellwiththepreviouslymeasuredvalueof1.05(3)ns[53].Thebesttresultforthe2677-keVstatein70NiispresentedinFig.3.58.Thetotaltime-dierencespectrumforthe434-to462-keVLaBr3energyregionisshowninblack.Thescaledbackgroundtime-dierencespectrumoverthe396-to424-keVLaBr3energyregionisshowninblue,whilethebesttconvolutionforthecountsunderthepeakisshowninredandtheresultingtotalbest-ttothedataisshownincyan.Onceagain,thetechniquedoesagoodjobofreproducingallthefeaturesofthedata.102Time Difference (ns)995100010051010Counts / 200 ps110100DataTotal FitBackgroundConvolutionFigure3.58:Resultsofthettingtechniqueforthe2677-keVstatein70Ni.Thetotaltime-dierencespectrumforthe396-to424-keVLaBr3energyregionisshowninblack.Thescaledbackgroundtime-dierencespectrumoverthe434-to462-keVLaBr3energyregionisshowninblue,whilethetotaltofthedetectorresponseforthecountsunderthepeakisshowninredandthetotaltisshownincyan.103Chapter4
ExperimentalResults
Inthischapter,thefullanalysisofthedecaysof68;70Coispresented.Eachsectionbeginsbysummarizingtheresultsofpriorexperimentalinvestigationsandconcludeswiththedecayschemesobtainedfromthepresentwork.Allspectraandrelevantanalyses,requiredtoobtainthenalresults,arepresentedanddescribedindetail.4.1Decayof68Co4.1.1DecayoftheLong-Lived68CoIsomerThelow-energylevelschemeof68Niwasstudiedfollowingthe-decayofthelow-spinisomerof68Co[12],selectivelypopulatedthroughthedecayof68Fe.Severalpriorexperimentsfocusedon68Nihavebeenperformed,andassuch,afairamountwaspreviouslyknownaboutthelow-energylevelschemeof68Ni.Morespecically,thecharacterizationofthethreelow-lying0+stateshasbeenofparamountimportanceforunderstandingtheevolutionofnuclearstructureintheregion.Themostrecentwork,describedinRef.[21],studiedthedecayofthelow-spinisomerof68Cointo68NiandyieldedthedecayschemeshowninFig.4.1.10468NiE (keV)JpI(%)!logft68Co= (1,2,3)+Jp+-bb--< 97.4 %,-n > 2.6 %t= 1.6(3) s
Q- = 11.54(15) MeV1/2b0160420332511274228473147330134054026416455145774
5549
31191603.62033.0478.1709.61139.02742.6814.2271.71114.41114.41268.2662.51514.52420.84027.01421.64161.93480.73515.63741.20+0+2+0+2+5-4+(3)-(4)+(2)+(2)+(4)-<422(3)18(4)10(2)2(1)2(1)1(1)8(2)4(1)1(1)2(1)
2(1)
2(1)8.8(1)9.6(5)6.2(1)6.3(1)9.1(2)6.9(2)9.3(2)6.1(1)6.4(2)6.5(3)6.1(2)
6.2(2)
7.0(3)< 15 ns0.31(5) ps270(5) ns0.86(5) msFigure4.1:Decayscheme,adaptedfromRef.[21],forthedecayofthelow-spin68Coiso-merpopulatingstatesin68Nirepresentingtheextentofknowledgepriortothepresentwork.Otherlow-energylevelsin68Ni,notshownhere,areknownfromreactionstudiesanddecayspectroscopyofthehigh-spin68Coisomer.Threespinandparityassignmentsof(1;+;2;3+)havebeenproposedforthelow-spin68CoisomerbyRefs.[12,21,55].The1.6(3)shalf-lifecomesfromRef.[12],asdoesthe<15nslimitonthehalf-lifeofthe2511-keV0+
3state.A-delayedneutronbranchof>2.6%wasreportedbyRef.[21].The-decayQ-valuewastakenfromRef.[56].Alllogftvaluesand-decayfeedingintensitiesweretakenfromRef.[21].Thehalf-livesof270(5)nsforthe1604-keV0+
2state,0.31(5)psforthe2033-keV2+
1,and0.86(5)msforthe2847-keV5stateweretakenfromRef.[22].105ThedecayschemeinFig.4.1representstheextentofexistingknowledgeofthelow-energylevelschemeof68Nipopulatedbythedecayofthelong-lived,low-spin68Coisomerpriortothepresentwork.Therstexcitedstatein68Niisthe0+
2state,originallyplacedat1770(30)keV,andwasdiscoveredusingthe70Zn(14C,16O)68Nitransferreactionandassigneda0+spinandparityfromangulardistributions[17].Asubsequentexperimentdeducedahalf-lifeof270(5)nsforthe0+
2[44].Morerecently,theworkofRef.[18]utilizedthesamemethodsdescribedinSection3.5.5todirectlyobservethe0+
2!0+
1E0transitionintheplanarGeDSSD.TheresultsofRef.[18]adjustedtheenergyofthe0+
2stateto1605(3)keVandyieldedahalf-lifeof268(12)nsforthe0+
2state.Theplacementofthe1139-keVtransitionwasmovedtofeedingthe0+
2state[18]fromthe2742-keV2+state[12,20].Asecondraywithanenergyof2420-keVwasalsoidentiedandplacedfeedingthe0+
2state[18]fromastateat4026-keV[12].Theadjustedenergyofthe0+
2statein68Niandplacementofthe1139-keVrayandwereconrmedinsubsequentexperimentsusingcomplimentarydeepinelasticscatteringandtwo-neutronknockoutreactions[19].ThemostrecentworkofRef.[21]wasalsoabletodirectlydetectthe(0+
2!0+
1)E0transitionusingcoincidencetechniquebetweentwoplasticscintilators,wheretheelectronfromthedecayof68CowasrecordedinonescintillatorfollowedashorttimelaterbydetectionoftheelectronfromthediscreteE0transitionintheother.The0+
2statewasplacedat1603.6(8)keVandfromatofthehistogramoftimedierencesbetweenthetwoplasticscintillators,accountingforbothspuriouscoincidencesandscattered-decayelectrons,ahalf-lifeof235(23)nswasobtained[21].Thetwomostrecentdecayspectroscopymeasurments[18,21]searchedfortheexpected430-keV(2+
1!0+
2)transition,butonlylimitsonthe(2+
1!0+
2)branchwereestablished106as<1%and<0.7%,respectively.Lackingameasurementoftransitionstrength,theworkofRef.[18]assumedmaximalmixingbetweensphericalanddeformedcongurationsinatwo-levelmixingmodelandobtainedadierenceinmean-squarechargeradiiof0.15fm2betweenthe0+
1and0+
2statesandavalueof|102efm2|fortheintrinsicquadrupolemomentofthe0+
2state.Whencomparedtothe-95efm2predictedbytheMonteCarloShellModel(MCSM),theseresultsprovidedtherstindicationofshapecoexistancein68Ni.The2511-keV0+
3statewasobservedintheworkofRef.[12]andsubsequentangularcorrelationmeasurementsconrmedthe0+spinandparityassignment[20].Untilthepresentwork,onlyalimitof<15nswasplacedonthehalf-lifeofthe0+
3state[12].TheworkofRef.[12]placedalimitof<50%forthe0+
3!0+
1E0transitionbranch.Subseqentmeasurementsplacedalimitof<4%forthesumofthe0+
3!0+
1and0+
3!0+
2E0transitionsbranch.Theremainderofthissectiondescribestheanalysisof68Codecaypopulatedbythedecayof68Fe.68Cohastwo-decayingisomericstates,withtentativespinandparityassignmentsof(1+;2;3+)[12,21,55]and(7)[12]andmeasuredhalf-livesof1600(300)ms[12]and200(2)ms[22],respectively.The(1+)spinandparityassignmentisadoptedforthelong-lived,low-spin68CoisomerfortheremainderofthischapterandthereasonsforthischoicearediscussedinSection.5.2.Theground-statespinandparityof68Feis0+[22],andthus,basedonthe-decayselectionrulesdiscussedinSection2.1,decaypredominatelypopulatespositive-paritylow-spin(J=0,1)statesin68Cowithlittlepopulationofthe(7)isomer68Coisomer.Previous-decaystudies[12]suggestthattheonlythedecayofthelow-spin68Coisomerleadstopopulationofthe0+
2statein68Ni.Ionsof68FewereimplantedintotheGeDSSD,describedinSection3.5,andtheseg-mentedplasticscintillator,describedinSection3.6duringexperimentse14039ande14057,107respectively.Subsequentdecayswerecorrelatedto68Feionsusingthetechniquesde-scribedinSection3.5.2andSection3.6.2fortheGeDSSDandsegmentedplasticscintillator,respectively,usinga4000mscorrelationwindow.The-delayed-raysrecordedwithin4000msofa68FeionimplantationareshowninFig.4.2.Transitionsidentiedasbelongingto68Niarelabeledwithanenergy,whileallothertransitionsfromthedecayofbothbeamcontaminantsanddaughter,granddaughter,etc.nucleiaredenotedwithsymbols.Thetwopeaksat1460and2614keV,denotedwithtwoasterisks,arethestrongbackgroundraysfromthedecayof40K[49]and208Tl[50],respectively./FloatBarrier
Alistofallobservedtransitionsplacedin68Ni,theirabsoluteintensities,andtheintialandnalstatesbetweenwhichthetransitionoccursispresentedinTable4.1.Absoluteintensitieswerecalculatedbydividingthenumberofcountsineachpeak,obtainedfromaGaussiantplusalinearbackgroundcomponent,correctedfor-rayeciency,bythenumberof68CodecayslistedinTable4.7anddiscussedinSection4.1.2.5./FloatBarrier1080100200300400500020000400006000080000Counts / 1 keV5006007008009001000010000200003000040000Counts / 1 keV100011001200130014001500010000200003000040000Counts / 1 keV1500160017001800190020000200040006000Energy (keV)Counts / 1 keV(b)
(c)(d)(a)271.7323.5,477.7511662.5693.9709.3786.6, 788.9961.91139.21282.61338.61010.91114.51268.41460**1421.31428.31521.51514.31603.61610.51632.21668.61717.8,     1720.21992.11898.369Ni69Cu69Zn70Cu70Ni68Co68Zn70Zn68Ni Double Escape68Ni Single EscapeFigure4.2:-delayed-rayspectrumrecordedinSeGAwithin4000msofanimplanted68Feion.Transitionsidentiedinthesubsequentanalysisasaliatedwiththedecayof68Niarelabeledwiththeirenergywhilecontaminatingtransitions,resultingfromspuriouscorrelationsofthedecayofotherimplantednuclei,aredenotedwithsymbols.Thepeaksat1460and2614keVareknownbackground-raysfromthedecayof40K[49]and208Tl[50],respectively.Theinsetin(e)showsthefullheightofthe2032.9-keVpeaktruncatedinthespectrumdisplayedin(e).109Figure4.2:(cont'd)250026002700280029003000010002000300040005000Counts / 2 keV30003100320033003400350001000200030004000Counts / 2 keV20002100220023002400250001000200030004000Counts / 2 keV3500360037003800390040000100020003000Counts / 2 keVEnergy (keV)(f)(g)(h)(e)200020302060200004000002032.92032.92130.52231.32422.02231.72614**2742.22362.02573.92457.12719.62830.22859.32877.22968.32989.93004.63031.93235.03230.43277.33287.03371.83378.63414.63433.43456.53451.63479.63153.83145.53515.43533.03656.1
3660.33713.63725.13741.53798.53872.33925.93962.63944.23991.369Ni69Cu69Zn70Cu70Ni68Co68Zn70Zn68Ni Double Escape68Ni Single Escape3711.0110Figure4.2:(cont'd)40004200440046004800500002004006008001000Counts / 2 keV50005200540056005800600002004006008001000Counts / 2 keV60006200640066006800700001020304050Counts / 2 keV70007200740076007800800005101520Energy (keV)Counts / 2 keV(i)
(j)(k)(l)4024.64077.94224.94239.54255.94328.54374.04394.44224.94506.14542.84588.04607.24622.04650.64719.05017.65054.25227.65297.45414.8
5421.95528.75543.85565.56487.86612.76771.86870.36359.27240.55232.469Ni69Cu69Zn70Cu70Ni68Co68Zn70Zn68Ni Double Escape68Ni Single Escape111Table4.1:Energiesandabsoluteintensitiesofthe-raytransitionsplacedin68Nifollowingthedecayofthelong-lived,low-spin,68Coisomerselectivelypopulatedbythedecayof68Fe.Theenergiesoftheinitialandnalstatesforeachtransitionarealsolisted.E(keV)Iabsolute(%)InitialState(keV)FinalState(keV)258.3(2)0.26(8)34063147
271.7(2)2.26(22)31192847
323.5(3)0.39(10)34423119429.8(3)b0.06(1)20331603477.7(2)6.18(56)25112033
662.5(2)1.31(11)34052742693.9(2)a5.53(50)709.3(2)5.10(47)27422033
786.6(5)0.35(13)28192033
788.9(3)0.87(22)28222033
862.8(4)0.27(8)28962033
961.9(2)0.54(8)410931471104.2(5)0.12(5)44053301
1114.5(2)4.22(39)31472033
1139.2(2)3.34(25)27421603
1268.4(2)1.68(17)33012033
1282.6(2)1.05(10)40252742
1338.6(2)1.61(36)337120331344.0(8)b0.22(8)569043461366.4(4)b0.40(17)553041641400.3(3)b0.70(22)556441641421.3(2)4.43(33)41642742
1428.3(3)0.44(10)57744346
1514.3(2)4.75(44)402525111540.7(4)b0.18(5)428327421554.9(7)b0.39(17)706755121579.2(3)b0.24(11)574441641603.6(2)1.29(11)43462742
1610.5(3)0.73(13)57744164
1631.2(3)0.16(4)437327421641.3(3)b0.04(1)577441331668.6(3)0.24(6)569440251705.3(7)b0.10(4)44482742aTransitionbelongsto67Nipopulatedby68Co-delayedneutronemissionbTransitionobservedonlyincoincidencespectracTransitionplacedwithoutcoincidencesbasedonenergydierencesbetweenknownlevels112Table4.1:(cont'd)E(keV)Iabsolute(%)InitialState(keV)FinalState(keV)1713.3(5)b0.29(8)445627421716.0(5)b1.03(40)375020331717.8(4)0.27(12)574340251898.3(5)b0.69(33)393120331992.1(5)0.27(8)40252033
2032.9(2)51.4(46)20330
2130.5(2)0.86(11)416320332231.3(8)b0.63(30)426420332362.0(4)0.36(7)43952033
2422.0(2)1.90(15)402516032529.8(3)b0.23(4)413316032573.9(4)0.41(8)460720332728.3(4)b0.13(8)476120332742.2(2)6.65(61)27420
2830.2(2)0.86(11)597831472844.6(3)b0.21(3)444816032947.1(6)b0.36(10)568927422989.9(5)0.24(6)636133713002.6(8)b0.13(9)640734053020.3(6)c0.52(11)553125113031.9(2)1.34(12)577427423054.9(5)b0.21(5)556525113092.8(5)b0.13(7)649834053095.3(12)b0.18(6)646733713218.4(11)b0.09(6)724240253235.9(6)b0.43(12)597727423265.2(5)b0.14(7)577625113277.3(10)0.12(4)488016033290.9(9)b1.42(47)532420333358.2(6)b0.18(11)650631473371.8(2)0.91(12)33720
3378.6(5)0.37(10)541220333455.0(8)b0.030(22)54892033bTransitionobservedonlyincoincidencespectracTransitionplacedwithoutcoincidencesbasedonenergydierencesbetweenknownlevels113Table4.1:(cont'd)E(keV)Iabsolute(%)InitialState(keV)FinalState(keV)3479.6(2)5.13(48)551220333496.5(6)b0.12(04)552920333508.8(7)b0.32(14)665631473515.4(2)3.59(34)55482033
3533.0(3)0.477(77)556620333608.5(10)b0.42(13)564120333656.1(3)1.16(28)56892033
3660.3(3)0.71(19)56932033
3711.0(3)0.49(11)57442033
3741.5(2)5.17(48)57742033
3872.3(3)0.49(11)59052033
3925.9(2)1.036(91)55291603
3944.2(2)0.378(66)59772033
3962.6(2)1.34(11)55661603
4024.6(2)1.92(19)402504198.7(13)b0.10(6)694127424224.9(3)0.55(10)62582033
4239.5(6)0.224(39)58431604
4255.9(7)0.264(78)62892033
4328.5(3)0.221(60)63612033
4374.0(9)0.219(69)64072033
4394.4(5)0.54(11)43940
4424.9(4)0.211(56)645820334500.1(3)b0.110(42)724227424588.0(3)0.358(69)66212033
4607.2(5)0.144(52)66402033
5227.6(8)0.148(61)726020335337.7(10)b0.022(11)694116035395.8(8)b0.060(18)699916035528.7(1)3.52(34)55290
5565.5(1)3.36(32)556605639.8(8)b0.016(8)724216035978.0(6)b0.008(4)758116036178.6(14)b0.016(8)778216037240.5(10)0.064(22)72410bTransitionobservedonlyincoincidencespectracTransitionplacedwithoutcoincidencesbasedonenergydierencesbetweenknownlevels114TheplacementofrayslistedinTable4.1wasdoneusingcoincidences.Ofparticularinterestforinvestigatingshapecoexistenceisthecoincidencespectrumgatedonthe1514.3-keVray,showninFig.4.3,whichisknowntofeedthe2511-keV0+
3state[12].Ifthe0+
3stateweretodecaybya2511-keVE0transition,itwouldproceedpredominatelybyinternalpair-formationwitha92.1%branch[34].The511-keVraysemittedfromthepositronanhilationwouldbepresentinthe-rayspectrum,showninFig.4.3,coincidentwiththe1514.3-keVfeedingtransition.450500550050100150Energy (keV)Counts / keV477.7Figure4.3:Background-subtractedcoincidencespectragatedonthe1514.3-keV(2+)!0+
3transitionin68Nifocusingaroundthe511-keVregion.Thebackgroundwastakenbelowthe1514.3-keVpeaktoavoidthe1521.5-keVsingleescapepeakfromthe2032.9-keVray.TheupperrangeofthegatewasalsoreducedbyacoupleofkeVtoavoidincludingthelow-energytailofthe1521.5-keVescapepeak.Thestrong477.7-keV0+
3!2+
1transitionisobservedinFig.4.3,asexpected.Noclearevidenceofa511-keVrayispresentandanalysisofthespectruminFig.4.3placesalimitof<1.7%0+
3!0+
1E0transitionbranch.Additionalcoincidenceswiththe1514.3-keVray,outsidetherangeofFig.4.3,areshowninFig.B.3qinAppendixB.AppendixBalsocontainesseveralothercoincidencespectra,andasummaryofallobservedcoincidencesispresentedinTable.4.2./FloatBarrier
InSections3.5.5and3.6.3,thetechniquesfordetectingthe0+
2!0+
1E0transitionin115Table4.2:Summaryofobserved-raycoincidencesfollowingthedecayofthelong-lived,low-spin,68Coisomerpopulatedbythedecayof68Fe.E(keV)CoincidentE(keV)258.3(2)1114.5,2032.9
271.7(1)323.5,
323.5(2)271.7
477.7(1)477.7,511,1514.3,2032.9,3054.9,3265.2
662.5(1)511,709.3,1139.2,2032.9,2742.2,3002.6,3092.8709.3(1)511,662.5,1282.6,1421.3,1428.3,1603.6,1610.5,2032.9,3031.9786.6(4)2032.9
788.9(2)2032.9
862.8(3)2032.9
961.9(1)1114.5,2032.91104.2(5)1268.4,2032.9
1114.5(1)511,969.1,2032.9,2830.2,3358.2,3508.8
1139.2(1)511,662.5,1282.6,1421.3,1428.3,1603.6,1610.51268.4(1)1104.2,2032.9
1282.6(1)709.3,1139.2,2032.9,2742.2
1338.6(1)2032.9,3095.3
1344.0(7)1603.6
1421.3(1)511,709.3,1139.2,1610.5,2032.9,2742.2
1428.3(1)1603.6,2032.9
1514.3(1)477.7,1668.6,1717.8,2032.9
1554.9(7)3479.6
1603.6(1)511,709.3,1139.2,1344.0,1428.3,2032.9,2742.21610.5(2)511,709.3,1421.3,2032.9,2742.2
1668.6(2)477.7,511,1282.6,1514.3,2032.9,2422.0
1716.7(5)2032.9
1717.8(3)477.7,511,1282.6,1514.3,2032.9
1898.3(5)2032.9
1992.1(5)2032.9
2032.9(1)477.7,511,662.5,709.3,786.6,788.9,862.8,961.9,1104.2,1114.5,1268.4,1338.6,1421.3,1514.3,1603.6,1610.5,1716.0,1898.3,1992.1,2130.5,2231.3,2362.0,2728.3,3031.9,3290.9,3378.6,3456.5,3479.6,3515.4,3533.0,3656.1,3660.3,3711.0,3741.5,3944.2,4224.9,4588.0,5227.52130.5(1)2032.9
2231.3(8)2032.9
2362.0(3)2032.9
2422.0(1)511,1668.6,1717.8
2573.9(3)2032.9116Table4.2:(cont'd)E(keV)CoincidentE(keV)2728.3(3)2032.9
2742.2(1)511,662.5,1282.6,1421.3,1428.3,1603.6,1610.5,3031.92830.2(1)1114.5,2032.9
2989.9(4)1338.6,2032.9,3371.8
3002.6(8)662.5
3031.9(1)511,709.3,1139.2,2032.9,2742.2
3054.9(5)477.7
3092.8(5)662.53095.3(12)1338.6,2032.93265.2(5)477.7
3290.9(9)2032.9
3358.2(6)1114.5
3371.8(2)2989.9,3095.3
3378.6(4)2032.9
3455.0(7)2032.9
3479.6(1)1554.9,2032.9
3496.5(6)2032.9
3508.8(6)1114.5
3515.4(1)2032.9
3533.0(2)2032.93608.5(10)2032.93656.1(3)2032.9
3660.3(3)2032.9
3711.0(3)2032.9
3741.5(1)2032.9
3872.3(3)2032.9
3925.9(1)511
3944.2(2)2032.9
3962.6(1)511
4224.9(3)2032.9
4239.5(6)511
4255.9(7)2032.9
4328.5(2)2032.9
4374.0(9)2032.9
4424.9(3)2032.9
4588.0(3)2032.9
5227.6(7)2032.9theGeDSSDandPSPMTweredescribed.Thesetechnqiuesprovideacleangatetoisolatetransitionsin68Nifeedingthe0+
2stateeitherdirectlyorindirectly.117Therayscoincidentwiththedecayofthe0+
2statein68NiareshowninFig.4.4.ThespectrumshowninFig.4.4isgatedontheenergyofthesecondpulsetoremovecontaminationfromotherdouble-pulseevents.Thesegateswerefrom400to2000keVand400to8000ADCunitsforsecondpulseenergyspectrashowninFigs.3.18and3.33recordedduringe14039ande14057,respectively.Besidesthestrong511-keVcoincidence,predominatelyfromthepair-productiondecaymodeoftheE0transition,thetwostrongestcoincidencesarewiththe1139.2-and2422.0-keVrays.Thesetwotransitionsareknowntofeedthe1603.3-keV0+
2statedirectly[18,19,21].Theratioofcountsobservedincoincidencewiththe0+
2!0+
1E0transitiontocountsobservedin-gated-raysinglesforthosetwotransitionswasusedtodeterminethedouble-pulse-detectioneciency.Severaladditionaltransitions,manyofwhicharetooweaktobeseenin-gated-raysingles,areobservedincoincidencewiththe0+
2!0+
1E0transition.Alistofthetransitionsobservedcoincidentwiththe0+
2!0+
1E0transitionandplacedinthe68NilevelschemeispresentedinTable4.3.Alsolistedaretheirabsoluteintensities,andtheintialandnalstatesbetweenwhichthetransitionoccurs.Theabsoluteintensitiesofrayscoincidentwiththe0+
2!0+
1E0transition,listedinTable.4.3,wereobtainedusingthenumberofcountsrecordedincoincidencewiththe0+
2!0+
1E0transition,thedoublepulsedetectioneciency,thebranchingratiosforeachstatethroughthe0+
2!0+
1E0transition,andthenumberof68CodecayslistedinTable4.7presentedinSection4.1.2.5.Branchingratiosmustbetakenintoconsiderationfortransitionsthatdonotdirectlyfeedthe0+
2inordertoreconcilethe-delayedsinglesanddouble-pulse-gated-delayed-rayspectra.Eachstateabovethe0+
2statecanpotentiallydecayviaoneormoreadditional-raycascades.Whenmultiplecascadesexist,the-delayed-raysinglesspectrumwillcontainthecountsfromothercascades,whilethedouble-pulse-gated-delayed-rayspectrumwill11802004006008001000050010001500Counts / 1 keV429.8511609.0662.51000120014001600180020000500100015001139.21282.61400.31421.31428.3, 1435.91460.51540.71579.21603.6, 1610.51631.2, 1641.31668.61713.3, 1717.81772.21910.81259.81366.420002200240026002800300001002003002422.02529.82844.62903.82931.92940.2Counts / 2 keVCounts / 2 keV230024002500050010002422.0110012000200040001139.2460510560040008000511(a)
(b)(c)Single Escape
Double Escape2947.1Energy (keV)Figure4.4:Spectrumofraysrecordedincoincidencewiththedetectionofthe0+
2!0+
1E0transitionin68Ni.Theinsetin(a)showsthefullheightofthe511-keVpeaktruncatedin(a).Theleftandrightinsetsin(c)showthefullheightsofthe1139.2-and2422.0-keVpeakstruncatedinpanels(b)and(c),respectively.Theinsetin(f)showsthe6000-to6400-keVregionofthesamespectrumpresentedin(a)through(f).Inallcasestransitionsarelabeledwiththeirenergiesand,whenapplicable,singleanddouble-escapepeaksaredenotedwithoneortwostars,respectively,inadditiontotheenergyofthepeak.notandthustheextractedintensityinthelatterwouldbesystematicallylow.Branchingratiosaredeterminedfromtheratioofthedouble-pulseeciencycorrectednumberofcountsinthedouble-pulse-gated-rayspectradividedbythenumberofcountsin-gated-raysinglesfortransitionsplacedinthe68Nilevelschemecommontobothspectra(denotedwith119Figure4.4:(cont'd)3000320034003600380040000100200300400500Counts / 2 keV3031.93112.43218.4
3235.03277.33361.03414.93451.73925.93962.63643.63728.0(d)4000420044004600480050000204060Counts / 2 keV4198.74239.54878.3500052005400560058006000510Counts / 2 keV5337.75395.85978.05639.86000620064000246178.6(e)
(f)Single Escape
Double Escape4884.84500.1Energy (keV)a\c"inTable4.3).Aweightedaverageoftheseratioswasperformedforeachexcitedstatetoobtainthebranching-ratiocorrecttionfortransitionsplacedfeedingthatstate.Oncecorrectedforthedouble-pulse-detectioneciencyandthebranchingratio,thenumberofcountsforeachtransitionwasdividedbythenumberof68CodecaysobtainedinSection4.1.2.5togivetheabsolute-rayintensitieslistedinTable4.3.SeveraltransitionsinTable4.3,denotedwitha\c",wereidentiedin-delayed-raysinglesandplacedusingcoincidences.Anyplacementmadeonenergydierences120bewtweenknownlevels(giventhecoincidencewiththe0+
2!0+
1E0transition)islabeledwitha\b".Transitionsnotconclusivelyplacedinthe68Nilevelschemecannotbecorrectedforthebranchingratiosinthemannerdescribedaboveandinsteadonlyrelativeintensitiescanbedisplayed.Alistofunplacedtransitionscoincidentwiththe0+
2!0+
1E0transitionandtheirintensitiesrelativetothe1139.2-keVtransitionispresentedinTable4.4.PerhapsthemostinterestingofthetransitionslistedinTable4.3isthe429.8-keV2+
1!0+
2transition,observedhereforthersttime.Basedontheabsoluteintensitiesofthe429.8-keVand2032.9-keVtransitions,abranchof0.12(3)%wasobtainedforthe429.8-keV2+
1!0+
2transition.Thedouble-pulse-gated-rayspectruminFig.4.4canalsobeusedtoplacelimitsonthe0+
3!0+
2E0transitionbranchingratio.Giventheshorthalf-lifeof0.57(5)nsforthe2511-keV0+
3state,obtainedinSection4.1.2.7,the0+
3!0+
2E0transitionwouldessentiallybeprompt,withthedecayinthedouble-pulseanalysisandappearasonerstriseindouble-pulseevents.ThesamespectrumpresentedinFig.4.4focusedonthe1514.3-keVregionisshowninFig.4.5.14801500152015401560020406080100Counts / keVEnergy (keV)Figure4.5:Spectrumofraysrecordedincoincidencewiththedetectionofthe0+
2!0+
1E0transitionin68Nifocusedinonthe1514.3-keVregion.121Thelackofthe1514.3-keVtransition,whichfeedsthe2511-keVstate,incoincidencewiththe0+
2!0+
1E0transitionmeansthatonlylimitscanbeplacedonthe0+
3!0+
2E0transitionbranch.Basedonthecountsinthe1514.3-keVregionofFig.4.5,alimitof<0.18%wasdeducedforthe0+
3!0+
2E0transitionbranch.Thelevelofstatisticspresentinthisworkallowsexaminationof-double-pulsecoin-cidencesforseveralofthetransitionsobservedinFig.4.4.ThesecoincidencespectraarepresentedinAppendixB.Asummaryofall-double-pulsecoincidencesispresentedinTable4.5.Usingtheabsolute-rayintensitiesfromTables4.1and4.3andthecoincidencerelation-shipsdescribedabove,summarizedinTables4.2and4.5,thedecayschemeforthelong-lived,low-spin,68CoisomerwasconstructedandispresentedinFig.4.6.The-decayQ-valueusedforthisanalysisis11.54(15)MeVandwastakenfromRef.[56].TheFermiintegralwascalculatedusingEq.(2.12)andthepartialhalf-lifefordecaytoeachstatewascalculatedusingEq.(2.10).Itiscurrentlyunknownwhich68Coisomeristhegroundstateandtheenergydierencebetweenthetwoisomersisalsounknown.Assuch,thereissomeadditionaluncertaintyontheQ-valueandthusthelogftvalues.Thedecayschemeforthelong-lived,low-spin,68CoisomerispresentedinFig.4.6.SomeofthetransitionsidentiedinFig.4.2wereunabletobeconclusivelyplacedinthe68Nilevelscheme,andarepresentedinTable4.6alongwiththeirabsoluteintensities.122Table4.3:Energiesandabsoluteintensitiesof-raytransitionsplaced68Ni,detectedincoincidencewiththe0+
2!0+
1E0transition,followingthedecayofthelong-lived,low-spin,68Coisomer.Theenergiesoftheinitialandnalstatesbetweenwhicheachtransitionoccursarealsolisted.E(keV)Iabsolute(%)InitialState(keV)FinalState(keV)429.8(2)b0.060(15)20331603662.5(1)c1.34(11)340527421139.2(1)c3.34(25)274216031282.6(1)c1.05(10)402527421366.4(4)b0.40(17)553041641400.3(3)b0.70(22)556541641421.3(0)c4.43(33)416427421428.3(2)c0.44(10)577443461540.7(4)0.176(49)42832742
1579.2(3)0.24(11)574341641603.6(1)c1.29(11)434627421610.5(2)c0.73(13)577441641631.2(2)0.168(46)43732742
1641.3(3)0.041(11)577441331668.6(2)c0.243(97)569440251705.3(6)b0.096(41)444827421713.3(5)0.294(84)445627421717.8(3)c0.27(12)574340252422.0(1)c1.90(15)402516032529.8(2)0.228(37)413316032844.6(2)b0.205(33)444816032947.1(6)b0.36(11)568927423031.9(2)c1.34(12)577527423218.4(10)0.089(56)724240253235.0(6)b0.38(11)597727423277.3(10)c0.12(4)488016033925.9(1)c1.05(14)552916033962.6(1)c1.37(18)556616034198.7(13)b0.103(62)694127424239.5(3)c0.208(36)584316034500.1(3)b0.110(42)724227425337.7(10)b0.022(11)694116035395.8(8)0.060(18)699916035639.8(8)b0.016(8)724216035978.0(6)0.008(4)758116036178.6(14)0.016(8)77821603bTransitionplacedin68NiwithoutadditionalcoincidencesusingonlyenergydierencescTranstionalsoobservedin-gated-raysingles123Table4.4:Energiesandrelativeintensities(I1139:2=100%)ofunplaced-raytransitionscoincidentwiththe0+
2!0+
1E0transition,followingthedecayofthelong-lived,low-spin,68Coisomer.E(keV)I1139:2=100%(%)609.0(2)0.93(32)1259.8(6)1.10(49)
1435.9(3)1.25(42)
1460.5(2)3.27(69)
1772.2(4)2.53(74)
2931.9(6)1.54(49)
3112.4(5)2.37(78)
3361.0(6)1.27(53)
3643.6(6)1.83(65)4878.3(17)0.55(28)
5001.2(10)0.36(26)Table4.5:Summaryof-double-pulsecoincidencesin68Nifollowingthedecayofthelong-lived,low-spin,68Coisomer.E(keV)CoincidentE(keV)662.5511,1139.2,845.4,969.6,1259.1,1392.91139.2511,662.5,1282.6,1421.3,1428.3,1603.6,1610.5,3031.91282.6511,1139.2
1421.3511,1139.2
1428.3511,1139.2,1603.6
1540.7511,1139.2
1579.2511,1139.2,1421.3
1603.6511,1139.2,1428.3
1610.5511,1139.2,1421.3
1631.2511,1139.2
1641.62529.8
1668.6511,2422.0
1713.3511,1139.2
1717.8511,2422.0
2422.0511,1668.6,1717.8
2529.8511,1641.3
3031.9511,1139.2124I(-) %blog(  )ftE (keV)68NiJp68Co= (1)+Jpbb--< 95.0 %,-n > 5.0 %t= 2.36(13) s
Q- = 11.54(15) MeV1/2bsd
sd272(3) ns0.57(5) ns2033
160302+4+0+
0+2+(2+)0+340525112819282228472896311933713442330127423749402539313147(4+)(3-)
(4-)(5-)5-4024.61992.12422.01514.31282.61898.31716.7323.5258.3662.51338.63371.81268.41114.5271.7862.8814.5788.9786.62742.21139.2709.3477.72032.9
429.81603.04.4(48)0.56(73)<16-0.33(52)4.05(92)0.35(13)0.87(22)-0.03(32)0.27(7)1.87(24)2.05(45)4.71(42)0.39(10)1.55(17)1.32(18)1.03(41)9.29(54)
0.69(33)6.84(48)7.63(56)>6.856.71(10)7.76(16)7.36(11)7.85(13)6.96(6)6.91(10)6.49(15)7.55(12)6.99(5)7.03(6)7.03(6)6.01(4)7.17(12)Figure4.6:Decayschemeforthelong-lived,low-spin,68Coisomerpopulatedthroughthedecayof68Fe.Statesin68NiarelabeledwithanenergyinkeVandthespininparity(ifknown)ontheright.Ontheleft,-decaybranchingratiosandlog10ftvaluesareshown.-decayQ-valuetakenfromRef.[56].The0.31(5)pshalf-lifeofthe2033-keV2+
1stateistakenfromtheevaluationinRef.[22].125Figure4.6:(cont'd)I(-) %blog(  )ftE (keV)68NiJp68Co= (1)+Jpbb--< 95.0 %,-n > 5.0 %t= 2.36(13) s
Q- = 11.54(15) MeV1/2bsd
sd272(3) ns410941334264434643734395444846074880
4283
4163440544564761532454885529
541255125548
33012742
2033
160302+4+0+
0+2+314725110+7.22(7)6.41(15)6.64(18)5.74(4)7.64(14)6.96(12)5.82(5)5.93(5)5528.73515.43925.93496.53020.31366.43479.63456.53378.63290.93277.32728.32573.91713.32844.61104.21705.34394.4
2362.01631.21603.61540.72231.32130.51421.3961.92529.80.19(4)0.63(30)0.63(17)0.16(4)0.90(13)0.30(5)0.41(8)0.12(4)
0.17(5)4.16(74)0.54(8)0.13(5)0.28(8)0.13(8)1.42(47)0.73(31)5.60(41)
0.37(10)4.74(51)3.59(34)7.67(12)7.77(18)7.40(13)7.63(27)6.32(8)6.92(7)7.38(8)7.19(8)7.11(21)7.67(9)7.67(12)7.09(12)126Figure4.6:(cont'd)I(-) %blog(  )ftE (keV)68NiJp68Co= (1)+Jpbb--< 95.0 %,-n > 5.0 %t= 2.36(13) s
Q- = 11.54(15) MeV1/2bsd
sd272(3) ns55665689574358435977
564156935774590543462742
2033
160302+4+0+
0+2+(2+)314740254163
413225110+2830.23235.93944.23872.34239.53711.03265.23031.91641.31610.51428.31717.81579.23660.31668.63656.12947.11344.03608.55565.53962.63533.03054.91400.36.10(43)1.73(31)1.01(20)0.22(4)1.60(16)
0.42(13)0.95(20)7.87(53)0.49(12)5.69(4)6.20(8)6.41(9)7.02(8)6.12(5)6.83(14)6.45(10)5.50(4)6.66(10)127Figure4.6:(cont'd)I(-) %blog(  )ftE (keV)68NiJp68Co= (1)+Jpbb--< 95.0 %,-n > 5.0 %t= 2.36(13) s
Q- = 11.54(15) MeV1/2bsd
sd272(3) ns6178.65978.05227.67240.6
7240.6
4500.13218.47240.65639.81554.95395.85337.74198.73508.84607.24588.03358.23092.83095.34424.94374.03002.64328.52989.94255.94224.95978.05227.67240.6
7240.6
4500.13218.47240.65639.81554.95395.85337.74198.73508.84607.24588.03358.23092.83095.34424.94374.03002.64328.52989.94255.94224.96289640764676506664069417067726075817782
625863616458649866216656699972423405
33714025
2742
2033
160300.54(12)0.18(6)0.18(11)0.14(5)0.12(6)0.39(17)0.15(6)0.55(10)0.27(8)0.21(6)0.13(7)0.36(7)0.33(14)0.06(2)0.28(7)0.008(4)0.016(8)7.25(22)6.42(10)6.87(14)6.85(25)6.89(16)6.83(22)6.25(19)6.58(18)6.47(8)6.78(13)6.80(12)7.01(23)6.50(9)6.53(19)7.10(13)6.32(12)7.70(20)2+Jp4+0+
0+(4+)2+(2+)314755120.46(9)6.50(9)128Table4.6:Summaryofunplacedrayspotentiallyaliatedwiththedecayofthelong-lived,low-spin,68Coisomer.E(keV)Iabsolute(%)1367.6(2)0.57(9)
1377.7(2)0.25(7)
2877.2(2)0.56(8)3153.8(11)0.16(6)3287.0(3)0.84(12)
3667.3(5)0.17(6)
3725.1(6)0.16(7)
3798.5(3)0.76(10)
3991.3(2)0.62(9)
4622.0(6)0.21(7)
4650.6(4)0.31(6)
5232.4(5)0.29(8)
5297.4(9)0.11(5)5414.8(11)0.11(7)5421.9(3)0.11(7)
5543.8(3)0.26(5)
6487.8(9)0.09(4)
6612.7(9)0.10(3)6771.8(13)0.10(3)6870.3(9)0.17(5)1294.1.2Half-LifeMeasurements
Inadditiontoaddingseveralnewtransitionsandlevelstothe68Nilevelscheme,half-lifemeasurementsof-decayingstatesin68Feand68Coaswellasexcited0+statesin68Niwereperformed.Theremainderofthissectionpresentsthehalf-lifemeasurementscarriedoutinthepresentworkandthetechniquesrequiredtoperformthem.4.1.2.1AssessingSpuriousCorrelations
ThecorrelationalgorithmsdescribedinSections3.5.2and3.6.2attempttoassociate-decayelectrons,aswellascoincidentrays,withtheirrespectiveimplantedions.Thiswasdonebysearchingforthemostrecentionimplantationinthesamespatialregionofthedetectorasthedetected-decayelectron.However,thesemethodsarenotperfectandtwocommonfailuremodesexist.Intherstfailuremode,asecondionimplantsintothesamespatialregionastherstbeforethedecayoftherstion.Thedecayisincorrectlyattributedtothesecondionandthetimedierencebetweenthedecayandsecondimplantedion,referredtoasthedecaytime,isnotrepresentativeofthedecayofthesecondimplantedion.Thesecondfailuremodeoccurswhenthe-decayelectrontraversespixelboundaries.Ifthemajorityofthe-decayelectronenergyisdepositedinanadjacentpixel,the-decayelectronmaybeassociatedwithanincorrectioninthatadjacentpixel.Theextracteddecaytimeisagainrandom.Correlationsduetothesefailuremodesarereferredtoasspuriouscorrelations.Thequantityanddecay-timedistributionofspuriousdecaysdependsontheionimplantationrateperpixel,thesizeofthecorrelationeld,andthe-decayhalf-lives.Ine14039theaverageimplantrateforallionswas40Hzgivinganaveragetimebetweenimplantsofˇ2sintheilluminatedpixels.Ine14057theaverageimplantratewas30130Hzgivinganaveragetimebetweenimplantsofˇ3sineachilluminatedpixel.Half-livesofthenucleiofinterestareseveralhundredmstoseveralseconds.Asaresultspuriouscorrelationsweresignicantinbothexperiments.Theninepixelcorrelationeldusedine14057tocompensateforthepoorpositionresolutioneectivelyreducesthetimebetweenimplantstoˇ300msandsignicantlyincreasesspuriouscorrelations.Thedistributionofdecaytimesforagivenisotopeiscalledadecaycurve.DecaycurvesareoftentwiththeBatemanequations,describedinSection2.1,todeducehalf-livesandthenumberofdecaysrecordedfromaparticularisotope.However,decaycurvesmaycontaincontributionsfromspuriouscorrelationsthatmustbeincludedinthet.Therefore,toaccuratelyperformthet,assessmentofthespurious-correlationcomponentiscrucial.AtechniquetodeterminethetimestructureandquantityofspuriouscorrelationswasdevelopedinRef.[57].Themethodinvolvesrunningthefullanalysisbackwardsthroughtime,whichisolatesthespuriouscorrelations.Decaycurvesgeneratedforeachisotopeinthebackwards-timeanalysisarethenusedasspurious-correlationcomponentinthedecaycurveforeachrespectiveisotopeintheforwards-timeanalysis.Applicationofthistechniqueremovesthewould-befreeparametersduetospuriouscorrelationsfromthedecaycurve,leavingthenumberofdecayingnucleiandtheirhalf-livesasfreeparametersinthet.4.1.2.2\ExclusionTechnique"forCorrelations
Thissectiondescribesanewcorrelationtechniquereferredtoasthe\exclusiontechnique".Thistechniquewasdevelopedtocombattheeectsoftherelativelyhighimplantationrate(average˘2implantsperpixelpersecond)andlongdaughterandgranddaughterhalf-lives(˘1'sto10'sofseconds)ofthedecayingnuclei.StandardcorrelationtechniquesdescribedinSections3.5.2and3.6.2resultinasystematicskewingofhalf-livestoshortervalues.Figure1314.7illustratesthiseectforthedecayof68Fe.Counts / 10 ms11021031041051001000200030004000-200200100020003000DataTotal Fit68Co Decay68Ni Decay68Fe DecayDataTotal Fit68Co Decay68Ni Decay68Fe DecayNon-ExclusionExclusionNormalizedFit Residual(c)(a)(d)(b)Time (ms)Time (ms)Figure4.7:Motivationforthedevelopmentoftheexclusiontechnique.Twodecaycurvesfor68Feareshowninblackin(a)and(b)obtainedfromtheanalysisusingthenon-exclusionandexclusioncorrelationtechniques,respectively.Thedecaycurveshavehadtheirspurious-correlationcomponent,determinedusingthetechniquesinSection4.1.2.1,subtractedoutandwerenormalizedhaveequivalentintegralnumbersofcounts.Foreachdecaycurveatotalt(red)wasperformedcomprisedof68Feparent(green),68Codaughter(magenta),and68Nigranddaughter(orange)decays.Thehalf-lifeof68Niwasxedtotheliteraturevalueof29s[22].Fitresiduals,normalizedtothebinerror,areshownin(c)and(d)forthetotaltcomparedtothedatain(a)and(b),forthenon-exclusionandexclusiondecaycurvets,respectively.Twodecaycurvesfor68Feobtainedfromthenon-exclusionandexclusioncorrelationtechniquesareshowninblackinFigs.4.7aand4.7b,respectively.Thespurious-correlationcomponent,determinedusingthemethodspresentedinSection4.1.2.1,wassubtractedfromeachandtheresultingdecaycurveswerenormalizedtohaveequivalentnumbersofcounts.EachdecaycurvewastwiththeBatemanequationscomprisedof68Feparent(green),68Codaughter(magenta),and68Nigranddaughter(orange)components.Thehalf-lifeof68Niwasxedtotheliteraturevalueof29s[22].Fitresiduals,normalizedtothebinerror,areshownin(c)and(d)forthenon-exclusionandexclusiondecaycurvets,respectively.ThedecaycurveinFig.4.7a,generatedfromthenon-exclusiontechnique,wasnotable132tobetbytheBatemanequationsusingthexed29shalf-lifeof68Ni[22].Onlywhenthe68Nihalf-lifewasreducedbyanorderofmagnitudedidthetbecomereasonable.Ifallparametersareleftfreethenon-exclusiontechniqueyieldsvaluesof180(5),800(30),and2100(200)msforthehalf-livesof68Fe,68Co,and68Nirespectively.Whilethe68Fehalf-lifedoesagreewiththeevaluatedvalueof188(4)ms[22],the68Cohalf-lifeisdiscrepantwiththe1600(300)msfromRef.[12].ThedecaycurveinFig.4.7bwastwellusingtheBatemanequationsandthexed29shalf-lifeof68Ni[22].Valuesof180(4)and2300(110)msareobtainedforthehalf-livesof68Feand68Co,respectively.The68Fehalf-liferemainsunchanged,butthe68Cohalf-lifeissignicantlylarger.ThoughalsodiscrepantwithRef.[12]thisresultagreeswellthehalf-lifeobtainedinSec.4.1.2.4.TheexclusiontechniqueisshownschematicallyinFig.4.8a.InFig.4.8thetimestructureofimplantations(blackverticallines),parentdecays(redverticallines),anddaughterdecay(blueverticallines)fortwoimplantedionsisshown.Solidanddashedlinesareusedtodistinguisheventsaliatedwitheachdierention.Horizontalbracketsrepresentthecorrelationsandtimeproceedsforwardlefttoright.InFig.4.8atheexclusionwindowoftimeisacrosshatchedrectangleabovethecorrelations.ThetechniquesdescribedinSections3.5.2and3.6.2areshownschematicallyinFig.4.8b,wheredecaysarecorrelatedwiththemostrecentionwithinthecorrelationwindowouttoatimedierencelessthanorequaltothecorrelationwindow.Thedecayoftherstimplantisshownasasolidredverticallinewhilethetimeofarrivaloftherstionistheblackverticalline.Thisrstdecaywouldbecorrelatedandhavethesameresultsusingineithermethod.AshorttimeaftertherstdecayasecondionimplantsinthesamespatiallocationandisdenotedwithadashedblackverticallineinFig.4.8.Inthenon-exclusiontechnique,allsubsequentdecayeventswouldcorrelatewiththismostrecentimplant.However,inthe133ExclusionTechniqueTimeTimeXExclusion WindowNon-ExclusionTechnique(a)
(b)Figure4.8:Schematicviewoftheexclusiontechniquehighlightingthedierenceswiththenon-exclusioncorrelationtechniques.Thetimestructureofimplantations(blackverticallines),parentdecays(redverticallines),anddaughterdecay(blueverticallines)fortwoimplantedionsisshown.Solidanddashedlinesareusedtodistinguisheventsaliatedwitheachdierention.Horizontalgreenbarsrepresentthecorrelationsandagrayhorizontalbarrepresentsadecayeventthatisoutsidethecorrelationwindow.In(a)theexclusionwindowoftimeisacrosshatchedrectangleabovethecorrelations.Implantsremovedfromtheanalysisbytheexclusiontechniquearelabeledwithan\X".Timeproceedsforwardlefttorightindicatedbytheblackarrowatthebottomofeachpanel.exclusiontechniquethissecondimplantationfallswithintheexclusionwindow,whichisthesamelengthasthecorrelationwindow,andtheimplantationisignored.Whenthesecondimplantediondecays,denotedbythedashedredverticalline,thenon-exclusiontechniquegetsthecorrelationcorrectandrecordsthecorrecttimedierence.Theexclusiontechniquethedecaycontributestothespurious-correlationcomponent.Spurious134correlationsarepresentinbothtechniques,buttheexclusiontechniqueincreasestheirfre-quency.However,usingthetechniquesinSection4.1.2.1,theircontributioninadecay-curvecanbeeasilyseparatedfromtherealcorrelations.Thepurposeoftheexclusiontechniquebecomesapparentwhenexaminingthedecayofthedaughteroftherstimplantedionshownasasolidblueverticalline.Inthenon-exclusionanalysisthedecayiscorrelated,incorrectly,tothesecondimplantedion.Ifthesecondimplantedionisthesameisotopeastherst,anincorrect,shorter,timedierenceisrecordedtherebyskewingextractedhalf-livestosmallervalues.Intheexclusionanalysisthedecayofthedaughteroftherstimplantedioniscorrectlycorrelatedandnoskewingofextractedhalf-livesoccurs.Finallyinthisexample,thedecayofthedaughterofthesecondimplantedion,shownasadashedblueverticalline,iscorrectlycorrelatedinthenon-exclusionanalysis,butisoutsidethecorrelationwindowintheexclusionanalysis.Ifitwereinthecorrelationwindowfortheexclusionanalysisitwouldcontributetothespuriouscorrelationcomponent.Theimpactofspuriouscorrelationstothetime-dierencedistributionsdependsontheoverallimplantationrateperpixel,thesizeofthecorrelationeld,andthehalf-livesofthenucleiofinterest.Fore14039ande14057theexclusiontechniqueisonepossibleapproachedneededtoextractaccuratevaluesforthehalf-livesofthe-decayingnuclei.4.1.2.3Half-Lifeof68FeThehalf-lifeof68Fewasextractedbygatingthedecaycurvesonthe161.8-keVand184.3-keVtransitionsfromthedecayoftwoexcitedstatesinthe68Codaughter[22].Theexclusiontechniqueforcorrelations,describedintheprevioussection,wasemployed.Thedecaycurvevs.coincident-rayenergyfor68FeisshowninFig.4.9a.Theprojectionontotheenergy135axisispresentedinFig.4.9b.0100020003000400014016018020010000150002000025000Counts / 1 keV01002003004005006000Time Difference (ms)Energy (keV)(b)(a)Figure4.9:(a)Decaycurvevs.coincident-rayenergy,recordedinSeGAduringe14039,fortheregionaroundthe161.8-and184.3-keVpeaks.(b)Projectionof(a)ontotheenergyaxis.Setsofsolidredverticallinesanddashedverticallinesidentifythepeakandbackgroundregions,respectively,foreachpeak.Decaycurvesforboththe161.8-keVand184.3-keVpeakregions(solidredlines)aswellasthebackgroundregions(dashedredlines)weregeneratedfromtheprojectionofFig.4.9ontothetime-dierenceaxis.ThesedecaycurvesareshowninFigures4.10aand4.10cforthepeakregionsregionsandinFigs.4.10band4.10dforthebackgroundregions.ThebackgrounddecaycurvesshowninFigs.4.10band4.10dwerescaledandsubtractedfromthoseinFigs.4.10aand4.10c,respectively.Thetworesultingbackground-subtractedtime-distributionsweresummedtogethertocreatethedecaycurveshowninblackinFig.4.11,usedtoextractthehalf-lifeof68Fe.136Counts / 20 ms05001000150020002500Time-DifferenceProjection from159 to 165 keVTime-DifferenceProjection from166 to 172 keV0100020003000050010001500Counts / 20 msTime-DifferenceProjection from181 to 187 keV01000200030004000Time-DifferenceProjection from189 to 195 keVTime (ms)Time (ms)(c)(a)(b)(d)Figure4.10:Decaycurvesobtainedbyprojecting4.27aontothetime-dierenceaxisovertheregionsof(a)159to165keV,(b)166to172keV,(c)181to187keV,and(d)185to195keV.Regionsshownin(a)and(c)representtheencompassthe161.8-keVand184.3-keVpeaks,respectively,while(b)and(d)arerepresentativebackgroundstobescaledandsubtractedforeachrespectivepeak.Thecountsinthebackground-subtracteddecaycurveinFig.4.11originatefromtwosources.Mostarefromrealcorrelationsbetweena68Feimplantanditssubsequentdecay,andasexpected,theircorrespondingdecaycurveexhibitsanexponentialdecaywiththehalf-lifeof68Fe.However,aportionofthetotalcountsoriginatefromspuriouscorrelationsandyieldaroughlyattime-dierencedistribution.Thespurious-correlationcomponentwasdeterminedusingthetechniquesinSection4.1.2.1.Figure4.12ashowsthetwo-dimensionaltime-dierencevs.coincident-rayen-ergyspectrumwiththeanalysisrunbackwardsintime.Figure4.12bshowstheprojectionofthetwo-dimensionalspectrumshowninFig.4.12aontotheenergyaxis.TheratioofthepeakareasbetweenFigs.4.9band4.12bistheratioofspuriouscor-relationstototalcountsinthebackground-subtracteddecaycurve.ThedecaycurveforspuriouscorrelationswasobtainedbyprojectingthespectrumshowninFig.4.12aontothe137Time (ms)40000100020003000Counts / 20 ms1001000NormalizedFit Residual-2002068Fe DecayRandom Correlations Data
Random Correlations FitDataTotal FitGated on161.8-keV
184.3-keV68Fe t= 175(9) ms1/2(a)
(b)Figure4.11:(a)Background-subtracted-gateddecaycurveforthedecayof68Feinto68Co.Gateswereplacedonthe161.8-keVand184.3-keVtransitionsin68Coandthebackground,scaledappropriatelyandsubtracted,wassampleddirectlyaboveeachpeak.Thebackground-subtracteddataareshowninblackwhilethespuriouscorrelationcomponent,obtainedusingthetechniquesinSection4.1.2.1,isshowninblue.Incyan,attothespuriouscorrelationcomponentisshown,andwasusedtorepresentthespuriouscorrelationsinthetotaltofthedatashowninred.Thecontributionfromthedecayof68Feisshowningreen.Thehalf-lifeof68Fe,extractedfromthet,is175(9)ms.Thiscomparestotheevaluatedvalueof188(4)ms[22].(b)Fitresidualsforthetotaltcomparedtothedatain(a)normalizedtothebinerrorin(a).
time-dierenceaxis,andisshowninblueinFig.4.11.Attothespuriouscorrelationdata,shownincyaninFig.4.11,wasusedinlieuofthedatatoprovideasmoothlyvaryingcomponentforuseinthetotaltshowninredinFig.4.11.Thetotaltwasacombina-tionofthespuriouscorrelationcomponentandanexponentialdecay.Theexponentialdecaycomponent,fromtherealcorrelationsbetween68Feanditssubsequentdecay,extractedfromthetisshowningreen.Theresultsofthetyieldahalf-lifeof175(9)msfor68Fe.The138002040608010012014016014016018020050001000015000Counts / 1 keV1000200030004000Time Difference (ms)Energy (keV)Figure4.12:Resultsoftheanalysisrunbackwardsintimethroughthedata.(a)Decaycurvevs.coincident-ray,recordedinSeGAduringe14039,fortheregionaroundthe161.8-and184.3-keVpeaks.(b)Projectionof(a)ontotheenergyaxis.evaluatedvalueis188(4)ms[22].1394.1.2.4Half-LifeoftheLong-Lived68CoIsomer05001000150020002500Counts / 40 ms01000200030004000-505Time (ms)NormalizedFit Residual68Co DecayDataTotal FitRnd Corr Data
Rnd Corr Fit(a)
(b)Figure4.13:(a)Double-pulse-gateddecaycurveforthedecayof68Cointo68Ni.Thedataareshowninblackwhilethespuriouscorrelationcomponent,obtainedbyrunningtheanalysisbackwardsintimeandscaledbythet,isshowninblue.Incyan,attothespuriouscorrelationcomponentisshown,andwasusedtorepresentthespuriouscorrelationsinthebesttotaltofthedatashowninredusingthehalf-lifeoftheminimumobtainedfromFig.4.14.Thecontributionfromthedecayof68Coisshowninmagenta.(b)Fitresidualsforthetotaltcomparedtothedatain(a)normalizedtothebinerrorin(a).The\double-pulse"analysisdescribedaboveprovidesacleanexperimentalsignaturetogatethe-decaytimespectrumpermittinginvestigationofthehalf-lifeofthelow-spin68Co-decayingisomer.Theonlyexistingmeasurementofthishalf-life,performedintheworkofRef.[12],yieldedavalueof1600(300)msdeducedfromtted-delayed-raygateddecaycurves.Figure4.13ashowsthedecaycurvecoincidentwith\double-pulse"eventsinboththe14015002000250030003500400450500550600Half-Life (ms)c268Co t= 2360(130) ms1/2Figure4.14:Distributionof˜2valuesasafunctionof68Cohalf-lifeobtainedfromttingthedatashowninblackinFig.4.13withacombinationofspuriouscorrelationsandthe68Codaughtergrow-in,describedbyequation(2.21).Thespurious-correlationcomponentandhalf-lifeof68Fewerexedleavingthe68Cohalf-lifeastheonlyfreeparameter.The˜2distributionwastwithafthorderpolynomial,showninred,forinterpolationbetweenpoints.Avalueof2360(130)mswasextractedforthehalf-lifeofthe68Colow-spinisomer.GeDSSDandsegmentedplasticscintillatorisshowninblack.Thespurious-correlationcomponent,showninblueinFig.4.13a,wasobtainedusingthesamebackwardtimeanalysistechniquesdescribedabove.Attothespuriouscorrelationcomponentusedinthetotaltisshownincyan.Thetotalt,showninredinFig.4.13a,wascomprisedoftwocomponents.Therstwasthespuriouscorrelationcomponent,determinedusingthetechniquesinSection4.1.2.1,andthesecondwasasinglegrowthanddecayoftheformofEq.(2.21).Thespurious-correlationcomponentandhalf-lifeof68Fewerexedleavingthe68Cohalf-lifeastheonlyfreeparameter.Severaltswereperformedwiththehalf-lifeofthelong-livedlow-spin68Coisomervariedin100msincrements.Thedistributionofreduced˜2valuesasafunctionofhalf-lifeisshowninFig.4.14.Afth-orderpolynomial,showninredinFig.4.14,wasusedtotthedistribution,141shownasblacksquaresinFig.4.14,andinterpolatebetweenpoints.Thehalf-lifeis2360ms,obtainedattheminimumoftheredcurveinFig.4.14.Aninitialuncertaintyof60mswasobtainedfromthecorrespondingvalueseithersideoftheminimumat1˜2unitupfromtheminimum[54].Anadditionaluncertaintyof110mswasobtainedfromthechangeinextractedhalf-lifewhenboththecontributionofthespuriouscorrelationsandthehalf-lifeof68Fewerevariedwithintheirerrors.Thetwoerrorswereaddedinquadrature,andanaluncertaintyof130mswasobtained.Thebesttresult,correspondingtotheminimumofthe˜2distribution,isshowninmagentainFig.4.13awiththetotalbesttshowninred.Fitresiduals,normalizedtotheerrorineachbin,arepresentedinFig.4.13bandremainroughlyatacrossmostofrangeintime.
4.1.2.5A=68DecayCurvesUsingthenewly-obtainedhalf-livesfor68Feand68Co,thedecaycurvesforalldecayeventscorrelatedwith68Feimplantswerettedforeachexperiment.Thedecaycurvesforthetimedistributionofrecordeddecayeventsfollowingwithin4000msofanimplanted68Feionfore14039ande14057areshowninFigs.4.15aand4.16a,respectively.Theexclusiontechnique,describedinSection4.1.2.2,wasusedinbothanalyses.FortheGeDSSD,thelocationoftheionandsubsequentdecayhadtobeinthesamepixel.Forthesegmentedplasticscintillator,thedecaycouldbeinthesamepixeloranyofthesurroundingeightimmediateneighborpixels.Thelargercorrelationeldfortheplasticscintillatorwaschosenduetothepoorpositionresolutionobtainedfromthesegmentedplasticscintillatorandalsoledtoalargeincreaseinspuriouscorrelations.Inbothcasesa4000mscorrelationwindowwaschosentoprovidealongtimeregiontoproperlytthe14201000200030004000Time (ms)101-505103104105106102NormalizedFit ResidualCounts / 10 msDataTotal FitRnd Corr Data
Rnd Corr Fit68Co Decay68Ni Decay68Fe Decay(a)
(b)Figure4.15:(a)Decaycurveforthedecayofionsof68Feine14039.Thedataareshowninblackwhilethespuriouscorrelationcomponent,obtainedbyrunningtheanalysisbackwardsintimeandscaledbythet,isshowninblue.Incyan,attothespuriouscorrelationcomponentisshown,andwasusedtorepresentthespuriouscorrelationsinthebesttotaltofthedatashowninredusingthehalf-lifeoftheminimumobtainedfromFig.4.14.Thecontributionfromthedecayof68Fe,68Co,and68Niisshowningreen,magenta,andorange,respectively.Thetotaltisshowninred.(b)Fitresidualsforthetotaltcomparedtothedatain(a)normalizedtothebinerrorin(a).
backgroundandtoencompassnearlytwohalf-livesofthethelong-lived68Coisomerdecayswhilenotexcessivelyremovingimplantsintheexclusionwindow.ThedecaycurvesinFigs.4.15and4.16werettedusingtheBatemanequationsconsist-ingofthe68Feparent(t1=2=175(9)ms)showningreen,68Codaughter(t1=2=2330+790
460ms)showninmagenta,andthe68Nigranddaughter(t1=2=29(2)s[22])showninorange.Thespurious-correlationcomponentforeachdecaycurvewasdeterminedusingthetech-niquesdiscussedinSection4.1.2.1.InbothFigs.4.15and4.16thespuriouscorrelation14301000200030004000101-505103104105106102Counts / 10 msDataTotal FitRnd Corr Data
Rnd Corr Fit68Co Decay68Ni Decay68Fe Decay(a)
(b)Time (ms)NormalizedFit ResidualFigure4.16:(a)Decaycurveforthedecayofionsof68Feine14057.Thedataareshowninblackwhilethespuriouscorrelationcomponent,obtainedbyrunningtheanalysisbackwardsintimeandscaledbythet,isshowninblue.Incyan,attothespuriouscorrelationcomponentisshown,andwasusedtorepresentthespuriouscorrelationsinthebesttotaltofthedatashowninredusingthehalf-lifeoftheminimumobtainedfromFig.4.14.Thecontributionfromthedecayof68Fe,68Co,and68Niisshowningreen,magenta,andorange,respectively.Thetotaltisshowninred.(b)Fitresidualsforthetotaltcomparedtothedatain(a)normalizedtothebinerrorin(a).
componentisshowninblueandthettothespuriouscorrelationdataisshownincyan.Thetotaltisshowninred.Thenumberofcorrelateddecaysrecordedforeach-decayingnucleuswasobtainedbyintegratingtheBatemanequationsandisrequiredtoobtaintheabsolute-rayecienciespresentedinTables4.1and4.3.However,thisnumbermustberstcorrectedforspuriouscorrelationsanddierencesbetweentheexclusionandnon-exclusioncorrelationtechniquestobecomparablewiththecorrelated-delayed-raystatisticsfromthenon-exclusionanalysis.144Thenumberofdecaysextractedfromthedecay-curvetisexclusivelythecontributionfromrealcorrelations.However,inthecorrelated-delayed-rayspectra,shownearlierinthischapter,eachpeak,associatedwithagivenisotope,hascountsfrombothrealandspuriouscorrelations.Thecontributionfromspuriouscorrelationswasdeterminedbycom-paringpeakareasoffourtransitionsin68Ni(477.7,709.3,2032.9,and2742.3keV)inthecorrelated-delayed-rayspectrabetweentheforwardsandbackwardsexclusionanalyses.Peakareasintheforwardtimeanalysisarethesumofbothspuriousandrealcorrela-tion.However,inthebackwardstimeanalysis,peakareasareexclusivelythecontributionofspuriouscorrelations.Theratioofpeakareas(backward/forward)representstheratioofspuriouscorrelationstothetotal.Therefore,theinverseofoneminusthisratioisthespuriouscorrelationcorrection.Inadditiontoincreasingthefractionofspuriouscorrelations,theexclusiontechnique,inthisapplication,alsoreducestheoverallquantityofcorrelations.Theeectwasquantiedbycomparingcorrelated-delayed-rayspectrabetweentheexclusionandnon-exclusiontechniquesintheforward-timeanalysis.Thepeakareasforthesamefour-raysusedaboveweredeterminedusingbothtechniques.Theratioofpeakareas(non-exclusion/exclusion)istheexclusiontechniquecorrection.Theintegratednumberofcountsfor68NifromtheBatemanequationsarepresentedinTable4.7alongwiththecorrectionsforspuriouscorrelationsandtheexclusiontechniqueforbothexperiments.UsingthenumbersfromTable4.7,thetotalnumberofcorrelated68Codecayswasdeter-minedtobe9.71(37)106.Thisnumberwasusedtoobtaintheabsolute-rayecienciesandsubsequentlythe-decayfeedingstovariousstatesin68Ni.Thelargedierencesin145Table4.7:Decaycurveintegrationresultsandcorrectionfactorsfor68Niineachexperiment.The\corrected"numberofdecaysisobtainedbymultiplyingtheintegratednumberofcountsbythespuriouscorrelationandexclusiontechniquecorrelationfactors.Thecorrectednumberofdecaysisthendirectlycomparabletothenon-exclusionanalysis-delayed-raystatistics.e14039e14057IntegratedNumberof68Codecays1.04(5)1060.48(2)106SpuriousCorrelationCorrection2.95(4)5.35(7)
ExclusionTechniqueCorrection1.24(1)2.31(2)
CorrectedNumberof68Codecays3.79(20)1065.92(31)106spuriouscorrelationandexclusiontechniquecorrectionvaluesbetweenthetwoexperimentsisduetothelargercorrelationeldusedfortheplasticscintillatorine14057.4.1.2.6Half-Lifeofthe0+
2statein68NiThehalf-lifeofthe0+
2statein68Nihadbeenmeasuredthreetimespriortothepresentwork,andvaluesof270(5)ns[44],268(12)ns[18],and235(23)ns[21]wereobtained.ThepresentworkemploysthesametechniquesusedinRef.[18],wherethehalf-lifeofthe0+
2statein68Niwasextractedbyexaminingthehistogramoftimedierencesbetweentherstandsecondpulsesinthe\double-pulse"analysis.Basedonthelevelschemefromthisworkandallpriorinvestigations,nostateswithsignicantlifetimesareknowntofeedthe0+
2statefollowingdecay.Therefore,onthenstimescale,thedecayof68Co,whichistherstpulseobservedintherecordeddouble-pulsesignals,canbeconsideredthetimeatwhichthe0+
2stateispopulated.Thesecondpulseofthedouble-pulsesignalsisthedecayofthe0+
2state.Thetimedierencebetweenthetwopulsescanbettedasarst-orderdecaytoextractthehalf-lifeofthe0+
2state.Thetime-dierencedistributions,showninFigs.4.17aand4.17b,wereobtainedbyhistogrammingthetimedierencebetweenthetwoconstituentpulsesofalldouble-pulse146signalsrecordedine14057ande14039,respectively.Thesamegatesusedintheprevioussectionswereappliedtotheenergyofthesecondpulsefortime-dierencespectratoremovecontaminationfromlowerenergydouble-pulseeventsdiscussedinSections3.5.5and3.6.3.Fore14039,thegatewasfrom400to2000keV;whileine14057,thisgatewasbetween400and8000ADCunits.InthespectrumdisplayedinFig.4.17a,thetime-dierencedistributioncoversarelativelyshorttime-dierencerangeduetotheavailablelengthoftracebeforetheinclusionofanexternaltime-referencesignal.Theexternaltimereferencewasnotusedinthepresentanalysis,butrestrictstherangeoftimedierencesobtainedfromthedouble-pulseanalysis.Atshorttimedierence,severalfeaturesarepresentduetothedetectorringingexceedingthedynamicdouble-pulse-detectionthreshold,discussedinSection3.6.1.Asingleexponentialdecaytoverthetime-dierencerangeof200to700nsyieldsahalf-lifeof279(6)ns.Thetime-dierencespectruminFig.4.17bspansalargerdynamicrange.Theeectofthenitetracewindowcoupledwithaamplitude-dependenttimewalkassociatedwiththeleading-edgetriggeringalgorithmcanbeseenatlarge-timedierence.TherelativelyslowrisetimeoftheGeDSSDdidnotpermitpositiveidenticationofdoublepulsesignalswithtimedierencelessthan˘200ns.AnexponentialdecaytofthehistograminFig.4.17boverthesame200to700nsrangeyieldedahalf-lifeof271(10),andwhentherangewasextendedoutto2000ns,theextractedhalf-lifebecame270(5)ns.Aweightedaverageoftheresultsfromthepresenttwoexperimentsgaveavalueof274(4)nsforthehalf-lifeofthe0+
2statein68Ni.Thisvalueisinexcellentagreementwiththepreviouslymeasuredvaluesof270(5)ns[44]and268(12)ns[18],butisdiscrepantwiththevalueof235(23)nsobtainedinRef.[21].AweightedaverageofthepresentworkwiththevaluesofRefs.[44]and[18]givesavalueof272(3)nsforthehalf-lifeofthe0+
2statein68Ni,14702004006008001000110100100010000Double PulseTime Difference (ns)Counts / 2 ns(a)e140570100020003000Counts / 2 ns1101001000(b)e14039Double PulseTime Difference (ns)Figure4.17:(a)and(b)Time-dierencedistributionsbetweenthetwoconstituentpulsesofdoublepulsesignalsrecordedine14057ande14039,respectively.Thesecondpulsewasrestrictedtoamplitudesbetween400and8000ADCunitsine14057andenergiesof400and2000keVfore14039.Aweightedaveragebetweenthetworesultsyieldsavalueof274(4)nsforthehalf-lifeofthe0+
2statein68Ni.displayedonthelevelschemeinFig.4.6.1484.1.2.7Half-Lifeofthe0+
3statein68Ni4004505001000200030004000Counts / 2 keVFigure4.18:Spectrumof-raysrecordedintheLaBr3detectorsaroundthe477.7-keVpeakcoincidentwithadecayeventinthesegmentedplasticscintillator.Thesetofsolidredanddashedredbarsrepresenttheenergywindowsusedforthepeakandbackgroundregionsofinterest,respectively.Ameasurementofthehalf-lifeofthe2511keV0+
3statewasperformedusingthetimingmethodspresentedinSection3.9.The477.7-keVraywasrecordedintheLaBr3detectors,describedinSection3.8,coincidentwiththe-decayelectrondetectedinthePSPMT,detailedinSection3.6.TheLaBr3energyspectrumintheregionofthe477.7-keVtransitionisshowninFig.4.18.InFig.4.18,thesolidredanddashedredbarsdenotetheenergywindowsusedforthepeakandbackgroundregionsofinterest(ROI),respectively.Thepeakaround448keVinenergyisfromthedecayofthe2677-keV6+
1statein70Ni.AtthetopoftheenergyrangeinFig.4.18,thelower-energyportionofthe511-keVpeakispresent.Thesetwospectralcontaminantsprecludeplacingthebackgroundregionintheimmediatevicinityofthe477.7-keVpeak.Therefore,theregionbetween402and426keVwaschosen.Thepeakregionofinterestrangesfrom464to488keV.149400450500110100Counts / 200 ps1010010001Time Difference (ns)9951000100510101015Energy (keV)(b)(a)Signal + Background101001000Counts / 200 ps(c)Background9901Figure4.19:(a)Two-dimensionalspectrumof-raysrecordedintheLaBr3detectorscoin-cidentwithadecayeventinthesegmentedplasticscintillatorvs.timedierencebetweentheLaBr3andsegmentedplasticscintillator.Thesolidredanddashedredbarsdenotetheenergywindowsusedforthepeakandbackgroundregionsofinterest(ROI),respectively.(b)and(c)Time-dierencespectra(LaBr3-segmentedplasticscintillator)obtainedbypro-jectingthespectrumin(a)ontothetime-dierenceaxisovertheregionsbetweenthesolid(peakROI)anddashed(backgroundROI)redlines,respectively.Thetime-dierencespectrabetweentheLaBr3detectorsandthesegmentedplasticscintillatorisshowninFig.4.19a.Thetime-dierencespectra(LaBr3-segmentedplastic150801001201401600.500.520.540.560.580.600.620.64Half Life (ns)c2Figure4.20:˜2asafunctionoftrialhalf-lifeusedineachconvolutiont,shownasblacksquares,andquadratict,showninred,forinterpolationbetweenpoints.Time Difference (ns)995100010051010Counts / 200 ps110100100010000DataBackgroundTotal FitConvolutionFigure4.21:Besttresultsforthelifetimeofthe0+
3statein68Ni.Inblackandbluearethetime-dierencespectraforthepeakandbackgroundROIsshowninFigs.4.19band4.19c,respectively.Theconvolutionofthedetectorresponsewiththebest-thalf-lifeisshowninRedandthetotaltofbackgroundplusconvolutionisshownincyan.scintillator),obtainedbyprojectingthespectrumin4.19aontothetime-dierenceaxisovertheregionsbetweenthesolid(peakROI)anddashed(backgroundROI)redlines,areshown151inFigures4.19band4.19c,respectively.Thetime-dierencespectrahaveanarticial1000nsosettoavoidnegativetimedierences.Basedonthetotalcountsinthepeak,obtainedfromaGaussiantintegratedoverthepeakROI,andthetotalcountsinthebackgroundROIthebackgroundspectrumwasscaledtocontainthepropernumberofcounts.ThenusingthetechniquesdescribedinSection3.8aseriesoftriallifetimeswereconvolvedwiththemeasureddetectorresponseandthe˜-squareminimizationprocedurewasusedtoextractthehalf-lifeandassociatederrorforthe0+
3statein68Ni.Figure4.20showsthe˜2asafunctionoftrialhalf-lifeusedineachconvolutiont.Theblacksquaresarethe˜2valuesforeachtrialhalf-lifeandtheredlineisaquadratictforinterpolationbetweenpoints.Thehalf-lifewastakenasthevalueattheminimumofthe˜2distribution.Thestatisticalerrorwasdeterminedfromthehalf-lifevaluesone˜2unitfromtheminimum.Systematicerrorswereinvestigatedbyvaryingquantitiessuchastheratioofcountsinthepeaktocountsinthebackground,thecentroidoftheunderlyingGaussiancomponentoftheconvolution,andthemagnitudeoftheDOIcorrection.Allerrorswereaddedinquadrature.Avalueof0.57(5)nswasobtainedforthehalf-lifeforthe(0+
3)statein68Ni.ThebesttisshowninFig.4.21.InFig.4.21,theblackandblue(blueisscaled)arethetime-dierencespectraobtainedforthepeakandbackgroundROIsfromFigs.4.19band4.19c,respectively.Theconvolutionofthedetectorresponsewiththebest-t0.57-nshalf-lifeisshowninRed.Thetotaltofthescaledbackgroundplusconvolutionisshownincyan.1524.2Decayof70CoThelow-energylevelschemeof70Niwasinvestigatedfollowingthedecayof70Co.decaysintheGeDSSDwerecorrelatedto70CoionsusingthetechniquesdescribedinSection3.5.2witha4000mscorrelationwindow.Therayscorrelatedtothedecayof70CoareshowninFig4.22.Transitionsidentiedinthepresentanalysisasbelongingto70Niarelabeledwiththeirenergywhilecontaminatingtransitions,resultingfromspuriouscorrelationsfromthedecayofotherimplantednuclei,areidentiedwithsymbols.1531500160017001800190020000100020003000SeGAEnergy (keV)1952.31943.81957.81866.51676.31641.6, 1644.5100011001200130014001500020004000600080001259.11392.91441.21037.51080.0500600700800900100005000100001500020000511594.1680.3, 683.3969.6915.3845.4607.6Counts / 1 keVCounts / 1 keVCounts / 1 keV(b)
(c)
(d)1230126012900500010000150001259.101002003004005000500010000150002000025000Counts / 1 keV448.4307.6234.7(a)68Co68Ni68Zn69Ni69Cu69Zn70Zn70Cu70Ni Escape PeaksFigure4.22:-delayed-rayspectrumrecordedinSeGAwithin4000msofanimplanted70Coion.Transitionsidentiedinthesubsequentanalysisasaliatedwiththedecayof70Niarelabeledwiththeirenergywhilecontaminatingtransitions,resultingfromspuriouscorrelationsofthedecayofotherimplantednuclei,aredenotedwithsymbols.Theinsetin(c)showsthefullheightofthe1259.1-keVpeakcutoinspectrumshownin(c).Theinsetin(e)showsthefullheightofthe2032.9-keVpeakcutoinspectrumshownin(e).154Figure4.22:(cont'd)35003600370038003900400001002003004005003984.03845.6
3853.4
3861.5
3871.73000310032003300340035000200400600SeGAEnergy (keV)3348.52500260027002800290030000500100015002614.62700.32777.42803.42950.7Counts / 2 keVCounts / 2 keVCounts / 2 keV(f)(g)(h)200021002200230024002500050010002104.82252.02294.3Counts / 2 keV(e)200020202040206002000400068Co68Ni68Zn69Ni69Cu69Zn70Zn70Cu70Ni Escape Peaks2190.53704.8155Figure4.22:(cont'd)30001002004215.34165.34132.44272.5
4294.94379.94479.34773.04822.54880.54901.25000520054005600580060000501004000420044004600480050001505131.05210.15711.460006200640066006800700002040606081.96283.76339.97000720074007600780080000246810SeGAEnergy (keV)Counts / 2 keVCounts / 2 keVCounts / 2 keVCounts / 2 keV(i)
(j)(k)(l)68Co68Ni68Zn69Ni69Cu69Zn70Zn70Cu70Ni Escape Peaks5772.64620.64313.61564.2.1-DecayingIsomersin70CoThe70Cobeamwasdeliveredtotheexperimentalendstationinamixtureoftwoisomericstates,bothobservedinpriorexperiments.Thebettercharacterizedofthetwohasaten-tative(6;7)spinandparityassignment[12]andanevaluatedhalf-lifeof114(7)ms[58].Thesecond-decaying70Coisomerhasbeenstudiedonceandhasanassigned,tentative,(3+)spinandparityandameasuredhalf-lifeof500(180)ms[12].TheworkofRef.[12]identiedseveral-delayed-raysuniquetothedecayofeachisomer.The448.5-keVtransitionisonesuchray,andisobservedfollowingthedecayoftheshort-lived,high-spin,70Coisomerexclusively.Forthisanalysis,theexclusiontechnique,describedinSection4.1.2.2,wasused.The70Codecaycurvevs.-rayenergyfrome14039intheregionaroundthe448.5-keVpeakisshowninFig.4.23a.TheprojectionontotheenergyaxisispresentedinFig.4.23b.ThedecaycurvesshowninFigs.4.24aand4.24bwereobtainedfromtheprojectionthe448.5-keVpeakregion(solidredlines)andbackgroundregion(dashedredlines),respectively,inFig.4.23ontothetime-dierenceaxis.ThebackgrounddecaycurveshowninFig.4.24bwasscaledandsubtractedfromthedecaycurveinFig.4.24a.Thebackground-subtracteddecay-curveisshowninblackinFig.4.25a.Thespurious-correlationcomponentwasdeterminedusingthetechniquesinSection4.1.2.1.Thetwo-dimensionaltime-dierencevs.coincident-rayenergyspectrum,withtheanalysisrunbackwardsintime,isshowninFig.4.12a.TheprojectionofthespectrumshowninFig.4.12aontotheenergyaxisispresentedinFig.4.26b.TheratioofthepeakareasbetweenFigs.4.23band4.26bistheratioofspuriouscorrelationstototalcountsinthebackground-subtracteddecaycurve.Thedecaycurve157010002000300040000100200300400500600420440460480500010000Energy (keV)Counts / 1 keVTime Difference (ms)(a)(b)Figure4.23:(a)Decaycurvevs.coincident-rayenergy,recordedinSeGAduringe14039,fortheregionaroundthe448.5-keVpeak.(b)Projectionof(a)ontotheenergyaxis.Setsofsolidredverticallinesanddashedverticallinesidentifythepeakandbackgroundregions,respectively,foreachpeak.0100020003000400001000200030000100020003000Time Difference (ms)Time Difference (ms)Counts / 20 msTime-DifferenceProjection from443 to 453 keVTime-DifferenceProjection from433 to 443 keV(a)(b)Figure4.24:(a)and(b)Decaycurvesobtainedbyprojecting4.23aontothetime-dierenceaxisovertheregionsof(a)443to453keVand(b)433to443keV.Theregionshownin(a)encompassesthe448.5-keVpeakwhile(b)isarepresentativebackgroundtobescaledandsubtractedfromthepeak.158-10-50510Counts / 20 ms100100070Co DecayRandom Correlations Data
Random Correlations FitDataTotal FitGated on448.5-keV70Co t= 104.5(20) ms1/2NormalizedFit Residual(a)01000200030004000Time (ms)(b)Figure4.25:(a)Background-subtracted,-gateddecaycurveforthedecayoftheshort-lived,high-spin,70Coisomerinto70Ni.Agatewasplacedonthe448.5-keVtransitionsin70Nitoisolatedtheshort-lived,high-spin,isomerexclusively.Thebackground,scaledappropriatelyandsubtracted,wassampleddirectlybelowthepeak.Thebackground-subtracteddataareshowninblackwhilethespuriouscorrelationcomponent,obtainedusingthetechniquesinSection4.1.2.1,isshowninblue.Incyan,attothespuriouscorrelationcomponentisshown,andwasusedtorepresentthespuriouscorrelationsinthetotaltofthedatashowninred.Thecorrelatedcontributionfromthedecayof70Coisshowningreen.Thehalf-lifeofshort-lived,high-spin,70Coisomer,extractedfromthet,is104.5(20)mswhichagreeswiththeevaluatedvalueof114(7)ms[58].(b)Fitresiduals,normalizedtothebinerror,forthetotaltcomparedtothedatain(a).
forspuriouscorrelationseventswasobtainedfromprojectingthespectrumshowninFig.4.26aontothetime-dierenceaxis,andisshowninblueinFig.4.25.Attothespuriouscorrelationdata,shownincyaninFig.4.25,wasusedinlieuofthedatatoprovideasmoothlyvaryingcomponentforuseinthetotaltshowninredinFig.4.25.Thetotaltwasacombinationofthespuriouscorrelationcomponentandanexponentialdecay.Theexponentialdecaycomponent,fromtherealcorrelationsbetween68Feanditssubsequent1594204404604800200040006000Counts / 1 keVEnergy (keV)420440460480010002000300040000102030405060Time Difference (ms)(a)(b)Figure4.26:Resultsoftheanalysisrunbackwardsintimethroughthedata.(a)Decaycurvevs.coincident-ray,recordedinSeGAduringe14039,fortheregionaroundthe448.5-keVpeak.(b)Projectionof(a)ontotheenergyaxis.
decay,extractedfromthetisshowningreen.Theresultsofthetyieldedahalf-lifeof104.5(20)msfortheshort-lived,high-spin,70Coisomerwhichagreeswiththeevaluatedvalueof114(7)ms[58].TheworkofRef.[12]identieda607.6-keVtransitionexclusivelyaliatedwiththedecayofthelong-lived,low-spin,70Coisomer.Thesameanalysistechniquesusedfortheshort-lived,high-spin,70Coisomerwereemployedagainforthisanalysis.The70Codecaycurvevs.-rayenergyduringe14039fortheregionaroundthe607.6-keVpeakisshowninFig.4.27a.TheprojectionontotheenergyaxisispresentedinFig.4.27b.ThedecaycurvesshowninFigs.4.28aand4.28bwereobtainedfromtheprojectionthe16005010015020025030001000200030004000Time Difference (ms)58060062064066010002000300040005000Counts / 1 keVEnergy (keV)(a)(b)Figure4.27:(a)Decaycurvevs.coincident-rayenergy,recordedinSeGAduringe14039,fortheregionaroundthe607.6-keVpeak.(b)Projectionof(a)ontotheenergyaxis.Setsofsolidredverticallinesanddashedverticallinesidentifythepeakandbackgroundregions,respectively,foreachpeak.
607.5-keVpeakregion(solidredlines)andbackgroundregion(dashedredlines),respectively,inFig.4.27ontothetime-dierenceaxis.ThebackgrounddecaycurveshowninFig.4.28bwasscaledandsubtractedfromthedecaycurveinFig.4.28a.Thebackground-subtracteddecay-curveisshowninblackinFig.4.29a.Thespurious-correlationcomponentwasdeterminedusingthetechniquesinSection4.1.2.1.Thetwo-dimensionaltime-dierencevs.coincident-rayenergyspectrumwiththeanalysisrunbackwardsintimeisshowninFig.4.12a.TheprojectionofthespectrumshowninFig.4.12aontotheenergyaxisispresentedinFig.4.30b.TheratioofthepeakareasbetweenFigs.4.27band4.30bistheratioofspurious1610100020003000400001000200030000100015002000Time Difference (ms)Time Difference (ms)Counts / 80 ms500Time-DifferenceProjection from603 to 613 keV(a)Time-DifferenceProjection from635 to 645 keV(b)Figure4.28:(a)and(b)Decaycurvesobtainedbyprojecting4.27aontothetime-dierenceaxisovertheregionsof(a)605to615keVand(b)635to645keV.Theregionshownin(a)encompassesthe607.6-keVpeakwhile(b)isarepresentativebackgroundtobescaledandsubtractedfromthepeak.
correlationstototalcountsinthebackground-subtracteddecaycurve.ThedecaycurveforspuriouscorrelationseventswasobtainedfromprojectingthespectrumshowninFig.4.30aontothetime-dierenceaxis,andisshowninblueinFig.4.29.Attothespuriouscorrelationdata,shownincyaninFig.4.29,wasusedinlieuofthedatatoprovideasmoothlyvaryingcomponentforuseinthetotaltshowninredinFig.4.29.Thetotaltwasacombinationofthespuriouscorrelationcomponentandanexponentialdecay.Theexponentialdecaycomponent,fromtherealcorrelationsbetween68Feanditssubsequentdecay,extractedfromthetisshowningreen.Theresultsofthetyieldahalf-lifeof470(20)msforthelong-lived,low-spin,70Coisomerwhichagreeswiththepreviousmeasuredvalueof500(180)ms[12].162-10-50510Counts / 80 ms1000NormalizedFit Residual(a)10070Co DecayRandom Correlations Data
Random Correlations FitDataTotal FitGated on607.6 keV70Co t= 473(20) ms1/201000200030004000Time (ms)(b)Figure4.29:(a)Background-subtracted-gateddecaycurveforthedecayoftheshort-lived,high-spin,70Coisomerinto70Ni.Agatewasplacedonthe607.5-keVtransitionsin70Nitoisolatedtheshort-lived,high-spin,isomerexclusively.Thebackground,scaledappropriatelyandsubtracted,wassampleddirectlybelowthepeak.Thebackground-subtracteddataareshowninblackwhilethespuriouscorrelationcomponent,obtainedusingthetechniquesinSection4.1.2.1,isshowninblue.Incyan,attothespuriouscorrelationcomponentisshown,andwasusedtorepresentthespuriouscorrelationsinthetotaltofthedatashowninred.Thecorrelatedcontributionfromthedecayof70Coisshowningreen.Thehalf-lifeofshort-lived,high-spin,70Coisomer,extractedfromthet,is470(20)msforthelong-lived,low-spin,70Coisomerwhichisconsistentwiththepreviouslymeasuredvalueof500(180)ms[12].(b)Fitresiduals,normalizedtothebinerror.16301000200030004000Time Difference (ms)(b)0204060805001000150020002500580600620640660Energy (keV)Counts / 1 keV(a)
(b)Figure4.30:Resultsoftheanalysisrunbackwardsintimethroughthedata.(a)Decaycurvevs.coincident-ray,recordedinSeGAduringe14039,fortheregionaroundthe607.6-keVpeak.(b)Projectionof(a)ontotheenergyaxis.1644.2.2A=70DecayCurvesWiththehalf-livesofthetwo-decaying70Coisomersmeasured,the70Codecay-curve,showninblackinFig.4.31a,wasttedandthenumberofdecaysfromeachisomerextracted.ThelocationoftheionandsubsequentdecayhadtobeinthesameGeDSSDpixelforthisanalysis.TheexclusiontechniquedescribedinSection4.1.2.2wasusedagainforthisanalysis.Boththeexclusionwindowandcorrelationwindowweresetto4000ms.The4000mscorrelationwindowwaschosentoprovidealongtimeregiontoproperlytthebackgroundandtoencompassnearlyallthelong-livedisomerdecays.Thetimedistributionofspuriouscorrelationswasobtainedrunningthefullanalysisbackwardsintime[57].InFig.4.31a,thedata(black)aretwiththesumofspuriouscorrelations(blue)andtwoindependentseriesofBatemanequations,oneforeach70Coisomer.Figure4.31bshowsthepercentdierencebetweenthetandthedataasafunctionoftime.Forboththeshort-(solid)andlong-lived(dashed)isomerdecays,the70Coparent,70Nidaughter,and70Cugranddaughtercontributionsareillustratedasgreen,cyan,andmagentalines,respectively.Thetotaltisshownasaredline.Thehalf-livesof70Niand70CuwerexedtotheNNDCevaluatedvaluesof6.0sand6.6s[59],respectively.Theshort-andlong-lived70Coisomerhalf-liveswerexedto104.5msand470ms,respectively.Thenumberofcorrelateddecaysrecordedforeach70Co-decayingisomerwasobtainedbyintegratingtheBatemanequations.Thestatisticalerrorwasobtainedfromtheerrorinthetwhilethesystematicerrorwasevaluatedbyvaryingallxedhalf-liveswithintheiruncertainties.Thetotalnumberofcorrelateddecayswasusedtoobtaintheabsolute-rayecienciespresentedinTables4.9and4.11.ThesametechniquesdiscussedinSection4.1.2.5165Counts / 10 ms10210310410510670CoSL70NiSL70CuSLDataTotal Fit
Rnd. Corr.70CoLL70NiLL70CuLLNormalizedFit Residuals(a)Time (ms)01000200030004000(b)-505Figure4.31:(a)Decaycurveshowingthetimedistributionofrecordeddecayeventsfollowingwithin4000msofanimplanted70Coion.A4000ms\exclusionwindow"wassetfollowingtheimplantationofeachionsuchthatallsubsequentionswithinthatwindowwereignored.Thetotaltisshowninred,thedataareshowninblack,andthetimedistributionofspuriouscorrelations,obtainedbyrunningtheanalysisbackwardsintime,isshowninblue.The70Coparent,70Nidaughter,and70Cugranddaughtercontributionsareillustratedasgreen,cyan,andmagentalines,respectively.Theshort-livedisomerdecayisshownassolidlineswhilethelong-livedisomerdecayisshownasadashedline.Thehalf-livesof70Niand70CuwerexedtotheNNDCevaluatedvaluesof6.0(3)sand6.6(3)s[59],respectively.Fromthet,thehalf-lifeoftheshort-lived70Coisomerwasdeterminedtobe104(4)mswhileahalf-lifevalueof450(13)mswasextractedforthelong-lived70Coisomer.(b)Fitresidualsnormalizedtotheerrorineachbin.
wereappliedheretoobtainthespuriouscorrelationandexclusiontechniquecorrections.Table4.8presentstheintegratednumberofcountsfor68NiintheBatemanequationsandthecorrectionsforspuriouscorrelationsandtheexclusiontechniqueforbothexperiments.The\corrected"numberofdecayswasobtainedbymultiplyingtheintegratednumberofcountsbythespuriouscorrelationandexclusiontechniquecorrelationfactors.166Table4.8:Decaycurvetresultsandcorrectionfactorsfor70Niine14039.The\corrected"numberofdecaysisobtainedbymultiplyingtheintegratednumberofcountsbythespuriouscorrelationandexclusiontechniquecorrelationfactors.Thecorrectednumberofdecaysisthendirectlycomparabletothenon-exclusionanalysis-delayed-raystatistics.e14039IntegratedNumberofShort-Lived,High-Spin,70CoIsomerDecays0.474(10)106IntegratedNumberofLong-Lived,Low-Spin,70CoIsomerDecays0.522(14)106SpuriousCorrelationCorrection2.06(2)ExclusionTechniqueCorrection1.22(1)CorrectedNumberofShort-Lived,High-Spin,70CoIsomerDecays0.96(2)106CorrectedNumberofLong-Lived,Low-Spin,70CoIsomerDecays1.31(4)106Theexistenceoftwoisomerscomplicatestheanalysisrequiredtocreateindividualdecayschemesforeach-decaying70Coisomer.Thenextsectiondescribestheadaptationofatechnique,developedinthemid1980s,thatultimatelyprovidesthecapabilitytodeterminethecontributionofeachisomerowingthroughanydetected-raytransition.4.2.370CoIsomerDeconvolutionInordertoconstructthedecayschemesforboth70Coisomersall-delayedraysmustbeidentiedandplaced.Indecayspectroscopy,onetypicallyexaminescoincidencestoplacetransitionsandidentifynewlevels.However,inthepresenceofmorethanone-decayingstatetheprocessismorecomplicatedandadditionaltechniquesareneeded.Onemethodtodeterminewhetheraparticularrayisaliatedwiththedecayofanisomeristoexaminethecorrespondingdecaycurve.Thistechniquewasdemonstratedearlierinthischapterforthe448.5-and607.6-keVtransitions.Inadditiontoprovidinghalf-lifeinformation,theratioofcountsineachexponentialdecaycomponentcanprovidethecontributionofeachisomertotheintensityofthattransition.Aprimeexampleisthe1259.1-keVtransitionwhichhasbeenobservedtocollectintensity167fromthedecayofboth70Coisomers[12].Figure4.32showsthebackground-subtracteddecay-timedistributiongatedonthe1259.1-keV(2+
1!0+
1)collectingtransition.TheprocedureusedtoobtaintheresultspresentedinFig.4.32isidenticaltotheprocessesdescribedforgeneratingFigs.4.25and4.29andthesameexclusionanalysistechniqueswereused.Thecorrelationandexclusionwindowsweresettothesame4000mstoencompassseveralhalf-livesofthelong-livedisomer.Counts / 20 ms10102103-505NormalizedFit Residuals70CoSLDataTotal Fit
Rnd. Corr.70CoLL(a)01000200030004000Time (ms)(b)Figure4.32:(a)Decaycurveshowingthetimedistributionofrecordeddecayeventsfollowingwithin4000msofanimplanted70Coiongatedonthe1259.1-keV(2+
1!0+
1)transition.Thesame4000ms\exclusionwindow"wassetfollowingtheimplantationofeachionsuchthatallsubsequentionswithinthatwindowwereignored.Thetotaltisshowninred,thedataareshowninblack,andthescaledtimedistributionofspuriouscorrelationsusedinFig.4.31,obtainedbyrunningtheanalysisbackwardsintime,isshowninblue.The70Coparentisshowningreenandtheshort-andlong-livedisomerdecaysareshownassolidanddashedlines,respectively.Half-livesof106(5)and446(42)mswereextractedfromthetfortheshort-andlong-lived70Coisomers,respectively.Thesevaluesareconsistentwiththe104.5(20)and470(20)msdeterminedearlierinthissection.(b)Fitresidualsnormalizedtothebinerror.168InFig.4.32,thedata(black)aretwiththesumofspuriouscorrelations(blue)andtwoexponentialdecays,ofthetypegiveninEq.(2.20),oneforeach70Coisomer,showningreensolidanddashedlinesfortheshort-andlong-livedisomers,respectively.Thespurious-correlationcomponentwasxed,butallotherparameterswerefree.ThepercentdierencebetweenthetandthedataasafunctionoftimeisshowninFig.4.32b.The1259.1-keV-gateddecaycurvetyieldsconsistenthalf-livescomparedtoboththe70Codecaycurvetaswellasthe448.5-and607.6-keV-gated70Codecaycurvets.Theintensitycontributionratio(short-lived/long-lived)throughthe1259.1-keVtransitionis0.77(8).Thisexampledemonstratestheabilitytoperform-gateddecaycurvetsforrelativelyhighstatisticscases,butformosttransitionsofinterestthismethodwillnotyieldusefulinformationpurelyduetostatisticslimitations.Fortunatelyatechnique,formulatedinRef.[60],existstotransformthedataoftraditionaldecaycurve,withlineartimeaxis,toatimedistributionwithlogarithmictimeaxis.Thefunctionalformofthedecaycurveforparentnucleus,givenoriginallyinEq.(2.20),ispresentedagaininEq.(4.1).dndt=net(4.1)Then,bymakingthetransformationln(t)=,thefrequencydistributionfromequation(4.1)becomesthatofequation(4.2)[60].dnd=neee(4.2)Thismethodeectively\compresses"thedataintoafunctionalform,peakedatln(1),towhichamorerobusttcanbeperformedevenincasesofpoorstatistics.Inthecase169ofthe1259.1-keV-gateddecaycurve,thesame400binsofdataoverthe4000mstimewindow,showninFig.4.32,arecompressedinto58binsinthetransformed1259.1-keV-gateddecaycurve,showninFig.4.33.ThedatainFig.4.33werettedwiththesamecomponentsasFig.4.32,butofthetransformedfunctionalforms.Counts0100020003000-505NormalizedFit Residual70CoSLDataTotal Fit
Rnd. Corr.70CoLL(a)123456789Ln [Time (ms)](b)Figure4.33:(a)Transformeddecaycurveshowingthenaturallogarithmofthetimedistribu-tionofrecordeddecayeventsfollowingwithin4000msofanimplanted70Coiongatedonthe1259.0-keV(2+
1!0+
1)transition.Thesame4000ms\exclusionwindow"wassetfollowingtheimplantationofeachionsuchthatallsubsequentionswithinthatwindowwereignored.Thetotaltisshowninred,thedataareshowninblack,andthescaledtimedistributionofspuriouscorrelationsusedinFig.4.31,obtainedbyrunningtheanalysisbackwardsintime,isshowninblue.The70Coparentisshowningreenandtheshort-andlong-livedisomerdecaysareshownassolidanddashedlines,respectively.Half-livesof104(5)and440(50)msfortheshort-andlong-lived70Coisomers,respectively,wereextractedfromthet.(b)Fitresidualsnormalizedtothebinerror.Thetransformed,backgroundsubtracted,1259.1-keV-gateddecaycurvetgivesshort-andlong-lived70Coisomerhalf-livesof104(5)msand440(50)ms,respectively,andaninten-170sitycontributionratio(short-lived/long-lived)of0.80(7)throughthe1259.1-keVtransition.Thetransformeddecay-curvetresultsareconsistentwiththatofthetraditionaldecaycurvetvalidatingthetechniqueforusewiththepresentdata.Thismethodcanbeextendedtotthetime-dierencedistributionfromtheprojectionofeachenergybinofthetwo-dimensionaltransformedtime-dierence(decay-implant)vs.coincident-rayenergyspectrum.InFig.4.34,thenaturallogarithmofthetimedierencebetweendecayand70Coionimplantationisshownontheyaxishistogrammedvs.coincident-delayed-rayenergyfrom0to1500keVonthexaxis.ThezaxisrepresentscountsperunittimedierenceperkeV.SeGAEnergy (keV)050010001500Ln[Time (ms)]12345678902004006008001000Figure4.34:Naturallogarithmofthetimedierencebetweendecayand70Coionimplan-tation,shownontheyaxis,ishistogrammedvs.coincident-delayed-rayenergyfrom0to1500keVonthexaxis.ThezaxisiscountsperunittimedierenceperkeV.AdecaycurvetlikethatshowninFig.4.33wasperformedontheprojectioneachenergybinofFig.4.34ontothelogarithmictimeaxis.Thetwascomposedoftransformed,short-andlong-livedisomercomponentsalongwithaspuriouscorrelationcomponent.Theintegratednumberofcountsundereachtateachenergybinisthecontributionfromeach171componentatthatcoincident-rayenergy.Thenumberofcountsineachcomponentateachenergybinwereadjustedforspuriouscorrelationsusingthespuriouscorrelationcorrectionfactorof2.06(2)presentedin4.8.InFig.4.35theresultsofthebin-wisedecay-curvettingdescribedaboveareshown,wheretheshort-andlong-livedisomercontributionsareshownasgreenandmagenta,respec-tively,whilethespuriouscorrelationcomponentisshowninblue.Thesumofallcomponentsisshowninredandthetotalprojectionofthetwo-dimensionalspectrumontotheenergyaxisisshowninblack.Thegoodagreementbetweentheredandblackspectraindicatesnocountsarelostinthedeconvolutionprocess.172010020030040005000100004005006007008000500010000800900100011001200050001000012001300140015001600010002000SeGAEnergy (keV)Counts / keVCounts / keVCounts / keVCounts / keV(a)
(b)
(c)
(d)12001300050001000015000DataTotal Fit
Background70CoSL70CoLLFigure4.35:Resultsofttingtheprojectionsofeachenergybinontothetimeaxisofthetwo-dimensionalhistogramofthenaturallogarithmofthetimedierencebetweendecayand70Coionimplantationvs.coincident-delayed-rayenergy.Theintegralofeachcomponentisshownasahistogram.Theshort-andlong-livedisomercontributionsareshownasgreenandmagenta,respectively,whilethespuriouscorrelationcomponentisshowninblue.Thesumofallcomponentsisshowninredandthetotalprojectionofthetwo-dimensionalspectrumontotheenergyaxisisshowninblack.Theinsetin(d)showsthefullheightofthe1259-keVtransitioncutoin(d).Theinsetin(e)showsthefullheightofthe2033-keVtransitioncutoin(f).173Figure4.35:(cont'd)160017001800190020000100020003000Counts / 2 keV200021002200230024000200400240025002600270028000200400600280029003000310032000100200300Counts / 2 keVSeGAEnergy (keV)Counts / 2 keVCounts / 2 keV(e)
(f)(g)(h)203020501000200030002010174Figure4.35:(cont'd)320034003600380040000200400Counts / 4 keV400042004400460048000200400Counts / 4 keV480050005200540056000100200Counts / 4 keV56005800600062006400020406080Counts / 4 keV(i)(j)(k)
(j)SeGAEnergy (keV)1754.2.4DecayoftheShort-Lived70CoIsomerMuchofthelow-energylevelschemeof70Nipopulatedbythedecayoftheshort-lived,high-spin,70Coisomerisknown.Thethreelowest-energyexcitedstatesoftheyrastbandin70Nihavemeasuredenergiesof1259keV,2229keV,2677keV[61]withassignedspinsandparitiesof2+,4+,and6+,respectively[23].Thesethreestatesareconnectedviathe448-keV(6+
1!4+
1),970-keV(4+
1!2+
1),and1259-keV(2+
1!0+
1)transitions.Afourthyrastbandmember,the(8+)stateat2860keVwithameasuredhalf-lifeof0.21(5)s[62],isalsoknownbutnotpopulatedinthepresentwork.ThedecayspectroscopyworkofRef.[12]identiedastateat3362keVandassignedatentative(6;7)spinandparitybasedoncomparisonswiththedecayof68Co.The3362-keVstatewasobservedtodecaytothe2677-keV6+
1stateviaa683-keVray[12].Asubsequentinvestigation[63]alsoobservedthe683-keV-rayandconrmedtheplacementfeedingthe2677-keVstate.TheworkofRef.[63]alsoidentiedanew916-keVrayandassignedittodepopulateanew(5)stateat3146keV.Recentmultinucleontransferandsecondaryfragmentationstudies[23]haveidentiedthesame683-and916-keVtransitionsin70NibutdisagreewiththeplacementsuggestedbyRefs.[12,63].Thismorerecentworkplacedthe683.1-keV-rayfeedingthe2229-keV4+
1fromanewstateat2912keVwitha(5)spinandparityandanew234-keVtransitionisalsoobservedtodepopulatethis2912-keV(5)statefeedingthe2677-keV6+
1state[23].Anewstateat3758-keV,witha(7)spinandparity,wasidentiedinRef.[23]todepopulateby1080-keVand846-keVtransitionsfeedingthe6+
1and(5)states,respectively.Furthermore,itwasproposedthatthe914.4-keVraydepopulatesanew(6)stateat3592keVfeedingthe2677-keV6+
1state[23].176Inthepresentworkalltransitionspreviouslyobservedhavebeenidentied,withtheexceptionofthe183-keV(8+
1!6+
1)transition.Threenewtransitionsandtwonewlevelsin70Niwerefoundandplacedtobefedexclusivelybytheshort-lived,high-spin,70Coisomer.Table4.9presentsalistofall-raytransitionsobservedfollowingthedecayoftheshort-lived,high-spin,70Coisomer,theirabsoluteintensities,andtheinitialandnalstatesbetweenwhicheachtransitionoccurs.Absoluteintensitieswerecalculatedbydividingthenumberofcountsineachpeak,obtainedfromaGaussiantplusalinearbackgroundcomponent,correctedfor-rayeciency,bythenumberofshort-lived,high-spin,70Coisomerdecays,correctedforbothspuriouscorrelationsandexclusiontechniquelosses,listedinTable4.8.Table4.9:Energiesandabsoluteintensitiesofthe-raytransitionsidentiedin70Nifol-lowingthedecayoftheshort-lived,high-spin,70Coisomer.Theenergiesoftheinitialandnalstatesbetweenwhicheachtransitionoccursarealsolisted.E(keV)Iabsolute(%)InitialState(keV)FinalState(keV)234.7(1)8.3(8)29122677
448.4(1)69.5(35)26772229
680.3(3)15.9(15)35922912
683.3(3)20.3(20)29122229
845.4(2)4.8(6)37572912
915.3(1)49.7(26)35922677
969.6(1)97.7(50)222912591080.0(2)5.5(4)37572677
1259.1(1)96.6(49)12590
1392.9(1)5.3(4)43052912
1641.6(2)3.1(4)43192677Theplacementofraysinthe70Nilevelschemewasaccomplishedusingcoinci-dences.AppendixCcontainsallcoincidencespectrafollowingthedecayoftheshort-lived,high-spin,70Coisomer,andasummaryofallobservedcoincidencesisshowninTable4.10Usingtheabsolute-rayintensitiesfromTable4.9,andthecoincidencerelationships177Table4.10:Summaryof-raycoincidencesobservedfollowingthedecayoftheshort-lived,high-spin,70Coisomer.E(keV)CoincidentE(keV)234.7448.4,680.3,845.4,969.6,1259.1,1392.9
448.4234.7,680.3,845.4,915.3,969.6,1080.0,1259.1,1641.6680.3234.7,448.4,683.3,969.6,1259.1
683.3680.3,845.4,969.6,1080.2,1259.1,1392.9
845.4234.7,448.4,683.3,969.6,1259.1
915.3448.4,969.6,1259.1
969.6234.7,448.4,680.3,683.3,845.4,915.3,1080.0,1259.1,1392.9,1641.61080.0448.4,969.6,1259.1
1259.1234.7,448.4,680.3,683.3,845.4,915.3,1080.0,1259.1,1392.9,1641.61392.9683.3,969.6,1259.1
1641.6448.4,969.6,1259.1describedabove,summarizedinTable4.10,thedecayschemefortheshort-lived,high-spin-decaying70Coisomerwasconstructed,presentedinFig.4.36.The-decayQvalueusedforthisanalysiswas12.3(3)MeV,takenfromRef.[56].Itiscurrentlyunknownwhich70Coisomeristhegroundstateandtheenergydierencebetweenthetwoisomersisalsounknown.ThisresultsinsomeadditionalsystematicuncertaintyontheQvalueandthusthelogftvalues.ThedecayschemepresentedinFig.4.36isdiscussedingreaterdetailinthenextchapter.1781259.1969.6448.4234.7683.3680.3915.3845.41080.01392.91641.670Ni2(3)70(3)3.1(4)10(1)02912359237572229
12594305267743190+(5)-(6)-(7)-4+2+6+E (keV)Jp3(4)
8(6)-1(7)I(%)!logft4.10(3)4.90(4)5.4(4)5.03(5)5.27(8)070Co= (6,7)--Jpb-100(9) %t= 104.5(20) ms
Q- = 12.3(3) MeV1/2ba(7)-(6)-5.70(65)
5.69(92)
5.37(50)Figure4.36:Decayschemefortheshort-lived,high-spin,70Coisomer.Statesin70NiarelabeledwithanenergyinkeVandthespininparity(ifknown)ontheright.Ontheleft,-decaybranchingratiosandlog10ftvaluesareshown.QvaluetakenfromRef.[56].1794.2.5DecayoftheLong-Lived70CoIsomerTherstobservationofthelong-livedlowspinisomerwasmadeinRef.[12].Thisworkaddedonenewstateinthe70Nilevelschemeat1868keV,assignedaspinandparityof2+,andfedexclusivelybythelong-lived,low-spin,70Coisomer.A607-keV(2+
2!2+
1)transitionanda1868-keV(2+
2!0+
1)transitionwereobservedtodepopulatethe1868-keV2+
2state[12].Subsequentstudiesconrmedthe1868-keV2+
2stateandthedepopulatingtransitionsfromRef.[12]andalsolocatedatentative(4+
2)statewhichdecaysbya640-keVraytothe1868-keV2+
2state[23].The(4+
2)stateisnotobservedinthecurrentwork,mostlikelydueto-decayselectionrules.Additionally,Ref.[23]reportedanew1950-keVtransitioncoincidentexclusivelywiththe1259.1-keV(2+
1!0+
1)transition.Assuch,thetransitionwasplaceddepopulatinganewlevelat3209keV.Theremainderofthissectionpresentsthefullanalysisofthedecayofthelong-lived,low-spin,70Coisomer.Alistofall-raytransitionsobservedfollowingthedecayofthelong-lived,low-spin,70CoisomerarepresentedinTable4.11alongwiththeirabsoluteintensities,andtheinitialandnalstatesbetweenwhicheachtransitionoccurs.Absoluteintensitieswerecalculatedbydividingthenumberofcountsineachpeak,obtainedfromaGaussiantplusalinearbackgroundcomponent,correctedfor-rayeciency,bythenumberoflong-lived,low-spin,70Coisomerdecays,correctedforbothspuriouscorrelationsandexclusiontechniquelosses,listedinTable4.8.180Table4.11:Energiesandabsoluteintensitiesofthe-raytransitionsidentiedin70Nifollowingthedecayofthelong-lived,low-spin,70Coisomer.Theenergiesoftheinitialandnalstatesbetweenwhicheachtransitionoccursarealsolisted.E(keV)Iabsolute(%)InitialState(keV)FinalState(keV)307.6(1)7.1(5)15671259594.1(1)a2.7(2)--607.7(1)23.4(13)186712591037.5(3)2.8(3)22961259
1259.1(1)65.1(33)12590
1441.2(1)2.0(3)27001259
1644.5(1)3.0(3)35111867
1676.3(1)3.4(3)29351259
1866.5(1)18.5(10)18670
1943.8(2)1.1(1)35111567
1952.3(2)3.0(2)321112591957.8(3)a1.04(5)--2104.8(1)2.8(4)33641259
2252.0(3)1.2(2)35111259
2294.3(7)0.6(3)22960
2531.0(5)0.6(2)37901259
2614.6(1)2.0(5)38741259
2700.3(3)2.1(3)270002777.4(3)b0.7(2)571229352803.4(3)b1.3(3)573829352950.7(5)b0.4(2)61623211aTransitionbelongsto69Nifollowing-delayedneutronemissionbTransitionplacedin70NiwithoutcoincidencesusingonlyenergydierencescTransitiononlyobservedincoincidences181Table4.11:(cont'd)E(keV)Iabsolute(%)InitialState(keV)FinalState(keV)3348.5(4)b1.2(3)628329353845.6(5)1.3(2)57121867
3853.4(5)1.4(2)51121259
3861.5(5)1.7(2)572818673871.7(5)b1.5(2)573818673984.0(5)1.2(3)585018674004.3(4)c2.0(7)526312594132.4(5)1.5(2)59991867
4165.3(3)2.6(2)60321867
4215.3(2)4.2(4)60821867
4272.5(5)1.5(2)613918674294.9(5)b1.3(2)616118674379.9(8)0.8(2)62461867
4479.3(5)1.2(2)573812594773.0(20))b0.4(2)603212594822.5(4)1.0(2)60821259
4880.5(8)0.6(1)614012594901.2(10)0.6(1)61611259
5711.4(10)0.7(1)571206081.9(5)0.9(1)60820
6283.7(7)0.7(1)62830
6339.9(8)0.4(1)63400aTransitionbelongsto69Nifollowing-delayedneutronemissionbTransitionplacedin70NiwithoutcoincidencesusingonlyenergydierencescTransitiononlyobservedincoincidences182InTable4.11,tworayswithenergiesof594.1keVand1957.8keVarelisted,whichbelongto69Niandarelikelypopulatedvia-delayedneutronemission.Any-delayedneutronemissionproceedingdirectlytothegroundstatewouldnotbeobservedinthepresentwork,sothesumoftheabsoluteintensityofthesetwotransitionsprovidesalowerlimitof3.5%onthemagnitudeofthe-delayedneutronemissionbranch.Thebackground-subtracted-rayspectrumcoincidentwiththe1259.1-keV(2+
1!0+
1)transitionwithin4000msofthedecayof70CoisshowninFigure4.37.InFig.4.38thebackground-subtracted-rayspectracoincidentwiththe607.6-keV(2+
2!2+
1)[panels(a)and(b)]and1866.5-keV(2+
2!0+
1)[panels(c)and(d)]transitionswithin4000msofthedecayof70Coarepresented.Thebackgroundwastakensymmetricallyonbothsidesofeachpeak.Coincidencesaliatedwiththelong-lived,low-spin,70Coisomerarelabeledwithanenergywhilecoincidencesaliatedwiththeshort-lived,high-spin,70Coisomeraredenotedwithblacksquares.Contaminatingcoincidencesaredenotedwithblackupside-downtrianglesandlabeledwiththeoendingisotope,ifknown.Thestrong1259.1-607.6-keVcoincidenceobservedinFig.4.37aaswellasinFig.4.38aisconsistentwiththepreviouswork.Furthermore,astrong1866.5-keVtransitionisobserved,whichisnotincoincidencewiththe1259.1-keV(2+
1!0+
1)transition,andis,alongwiththe607.6-keVtransition,coincidentwithstrongtransitionsthatareproposedtofeedthe2+
2state.Theexistenceandplacementofthe607.6-keVand1866.5-keVraysisconsistentwithpreviousworkofRefs.[12,23].Theobservationofthe307.6-keVtransitionisnewfromthiswork.Astrong307.6-1259.1-keVcoincidenceisshowninFig.4.37.NocoincidenceswereobservedhigherinthelevelschemeinFigs.4.38aor4.38c.Furthermore,nocoincidenceswereobservedinFigs.C.1bthroughC.1jbetweenthe307.6-keVrayandtransitionsaliatedwiththeshort-lived,low-183100005002000150025003000250040003500450050001510050200400600Counts / 2 keVCounts / 2 keV4004.0*4132.44822.542154165.34880.5, 4901.2607.6307.61037.51441.21644.51676.31943.8, 1952.32104.82252.0511x102614.5Energy (keV)Gated1259.1 keV(b)(a)1259.1Gated4004 keVRegion5
01100120013001400Energy (keV)Counts / 2 keV3704.870Co Short-Lived IsomerEscape PeaksFigure4.37:Backgroundsubtractedcoincidencespectrumgatedonthe1259.1-keV(2+
1!0+
1)transitionwithin4000msofthedecayof70Cofrom(a)0to2500keVand(b)from2500to5000keV.Thebackgroundwastakensymmetricallyeithersideofthe1259.1-keVpeak.Coincidencesaliatedwiththelong-lived,low-spin,70Coisomerarelabeledwithanenergywhilecoincidencesaliatedwiththeshort-lived,high-spin,70Coisomeraredenotedwithblacksquares.Escapepeaksaredenotedwithblackstarsandtransitionsseenincoincidencesbutnotinsinglesaredenotedwithasingleasterisk.spin,70Coisomer.Theonlyothercoincidenceobservedwiththe307.6-keVtransitionisa1943.8-keVtransition.Thecoincidencespectraaliatedwitthe307.6-and1943.8-keVtransitionsareshowninFigs.4.39aand4.39b,respectively.18410500100200300Counts / 2 keV1259.11644.510000500200015002500300025004000350045005000Counts / 2 keV(b)(a)x103984.03845.6
3861.54132.44165.34215.0
4272.54294.94380.0100005002000150025003000250040003500450050004165.34215.04380.01644.551170Zn69Cu69Cu70Zn70ZnEnergy (keV)Energy (keV)Counts / 2 keVCounts / 2 keV(d)(c)50040
20x5Gated1866.5 keVGated607.7 keVFigure4.38:Backgroundsubtractedcoincidencespectrumgatedonthe607.6-keV(2+
2!2+
1)[panels(a)and(b)]and1866.5-keV(2+
2!0+
1)[panels(c)and(d)]transi-tionswithin4000msofthedecayof70Co.Thebackgroundwastakensymmetricallyeithersideofeachpeak.Coincidencesaliatedwiththelong-lived,low-spin,70Coisomerarelabeledwithanenergywhilecoincidencesaliatedwiththeshort-lived,high-spin,70Coisomeraredenotedwithblacksquares.Contaminatingcoincidencesaredenotedwithblackupside-downtrianglesandlabeledwiththeoendingisotope,ifknown.185-50050Counts / 2 keV1259.11943.8-5051015Counts / 2 keV1259.1307.6Gated1943.8 keVGated307.6 keV(a)(b)010002000Energy (keV)010002000Energy (keV)Figure4.39:Backgroundsubtractedcoincidencespectrumgatedonthe(a)307.6-keVand(b)1943.8-keVtransitionswithin4000msofthedecayof70Co.Thebackgroundwastakensymmetricallyeithersideofthe307.6-keVpeakandbelowthe1943.8-keVpeakduecloselyneighboringtransitions.Coincidencesaliatedwiththelong-lived,low-spin,70Coisomerarelabeledwithanenergy.Basedonthecoincidencerelationshipsandtheratioof-rayintensities,itwasdeterminedthatthe1943.8-keVtransitionisabovethe307.6-keVtransitioninthe1943.8-307.6-1259.1-keV-raycascade,placinganewlevelat1567keVaswellasanewlevelat3511-keV.Asearchforagroundstatetransitionoutofthenew1567-keVstatewasunsuccessful.InFigs.4.40aand4.40btheregionaround1567-keVinthe1943.8-keVgatedand-gated-raysinglesspectra,respectively,isshown.1550156015701580350400450Counts / 1 keV-202Counts / 2 keV1550156015701580Energy (keV)Energy (keV)(a)(b)Gated1943.8 keVb-GatedSinglesFigure4.40:(a)Backgroundsubtractedcoincidencespectrumgatedonthe1943.8-keVtransitionwithin4000msofthedecayof70Co.(b)Beta-gated-raysinglesspectrumwithin4000msofthedecayof70Co.Bothspectrahighlighttheregionaround1567keVandno1567-keVpeakisobservedineitherspectrum.Basedonthelackofagroundstatetransition,exclusivealiationwiththedecayof186thelong-lived,low-spin70Coisomer,andnon-observationinmultinucleontransferreactionspopulatingyraststates[23]atentativespinandparityof(0+
2)isassignedtothe1567-keVstate.AdditionalsupportforthisassignmentwasprovidedbythegoodagreementbetweentheMCSMcalculations,discussedfurtherinthenextchapter,andthedata.AnattemptwasmadetolookfortheE0transitionconnectingthe(0+
2)and0+
1states,butnothingwasobservedintheplanarGeDSSD.However,theshorthalf-lifeofthe(0+
2)(resultspresentedlaterinthissection)meansthatadouble-pulseanalysisintheGeDSSDwouldnotbesensitivetoit.Basedonthe-raystatisticsobtainedhereandusingtheBrIccinternalconversioncoe-cientdatabase[34]alimitwasplacedontheexpectedE0intensity.A1567-keVE0transitionin70Niwoulddecayby40.4%pairproduction,withtherestbeinginternalconversion.Byexaminingthe511-keVregionofthespectrumshowninFig.4.39b,aminimumof˘5countswouldberequiredtoseeapeakat511keV.Correctingfortheeciencyofsucha511-keVtransition,108raysofthisenergywouldbeexpectedtobeemittedincoincidencewiththe1943.8-keVfeedingtransition.Dividingthisresultbytwo,toaccountforthefactthattwo511-keVraysareemittedperpair-productionevent,andconsideringthe40.4%pair-productionbranch,approximately133E0transitionswouldfollowthe1943.8-keVtransition.InFig.4.39b,thereare26(8)countsinthe1943.8-307.6-keVcoincidence.Whencorrectedfortheeciencyofthedetectorarrayfora307.6-keVray,onewouldexpect400(150)307-keVrayscoincidentwiththe1943.8-keVtransition.TheratiooftheupperlimitofE0transitionstothetotal,E0transitionsplus307.6-keVrays,givesanupperlimitontheE0branchof33%outofthe1567-keVstate.Inadditiontothe307.6-keVtransition,severalothernewrayshavebeenobserved.ThecoincidencespectrausedtoplacethesetransitionsarepresentedinAppendixD.187AsumofallobservedcoincidencesisshowninTable4.12
Table4.12:Summaryof-raycoincidencesobservedfollowingthedecayofthelong-lived,low-spin,70Coisomer.E(keV)CoincidentE(keV)307.6(1)1259.1,1943.8
607.7(1)1259.1,3845.6,3861.5,3984.0,41324,4165.3,4215.0,4272.5,4294.9,4380.01037.5(3)1259.1
1259.1(1)307.6,607.6,1037.5,1441.2,1644.5,1676.3,1943.8,1952.3,2104.8,2252.0,2614.5,4132.4,4004.0c,4132.4,4165.3,4215.0,4822.5,4880.5,4901.21441.2(1)1259.1
1644.5(1)607.6,1259.1,1866.5
1676.3(1)1259.1
1866.5(1)1644.5,4165.3,4215.0,4380.0
1943.8(2)307.6,1943.8
1952.3(2)1259.1
2104.8(1)1259.1
2252.0(3)1259.1
2531.0(5)1259.1
2614.6(1)1259.1
3845.6(5)607.6
3853.4(5)1259.1
3861.5(5)607.6,1259.1,1626c,1866.53984.0(5)607.6,1259.1,1866.54004.3(4)c1259.14132.4(5)607.6,1259.1,1866.5
4165.3(3)607.6,1259.1,1866.5
4215.3(2)607.6,1259.1,1866.5
4272.5(5)607.6
4379.9(8)607.6,1259.1,1866.5
4479.3(5)771.9c,1259.14822.5(4)1259.1
4880.5(8)1259.14901.2(10)1259.1cTransitiononlyobservedincoincidencesUsingtheabsolute-rayintensitiesfromTable4.11andthecoincidencerelationshipsdescribedabove,summarizedinTable4.12,thedecayschemeforthelong-lived,low-spin,70Coisomerwasconstructed,andispresentedinFig.4.36.The-decayQvalueusedforthisanalysiswas12.3(3)MeV.takenfromRef.[56].Asstatedintheshort-livedisomer188analysis,itisnotknownwhich-decaying70Coisomeristhegroundstate.Inaddition,theenergydierencebetweenthetwo-decayingisomersisalsounknown.Assuch,someadditionaluncertaintyontheQ-valueandthusthelogftvaluesexists.Thedecayschemeforthelong-lived,low-spin,70CoisomerispresentedinFig.4.41.InadditiontotheraysplacedinthelevelschemeshowninFig.4.41,thereweresomeunplacedrayspotentiallyaliatedwiththelong-lived,low-spin,70Coisomer.TheenergyandabsoluteintensitiesoftheseunplacedtransitionsarelistedinTable4.13.Table4.13:Summaryofunplacedrayspotentiallyaliatedwiththedecayofthelong-lived,low-spin,70Coisomer.E(keV)Iabsolute(%)771.9(1)c0.6(4)1026.2(1)c1.1(7)2585.4(4)0.9(2)
5131.0(4)1.3(2)5210.1(10)0.7(2)cTransitionobservedexclusivelyincoincidencesandisnotconclusivelyaliatedwiththelong-lived,low-spin,70Coisomerdecay4.2.6Half-Lifeofthe(0+
2)statein70NiAmeasurementofthehalf-lifeofthe1567-keV(0+
2)statewasperformedusingthetimingmethodpresentedinSection3.9.The307.6-keVraywasdetectedintheLaBr3detectors,describedinSection3.8,coincidentwiththe-decayelectrondetectedinthePSPMT,detailedinSection3.6.The-gated70Cocorrelated(2000mscorrelationtime)LaBr3energyspectrumintheregionofthe307.6-keVtransitionisshowninFig.4.42a.Unfortunately,duetothesmallnumberof70Coionsdeliveredtotheexperimentalendstationduringe14057,comparedtoe14039,andtherelativelypoorenergyresolutionoftheLaBr3detectors,comparedto1896339.96283.73348.54379.94901.24294.92950.76081.94822.54215.04773.04165.34132.44479.33871.72803.43984.03861.54004.03853.42614.52531.01644.51943.82252.02252.01952.31676.32700.31441.22294.31037.51866.5607.6307.61259.1125915671867229627002935321133643874351137905113526357285738585159996032608261396162624662846340571102+(0)+2+0+10(4)6.0(6)21(2)3.5(4)4.1(4)0.2(6)2.6(3)2.8(4)2.0(5)5.4(4)0.6(2)2.0(6)2.6(3)1.7(2)4.0(4)1.2(3)1.5(2)3.1(3)6.1(5)2.1(2)2.3(3)0.8(2)1.9(3)0.5(1)1.4(2)<76.14(25)6.28(6)5.67(6)6.37(7)6.20(6)7.50(196)6.27(7)6.21(8)6.23(17)5.89(5)6.75(20)5.84(20)6.03(9)5.77(8)5.38(7)5.87(15)5.71(8)5.40(7)5.09(5)5.48(8)5.90(13)5.51(11)6.13(14)5.57(7)>6.86E (keV)I(%)!70Ni70Co= (1)+Jpbb--< 96.5 %,-n > 3.5%t= 473(20) ms
Q- = 12.3(3)MeV1/2baa4880.5
4272.53845.6
2777.45711.4Jplogft1.6      ns+1.2-0.85.53(7)Figure4.41:Decayschemeforthelong-lived,low-spin,70Coisomer.Statesin70NiarelabeledwithanenergyinkeVandthespininparity(ifknown)ontheright.Ontheleft,-decaybranchingratiosandlog10ftvaluesareshown.aQ-valuetakenfromRef.[56].SeGA,the307.6-keVpeakisnotapparentinFig.4.42a.However,the307.6-keVtransitionisclearlyobservedinthe-gated70CocorrelatedSeGAspectrumshowninFig.4.42b.190100200
150Counts / 1 keVCounts / 2 keV300350400Energy (keV)40005000600070008000900005101520(a)
(b)LaBr3with2000 msCorrelationTimeSeGAwith2000 msCorrelationTime100200
150Counts / 2 keV300350400Energy (keV)Counts / 2 keVLaBr3with noIon CorrelationPrompt (50 ns)with theDecaybSpectrum in (c) gatedon the 1259-keVtransition in SeGA(c)
(d)Figure4.42:(a)and(b)Spectrumof-raysrecordedintheLaBr3andSeGAdetectors,respectively,coincidentwitha70Codecayeventinthesegmentedplasticscintillator.(c)Spectrumof-raysrecordedintheLaBr3coincidentwithadecayeventinthesegmentedplasticscintillator.(d)Spectrumshowninpanel(c)gatedonthe1259.1-keVtransitioninSeGA.Inpanels(c)and(d)thecoincidencewindowbetweentheLaBr3detectorsandPSPMTwas50nsandin(d)theLaBr3-SeGAcoincidencewindowwas600ns.Inallpanelsthesetofsolidredanddashedredbarsrepresenttheenergywindowsusedforthepeakandbackgroundregionsofinterest,respectively.Anattemptwasmadetoforgoioncorrelationsandexaminethe-gatedLaBr3energyspectrum.SincethePSPMTandLaBr3detectorshavegoodtimeresolution,thecoincidencewindowwasshortenedfrom10sto50nstoelminaterandomcoincidences.The-gatedLaBr3energyspectrumintheregionofthe307.6-keVtransitionisshowninFig.4.42c.Thenumberofimplanted70Coionswasarelativelysmallcomponentofthetotalimplantedionsandthereisnoevidenceofthe307.6-keVpeakinFig.4.42c.The307.6-keVtransitionisknowntofeedthe1259-keV2+
1statewhichdecaysbya1259.1-keV-ray.Agateonthe1259.1-keV-rayrecordedinSeGAwasplacedonthespectrumshowninFig.4.42candtheresultingspectrumispresentedinFig.4.42d.TheLaBr3-SeGAcoincidencewindowwas600ns.Withthepresentstatistics,andthedetectionecienciesofthe307.6-keVtransition191300350400110100(a)Energy (keV)Counts / 400 ps1101001000(b)Signal + BackgroundCounts / 400 ps1101001000Time Difference (ns)9951000100510101015990(c)BackgroundFigure4.43:(a)Two-dimensionalspectrumof-raysrecordedintheLaBr3detectorscoin-cidentwithadecayeventinthesegmentedplasticscintillatorvs.timedierencebetweentheLaBr3andsegmentedplasticscintillator.Thesolidredanddashedredbarsdenotetheenergywindowsusedforthepeakandbackgroundregionsofinterest(ROI),respectively.(b)and(c)Time-dierencespectra(LaBr3-segmentedplasticscintillator)obtainedbypro-jectingthespectrumin(a)ontothetime-dierenceaxisovertheregionsbetweenthesolid(peakROI)anddashed(backgroundROI)redlines,respectively.1920.51.01.52.02.53.030405060c2Half-Life (ns)Figure4.44:˜2asafunctionoftrialhalf-lifeusedineachconvolutiont,shownasblacksquares,andquadratict,showninred,forinterpolationbetweenpoints.Time Difference (ns)9951000100510101015Counts / 400 ps1101001000DataTotal FitBackgroundConvolutionFigure4.45:Besttresultsforthelifetimeofthe(0+
2)statein70Ni.Inblackandbluearethetime-dierencespectraforthepeakandbackgroundROIsshowninFigs.4.43band4.43c,respectively.Theconvolutionofthedetectorresponsewiththebest-thalf-lifeisshowninRedandthetotaltofbackgroundplusconvolutionisshownincyan.intheLaBr3detectorsandthe1259.1-keVtransitioninSeGA,35(7)countsareexpectedinthe307.6-keVpeakinFig.4.42d.BasedontheLaBr3resolutionandthebinningofFig.1934.42d,a307.6-keVpeakwouldbeˇ4countsinheight,whichissmallerthanthevariationinthebackground.Thislevelofstatisticsprecludestheuseoftimingtechniques.SincenostrongpeakwasobservedintheLaBr3spectruminFig.4.42athenumberofcountsexpectedinthepeakROIwasdeducedfromthesimulated-raydetectionecienciesofSeGA,showninFig.3.40,andthemeasuredratioofeciencies(LaBr3/SeGA)presentedinFig.3.44.ThepeakROIisdenotedwithsolid-redverticallinesinFigs.4.42aand4.43aandcoverstheregionof296to318keV.ThebackgroundROI,denotedwithdashed-redverticallinesinFigs.4.42aand4.43a,wastakendirectlyabovethepeakROIfrom326to358keVandthecorrespondingbackgroundspectrawerescaledappropriatelyinthet.ThetwosmallpeaksobservedinFig.4.42bat327.0keVfrom68Coand339.6keVfrom70CucontaminatethebackgroundROIbuthavenomeasurablehalf-livesandthusdidnotaecttheanalysis.Thetime-dierencespectrabetween-rays,detectedintheLaBr3detectors,andcoin-cidentdecays,detectedinthesegmentedplasticscintillator,wasextractedbyprojectingthetwo-dimensionalLaBr3energyvs.time-dierencespectrum,showninFig.4.43a,ontothetime-dierenceaxisforeachofthetworegions.Anarticialosetof1000nswasaddedtothetime-dierencetoavoidnegativetimedierences.Thetime-dierencespectra(LaBr3-segmentedplasticscintillator)obtainedfromprojectingthespectrumin(a)ontothetime-dierenceaxisovertheregionsbetweenthesolid(peakROI)anddashed(backgroundROI)redlinesareshowninFigs.4.43band4.43c,respectively.BasedonthetotalcountsexpectedinthepeakandthetotalcountsrecordedinthebackgroundROIthebackgroundspectrumwasscaledtocontainthepropernumberofcounts.Then,usingthetechniquesdescribedinSection3.8,aseriesoftriallifetimeswereconvolvedwiththemeasureddetectorresponseandthe˜-squareminimizationprocedure194wasusedtoextractthehalf-lifeandassociatederrorforthe(0+
2)statein70Ni.The˜2asafunctionoftrialhalf-lifefromeachtispresentedinFig.4.44.Theblacksquaresarethe˜2valuesforeachtrialhalf-life,andtheredlineisaquadratictforinterpolationbetweenpoints.Thehalf-lifeforthe(0+
2)statewastakenfromthehalf-lifecorrespondingtotheminimumofthechisquaredistributioninFig.4.44.Thestatisticalerrorwasdeterminedfromthehalf-lifevaluesone˜2unitfromtheminimum.Systematicerrorswereinvestigatedbyvaryingquantitiessuchastheratioofcountsinthepeaktocountsinthebackground,thecentroidoftheunderlyingGaussiancomponentoftheconvolution,andthemagnitudeoftheDOIcorrection.Allerrorswereaddedinquadrature.Avalueof1.65+0:300:25nswasobtainedforthehalf-lifeforthe(0+
2)statein70Ni.ThebesttisshowninFig.4.45.InFig.4.45,theblackandblue(blueisscaled)arethetime-dierencespectraobtainedforthepeakandbackgroundROIsfromFigs.4.43band4.43c,respectively.Theconvolutionofthedetectorresponsewiththebest-t1.65-nshalf-lifeisshowninRed.Thetotaltofthescaledbackgroundplusconvolutionisshownincyan.195Chapter5
DiscussionandOutlook
Inthischapterthesignicanceofthepresentresultsarediscussed.Inparticular,theresultssuggestthepresenceofshapecoexistencein68NiandprovideevidencethatshapecoexistenceextendsfurtheralongtheNiisotopicchaininto70Ni.Comparisonswithadvancedshellmodelcalculationsaremadeandprovidesomeinsightintotheimportanceofvariousexcitationsandcongurationstodescribingthestructuresof68;70Ni.Attheconclusionofthischapter,anoutlookisprovidedtodirectfurtherinvestigationsintheregion.5.1ShapeCoexistencein68;70NiThepresentresultsreportnewlifetimeandbranchingratiomeasurementsfor68;70NithatcanbeusedtodeducetransitionprobabilitiesforE0andE2transitions.Measuredlifetimesforexcitedstatesin68;70Ni,bothfromthepresentworkandtheliterature,aredisplayedinTable5.1.Additionally,measuredbranchingratiosforseveraltransitionsconnectingthesestatesarealsopresentedalongwithˆ2(E0)andB(E2)valuesdeterminedusinghalf-livesandbranchingratioswithEqs.(2.39)and(2.28),respectively.Thesevaluesextractedfromexperiment,showninTable5.1,arecomparedwiththere-sultsofshellmodelcalculationsemployingtheA3DA[(0f1p0g9=21d5=2)ˇmodelspace]andLNPS[(0f1p)ˇ(0f1p0g9=21d5=2)modelspace]eectiveinteractionsinFig.5.1.Additionalshell-modelcalculations,witheectiveinteractions[65{67]overmodelspaceslackingproton196Table5.1:Half-lives,branchingratios,andeitherabsoluteB(E2)ine2fm4orˆ2(E0),de-pendingonthenatureofthetransition.Jˇit1=2JˇfBRB(E2)ˆ2(E0)68Ni0+
2272(3)ns0+
11.0-0.0075(1)2+
10.31(5)psa0+
10:999+0:0010:0552.5(84)-0+
21.2(3)103147(46)-0+
30.57(5)ns0+
1<0:0173-<0:00500+
2<0:0018-<0:02582+
1>0:98139.0(34)-70Ni2+
11.04(17)psb0+
11.0172(28)b-(0+
2)1.65+0:300:25ns2+
1>0:66>70-0+
1<0:33-<0:54afromRef.[22]bfromRef.[64]excitations,successfullyreproducetheenergyofthe0+
2in68Nistatebutfailtopredictboththe0+
3[18,19]statein68Niandthe(0+
2)[23]statein70Ni,andarenotconsideredhere.Beginningwiththe0+
2in68Ni,thededucedB(E2:0+
2!2+
1)valueof147(46)e2fm4agreeswellwithboththeA3DAandLNPSinteractions,whichgive168and182e2fm4,respectively.Theobservationofthisstrongcollectivetransition0+
2!2+
1lendsexperimentalsupportthatthe2+
1and0+
2havesimilarcongurationsaspredictedbythecalculations[7].The0+
2statewasfurtherinvestigatedwithintheframeworkofatwo-levelmixingmodel,discussedinSec.1.3,assumingthe0+
2statecanbedescribedbythemixingofsphericalanddeformedcongurations.UsingEq.(2.47)andtheB(E2)valuesforthe2+
1!0+
2and2+
1!0+
1transitions,themixingangle,,wasdeducedandusedtocalculateamixingamplitudeofcos2()=0:74(7).Thisvalueagreeswellwithcomplimentaryrelativecrosssectionmeasurementsforthepopulationofthe0+
1and0+
2statesinthe66Ni(t,p)68Nireaction[70]whichresultedinalowerlimitofcos2()>0:7.Whilethemixedandclosed-shellcongurationscouldnotbedistinguishedinRef.[70],thepresentresultsstronglyfavormixing.19768Ni70Ni0+23262+1820A3DA160028880.210+108 ns15.11.1 ps19892+0+0+1368LNPS0262915.10+168411.5 ns
0.4 ps2+0+0+2033
1604
0147(46)Exp.25110+0.31(5) ps0.57(5) ns268(12) ns39.0(34)52.5(84)r2(E0) < 0.0050r2(E0) < 0.0258r2(E0) = 0.0075(1)312131213110+228.9>70(0)+2Exp.012591567A3DA0137715250+12+10+22+10+1r2(E0) < 0.547.1 ns74.2172(28)1.04(17) ps2.4 ps1.65          ns-0.25+0.30Figure5.1:Half-livesandtransitionstrengthsofthelowestfourstatesin68Ni(left)andthelowestthreestatesin70Ni(right)comparedwithpredictionsofadvancedshellmodelcalculationsusingtheLNPS[21]andA3DA[68]eectiveinteractions.Half-livesofthestates,whenknown,aregivenontheupperleftsideofeachlevelwiththeassociatedenergies(inkeV)onthelowerleftside.Unobservedtransitionsareindicatedbydottedlines.ElectricmonopoletransitionstrengthsaregivenfortheE0transitions,whileB(E2)values,inunitsofe2fm4,aregivenforE2transitions.Experimentalvaluesforthe2+
1statehalf-lifeandB(E2)for70NiareadoptedfromRef.[64].Notethat,whileLNPSpredictionsofthe70NiB(E2:0+
2!2+
1)valuehavenotbeenpublishedsofar,Ref.[69]indicatesacalculatedB(E2:2+
1!0+
1)valueof102e2fm4withthisinteraction(notshown).UsingEq.(2.44),themeasuredˆ2(E0)forthe0+
2!0+
1transition,andthemixingamplitude,cos2(),thedierenceinmeansquarechargeradiibetweenthe0+
2and0+
1stateswasdeterminedtobehr2i=0:17(2)fm2.Assumingaspherical0+
1state,theabsolutevalueoftheintrinsicquadrupolemomentofthe0+
2stateisjQ0j=93(5)efm2,whichagreeswellwiththeboththeA3DAandLNPSpredictionsofQ0=95efm2[18]andjQ0j=93efm2[8],respectively.Examiningthe0+
3statein68Ni,themeasuredhalf-lifeof0.57(5)nsismuchshorterthanthevalueoftheA3DApredictionof108ns[21],butcomparesmorefavorablywiththe1.5-ns[21]half-lifefromtheLNPSpredictions.Assuch,theabsoluteB(E2:0+
3!2+
1)of19839.0(34)e2fm4deducedfromexperimentissignicantlylargerthanthe0.21e2fm4fromtheA3DAcalculations,butagainagreesbetterwiththe15.1e2fm4fromtheLNPScalculations.Thecurrentworkisonlyabletoplacelimitsonthe0+
3!0+
2and0+
3!0+
1E0transitionbranches.Usingthebranchingratiolimits,andthenewlymeasuredhalf-lifeofthe0+
3state,limitsonˆ2(E0)of<0:0258and<0:0050canbeplacedfortheformerandthelatter.Duetothemorecomplicatedcongurationspredictedbytheoryforthe0+
3state,atreatmentwithinthetwo-levelmixingmodel,similartowhatwasdoneforthe0+
2state,wouldnotbeinstructive.Transitioningfrom68Nito70Ni,theA3DAcalculationspredictadeepeningoftheprolatepotentialwell[7]andaconcomitantdropintheenergyoftheassociatedprolate-deformed0+statefrom2511keVin68Nito1525keVin70Ni.Thedeepeningoftheprolatewellisex-plainedbythestrengtheningoftheattractive0g9=2ˇ0f5=2andrepulsive0g9=2ˇ0f7=2monopoleinteractionsofthetensorforcewithadded0g9=2occupancy.Theseinteractionsservetodecreasetheenergydierencebetweentheˇ0f7=2andˇ0f5=2singleparticlestatesincreasingthelikelihoodofexcitationsintotheˇ0f5=2,whichisthedominantprotonexci-tationintheprolate-deformed0+statesin68;70Ni[7,23].Inthepresentwork,the(0+
2)stateisobservedat1567keV,ingoodagreementwiththeenergyvalueof1525keVpredictedbytheA3DAcalculations.TheworkofRef.[23]proposedthe2+state,observedat1867keVinthepresentwork,andthe2508-keV4+state,notpopulatedinthepresentwork,asmembersofadeformedbandbuiltonthe(02+)state.Theirclaimwasbasedontheabsenceofcorrespondingstatesat1867and2508keVinshell-modelcalculationsexcludingprotonexcitations.ThestrongE5dependenceintheB(E2)favorsthe1867-keV2+
2!0+
1transitionoverthe300-keV2+
2!(0+
2)transition.ThepredictedratioofB(E2;2+
2!0+
2)/B(E2;2+
2!(0+
1)of400[23]precludedobservationof199the2+
2!(0+
2)transitionbothinsinglesandincoincidencewiththe1643.5-keVtransition.TheA3DAcalculationspredictavalueof7.2ns[68]forthehalf-lifeofthe(0+
2)state,whichisthecorrectorderofmagnitudewhencomparedwiththemeasuredhalf-lifeof1:65+0:300:25ns.TheexperimentalvaluefortheB(E2:0+
2!2+
1)hasalowerlimit(1˙)of>70efm2basedonthe>66%branchforthe307.5-keV0+
2!2+
1)transition.Ifoneassumesa100%-raybranchthenthevaluebecomes123+19
18efm2.Regardless,theB(E2:0+
2!2+
1)of28.9efm2predictedbytheA3DAcalculationsislowerthantheexperimentallowerlimit.Overall,whileboththeA3DAandLNPScalculationscorrectlypredicttheenergiesofallthestatesshowninFig.5.1,thetenuousagreementforthehalf-livesofthe0+
3statein68Niandthe0+
2statein70Niindicatesthereisroomforimprovementonthetheoreticalfront.Theinabilitytotreatthe0+
3statein68Niwithintheframeworkofthetwo-levelmixingmodelprecludesextractionoftheintrinsicquadrupolemomentandanystrongstatementsaboutexperimentalevidenceoftripleshapecoexistence.However,thequantitativedescriptionofthe0+
2veriesthepresenceofshapecoexistencein68Ni.5.2Analysisof-DecayStrengthandIntensityDis-tributionsin68;70NiInthissection,thecumulative-decaystrengthandintensitydistributionsarepresentedandcomparedwithshell-modelcalculations.Experimentally,the-decayfeedingsweredeterminedbythebalanceofabsolute-rayintensityrecordedinandoutofeachlevel.Sincethesefeedingsarebasedon-rayintensitybalancestheyarereferredtoas\apparent"feedings.Fromtheapparent-decayfeedingsandameasurementofthe-decayhalf-life,thepartialhalf-lifeiscalculatedusingEq.(2.10).TheFermiintegralisevaluatedforeach200stateusingEq.(2.12).B(GT)valuesaredeterminedusingEq.(2.11)assumingB(F)0.Whilethisassump-tionisnotentirelytrue,themajorityoftheFermistrengthwillbetotheisobaricanaloguestate,whichforneutron-richnuclei,isoutsidethe-decayQ-valuewindow.ThisisduetoanincreaseintheCoulombenergywiththeconversionofaneutrontoaproton.Inthecaseof68;70Nitheisobaricanaloguestatewouldbelocatedaroundˇ15MeVofexcitationenergy.Furthermore,sincethemajorityofthespinandparitiesremainunknownin68;70Ni,someambiguityregardingthecharacterof-decaytransitionsexists,andtheexperimen-tallydeterminedcumulativeB(GT)valuespresentedhereinwillcontaincontributionsfromforbiddendecay.Shell-modelcalculationspresentedinthissectionwereperformedusingthe0f1p0g9=20g7=2modelspaceforneutrons.TheprotoncongurationswerexedinthesecalculationssuchthatNiisotopespossessedalledZ=28shell,whileCoisotopeshadalledZ=28shellwithaholeintheˇ0f7=2single-particlestate.TheGXFP1AHamiltonian[71]wasusedforthe0f1pportionofthemodelspacewhilethe0gpartwascreatedusingtheN3LOinteraction[72]withaVlowkrenormalizationinto6majoroscillatorshells.Theeectivein-teractionwascreatedusingmany-bodyperturbationtheoryuptosecondorder[73].Single-particleenergieswereobtainedfromrelativebindingenergiesandlow-lyingexcitedstatesin69;70Ni,69Co,and71Cu.Thesingle-particleenergyspacingsbetweenthe0f7=20f5=2and0g9=20g7=2weresettoaround6MeV.Aquenchingfactorof0.6wasappliedtoallGamow-Tellerstrengths.2015.2.1Short-Lived,High-Spin,70CoIsomerThecongurationoftheshort-lived70Coisomerwastakentobe(0g9=2)3(ˇ0f7=2)1relativetotheclosedZ=28protonshellandN=40neutronsubshellclosures.A6spinandparityfromthecouplingofthe0g9=2neutronandˇ0f7=2protonholewasused.Statesin70Niwereformedfromallpossibleneutronone-particleone-hole(1p1h)excitationsrelativeto70Co.Acomparisonbetweentheapparentcumulative-decayintensitydistributionfromexperiment(blacklinewithsalmonerrorband)withthetheoreticalcumulative-decayintensitydistributionfromtheshellmodelcalculations(darkbluedashedline)ispresentedinFig.5.2.Theverticalreddashedlinerepresentsthe7792-keVneutronseparationenergy[22].Excitation Energy (keV)0200040006000800010000CumulativebIntensity (%)-20020406080100120ExperimentShell ModelShort-LivedCo Isomer Decay70Figure5.2:Apparentcumulative-decayintensitiesdeducedfromtheexperimentaldecayschemeinFig.4.36(blacklinewithsalmonerrorbars)comparedwithshellmodelcalcula-tions(dasheddarkblueline).Reasonableagreementbetweentheexperimentalandtheoreticalcumulative-decayin-tensitiesisobtainedandthecalculationgivesa104.5mshalf-lifewhichagreesquitewellwiththe104(2)msobtainedfromthepresentwork.Acomparisonbetweentheapparentcumulative-decaystrengthdistributionfromexperiment(blacklinewithturquoiseerror202band)withthetheoreticalcumulative-decaystrengthdistributionfromtheshellmodelcalculations(darkbluedashedline)ispresentedinFig.5.3.Againverticalreddashedlinerepresentsthe7792-keVneutronseparationenergy[22].020004000600080001000000.20.40.60.81.0Cumulative B(GT)ExperimentShell ModelShort-LivedCo Isomer Decay70Figure5.3:Apparentcumulative-decayintensitiesdeducedfromtheexperimentaldecayschemeinFig.4.36(blacklinewithturquoiseerrorbars)comparedwithshellmodelcalcu-lations(dasheddarkblueline).Inboththeexperimentalandtheoreticalstrengthdistributionsthemajorityofthestrengthistohigher-lyingnegativeparity5,6,and7states.Thisisexpectedsincedecayofthe6parenttothe0+,2+,4+,and6+statesofthe70Niyrastbandarefor-bidden,andthussignicantlyhindered.Lowe-energystatesstartingaround3592keVin70Niarepopulatedby0f5=2to0ˇf7=2decays,whilethesteadyrisestartingat˘6MeVexperimentaldistributionismostlikelyduetocontributionsfrom1ptoˇ1p,0f5=2toˇ0f5=2,and0g9=2toˇ0g9=2decayswhichcreatehigherenergyprotonholestatesin70Ni.Experimentally,most(˘70%)oftheapparent-decayfeedingistothe3592-keV(6)state.Inacomplimentaryexperiment,notdetailedinthisdissertation,atotalabsorptionspectroscopy(TAS)experimentwasperformedonthedecayofthis70Coisomer[29].Acomparisonoftheapparant-decayfeedingsbetweenthepresentworkandtheTASmea-203surementsuggeststhatwhilemostofthe-decayfeedingdoesindeedgotothe3592-keV(6),statethepresenthigh-resolutionspectroscopyattributesafactorof2excessfeedingtothe3592-keV(6)state.Thisispresumeablyduetothepandemoniumeect[74]wherealargenumberofundetectedlow-intensitytransitionsfeedthisstatefromseveralhigher-lyingstates.Thepandemoniumeectisunavoidableinthepresentlow-eeciencyhigh-resolutionspectroscopyexperiment,butismitigatedinTASduetothehighintrinsic-raydetectioneciencies(upto˘85%)ofTASdetectors[75].Inaddition,theTASmeasurementofRef.[29]observesastrongpreferencefor-rayemis-sionover-delayedneutronemissionabovetheneutronseparationenergy.Inthepresentworknoevidenceof-delayedneutronemissionisobservedconsistentwiththeTASmea-surment.TheoriginofthisbehaviourasexplainedbyRef.[29]ispoorspectroscopicoverlapbetweenneutron-unboundstatesin70Niandlow-lyingstatesin69Niwhichhindersneutronemission.Theoverallgoodagreementbetweenthepresentwork,theTASmeasurment,andtheshellmodelcalculationsuggeststhattheshort-lived,high-spin,70Coisomeriswelldescribedasaspherical6statewitha(0g9=2)3(ˇ0f7=2)1conguration.5.2.2Long-Lived,Low-Spin,70CoIsomerThecongurationofthelong-lived,low-spin,70Coisomerwastakentobe(0g9=2)4(1p1=2)1(ˇ0f7=2)1relativetotheclosedZ=28protonshellandN=40neutronsubshellclosures.Withintheframeworkofthesphericalshelhmodel,a3+spinandparityfromthecouplingofthe1p1=2andˇ0f7=2holeswasadoptedfromRef.[12].Asbefore,statesin70Niwereformedfromallpossibleneutronone-particleone-hole(1p1h)excitationsrelativeto70Co.Acomparisonbetweentheapparantcummulative-decayintensitydistributionfromexperi-204ment(blacklinewithsalmonerrorband)withthetheoreticalcummulative-decayintensitydistributionfromtheshellmodelcalculations(darkbluedashedline)ispresentedinFig.5.4.Theverticalreddashedlinerepresentsthe7307-keVnuetronseparationenergy[59].ExperimentShell ModelExcitation Energy (keV)0200040006000800010000CumulativebIntensity (%)-20020406080100120Long-LivedCo Isomer Decay70Figure5.4:Apparentcumulative-decayintensitiesdeducedfromtheexperimentaldecayschemeinFig.4.41(blacklinewithsalmonerrorbars)comparedwithshellmodelcalcula-tions(dasheddarkblueline).Thenatureofthe-decayfromthelong-lived,low-spin,isomerismostlikelyidenticaltothatoftheshort-lived,high-spin,isomer,wherebythelow-lyingGamow-Tellerstrengthisdominatedbythe0f5=2toˇ0f7=2decayswhiletheriseat˘6MeVintheexperimentaldistributionisagainduetocontributionsfrom1ptoˇ1p,0f5=2toˇ0f5=2,and0g9=2toˇ0g9=2decayswhichleavehigherenergyprotonholestatesin70Ni.Acomparisonbetweentheapparantcummulative-decaystrengthdistributionfromexperiment(blacklinewithturqoiseerrorband)withthetheoreticalcummulative-decaystrengthdistributionfromtheshellmodelcalculations(darkbluedashedline)ispresentedinFig.5.5.Again,theverticalreddashedlinerepresentsthe7307-keVnuetronseparationenergy[59].205Long-LivedCo Isomer Decay7000.20.10.30.4Cumulative B(GT)ExperimentShell ModelExcitation Energy (keV)0200040006000800010000Figure5.5:Apparentcumulative-decayintensitiesdeducedfromtheexperimentaldecayschemeinFig.4.41(blacklinewithturquoiseerrorbars)comparedwithshellmodelcalcu-lations(dasheddarkblueline).Thecalculationsignicantlyoverpredicts-decayfeedingtothe1260-keV2+
1state.Asaresult,the-decaystrengthdistributionisalsodiscrepantwithexperimentalresults.Despitethisdiscrepancy,thecalculationprovidesareasonablepredictionof592msforthehalf-lifeofthelong-lived,low-spin,70Coisomerforwhichtheexperimentalymeasuredvalueis450(13)ms.Thelargediscrepancyinthefeedingpatternpointstoadeciencyinourunderstandingofthecongurationofthelong-lived,low-spin,70Coisomer.Itsuggeststhatthelong-lived,low-spin,70Coisomerisnotwelldescribedbythespherical(0g9=2)4(1p1=2)1(ˇ0f7=2)1conguration,butinsteadhasamorecomplicatedcongurationand/oranincorrectspinandparityassignment.Recentlarge-scaleshell-modelcaclulationsusingtheA3DAinteraction[76]suggestthatlong-lived70Coisomerisprolatedeformedwith˘3protonsand˘3neutronsonaverageexcitedacrossZ=28andN=40,respectively.Basedontheevidenceofthedescending1=2intruderorbitalintheodd-Acobaltisotopes[15,16,77]withaddednuetronoccupancy206ofthe0g9=2,alikelycongurationforthelong-lived70Coisomerinvolvesthecouplingofthe[301]p1=2and[321]ˇp3=2Nilssonorbitals[55].Thiswouldyield1+and0+stateswiththe1+locatedlowerinenergy[78].Additionalsupportfora1+spinandparityassignmentcanbeobtainedbyexaminingthespinandparityofstatesfedin-decay.Thestrongestfeedingistothe1867-keV2+
2state(ˇ21%)followedbythe1260-keV2+
1state(ˇ10%).Whilethefeedingof2+statesalonedoesnotdiscriminatebetween1+and3+assigments,thelackoffeedingtothe2229-keV4+
1and2508-keV(4+
2)[23]states,butrelativelystrongfeedingtothe1567-keV(0+
2)state,favorsthe1+assignment.Thelargefeedingtothe2+
2comparedtothe2+
1,despitethedisadvantagefromthedecayenergydependenceoftheFermiintegral,suggestssimilarityintheunderlyingcongurationsbetweenthelong-lived,low-spin,70Coisomerandthe2+
2statein70Ni.BasedontheA3DAcalculationresults[7],the0+
2and2+
2areexpectedtobeprolateddeformedandhavecongurationswithalargecontributionfromprotonexcitations.Thislendsfurthersupportforaprolate-deformed1+long-lived,low-spin,70Coisomerwithacongurationcomprisedofmultipleparticle-holeexcitations.
5.2.3Long-Lived,Low-Spin,68CoIsomerAnalogoustothelong-lived70Coisomer,thecongurationofthelong-lived68Coisomerwastakentobe(0g9=2)2(1p1=2)1(ˇ0f7=2)1,relativeto68Ni,andthesame3+spinandparityfromthecouplingofthe1p1=2andˇ0f7=2holeswasadoptedfromRef.[12].Statesin68Niwereformedfromallpossibleneutronone-particleone-hole(1p1h)excitationsrelativeto68Co.Acomparisonbetweentheapparantcummulative-decayintensitydistributionfromexperiment(blacklinewithsalmonerrorband)withthetheoreticalcummulative-decay207intensitydistributionfromtheshellmodelcalculations(darkbluedashedline)ispresentedinFig.5.6.Theverticalreddashedlinerepresentsthe7307-keVnuetronseparationenergy[59].Excitation Energy (keV)0200040006000800010000CumulativebIntensity (%)-20020406080100120ExperimentShell ModelExcitation Energy (keV)0200040006000800010000CumulativebIntensity (%)-20020406080100120Long-LivedCo Isomer Decay68Figure5.6:Apparentcumulative-decayintensitiesdeducedfromtheexperimentaldecayschemeinFig.4.6(blacklinewithsalmonerrorbars)comparedwithshellmodelcalculations(dasheddarkblueline).Justaswiththedecayof70Co,itislikelythatthelow-lyingGamow-Tellerstrengthisdominatedbythe0f5=2to0ˇf7=2decayswhiletherisesat˘4MeVand˘6MeVintheexperimentaldistributionareduetocontributionsfrom1ptoˇ1p,0f5=2toˇ0f5=2,and0g9=2toˇ0g9=2decays,whichleavehigher-energyprotonholestatesin68Ni.Acomparisonbetweentheapparantcummulative-decaystrengthdistributionfromexperiment(blacklinewithturqoiseerrorband)withthetheoreticalcummulative-decaystrengthdistributionfromtheshellmodelcalculations(darkbluedashedline)ispresentedFig.5.7.Again,theverticalreddashedlinerepresentsthe7307-keVnuetronseparationenergy[59].Thepooragreementbetweenthecalculatedandexperimentalstrengthandintensitydistributionscloselymirrorsthatofthelong-lived,low-spin,70Coisomer.Thecalculation208Excitation Energy (keV)0200040006000800010000Cumulative B(GT)00.10.20.30.40.50.6ExperimentShell ModelLong-LivedCo Isomer Decay68Figure5.7:Apparentcumulative-decayintensitiesdeducedfromtheexperimentaldecayschemeinFig.4.6(blacklinewithturquoiseerrorbars)comparedwithshellmodelcalcu-lations(dasheddarkblueline).
signicantlyoverpredicts-decayfeedingtothe2+
1state,andthe115mshalf-lifepredictedbythecalculationisverydierentthanthemeasuredvalueof2330+790
460ms.Similartothelong-lived,low-spin,70Coisomer,thelong-lived,low-spin,68Coisomerisalsonotwellde-scribedbythespherical(0g9=2)2(1p1=2)1(ˇ0f7=2)1congurationanditlikelypossessesamorecomplicatedcongurationand/oranincorrectspinandparityassignment.Recently,twootherspinandparityassignmentshavebeenproposedforlong-lived,low-spin,68Coisomer.Themostrecentspinandparityassignemntis(2)fromthecouplingofthesamedownsloping[321]1=2+proton(originatingfromthesphericalˇ1p3=2)orbitalwiththe,alsodownsloping,[431]3=2+and[440]1=2+nuetron(originatingfromthespherical0g9=2)orbitals,atprolatedeformation[21].Experimentally-determinedlogftvaluespro-videsomesuppportforthisinterpretation,sincealldecaysto0;2;4+statesappeartoberst-forbiddendecay(logft>6).However,thelargelogftvalue(˘7)forthedecaytothe3301-keV(3)state,whichshouldbeanalloweddecay,isconicting.209Amoreplausiblespinandparityassignmentof1+wasproposedinRef.[55],deducedfromthelarge-decayfeedingtothisisomerfromthe0+groundstateof68Fe.The1+stateisexplainedbythecouplingofthe[321]1=2proton(originatingfromthesphericalˇ1p3=2)and[301]1=2neutron(originatingfromthespherical1p1=2)orbitalsatmodestprolate(ˇ0:2)deformation.Giventherecentpredictionsofthelarge-scaleshellmodelcalculationsusingtheA3DAinteractionfor70Co[76],andthealready-discussedsystematicsofintruderstatesintheregion,this(1+)isomerwouldlikelybequitesimilarincongurationto70Co.Justlikethecaseof70Co,thecouplingofthe[321]1=2proton(originatingfromthesphericalˇ1p3=2)and[301]1=2(originatingfromthespherical1p1=2)neutronstatesshouldgiverisetoa1+stateanda0+stateslightlyhigherinenergy[78].Basedonthe-decayschemepresentedinRef.[55],asecondstateatanenergyof45keVabovethe(1+)isomerispresentandalsostronglyfedbythedecayofthe0+ground-stateof68Fe.Basedonthe-raycoincidencesandtheestablished68Colevelscheme,theworkofRef.[55]deducedaninternalconversioncoecientof=1:0(4)forthe45-keVtransition.Valuesof=0:52and=0:37[34]areexpectedfortheinternalcoecientforE1andM1multipolarities,respectively.AssuminganE1transitionthe45+xcouldhaveaspinandparityof2,whichisdiscrepantwiththelogftof4.7(3)forthedecaytothisstate.However,thepresentworkcontainsafactorof˘5increaseinstatisticsoverRef.[55].Ameasurmentoftheinternalconversioncoecient,usingthesametechniques,givesavalueof0.18(10).Theexperimentally-deducedof0.18(10)comparesmorefavorablywiththe=0:37foranM1transition,suggestingthatthestateabovetheisomeristhesameparitywithJ=1.Sincethegroundstateof68Feisa0+state,itismostlikelythatthe45+xstateinRef.[55],fedstronglyby-decay,isaalsoa0+state.Thereforetheexpected0+210and1+states,closetooneanotherinenergy,fromthecouplingofthe[321]1=2proton(originatingfromthespherical1ˇp3=2)and[301]1=2(originatingfromthespherical1p1=2)neutronorbitals,appeartobesupportedbycurrentexperimentalevidence.Whilethe1+spinandparityisthefavoredassignmentforthelong-lived68Coisomer,thepresentspectroscopicevidenceisnotsucienttomakeadenitiveargument.Manystatesin68Nihaveonlytentativespinandparityassignmentsandthusfurtherinformationaboutthespinsandparitiesofadditionalstronglyfedstates,suchasthe4163-,5512-,5529-,5548-,5566-,and5774-keVstates,wouldhelpmakeamoresubstantivearguementaboutthespinandparityofthelong-lived,low-spin,68Coisomer.5.3Outlook
Theresultsofthisworkconstituteaquantitativedescriptionofexcited0+statesintheneutron-richnickelisotopesneartheN=40subshellclosure,andhavedemonstratedthatshapecoexistenceoccursin68Ni.However,therearemanyquestionsthatremainunan-swered.Doestripleshapecoexistance,likethatof186Pb,occurin68Ni?HowfaralongtheNiisotopicchaindoesshapecoexistenceextendandhowdoesitcomparewithcurrenttheoreticalpredictions?Whatisthenatureofthe-decayingisomersintheneutron-richCoisotopesandwhataretheirimplicationsforshapecoexistenceintheCoistopes?Thesequestionswillrequirealargeeortfromexperimentandtheoryalike.Inordertodeterminetheexistenceoftripleshapecoexistencein68Ni,aspredictedbylarge-scaleshellmodelcalculations[5,7{9],measurementsofthe0+
3!0+
2and0+
3!0+
1E0transitionsmustbemade.Togetherwiththenewly-measured0+
3statehalf-life,theelectricmonopoletransitionstrengthcouldbedeterminedandrelatedtothedierenceinmeansquarecharge211radiibetweenthe0+
3and0+
2,0+
1states.Furtherinvestigationintothenatureofthe(0+
2)statein70NimustbeperformedtoconclusivelyextendshapecoexistencefurtheralongtheNiisotopicchain.Firstconrmationofthe0+spinandparityisrequiredandthenobservationofthe(0+
2)!0+
1E0transitioncoupledwithamoreprecisehalf-lifemeasurementwillbeneededtodeducetheelectricmonopoletransitionstrenthandextractthedierenceinmeansquarechargeradiibetweenthe(0+
2)and0+
1states.Fromatheoreticalstandpoint,theabilitytomoreaccuratelyreproduceexcited-staethalf-livesandelectromagnetictransitionprobabilitiesisimportantforunderstandingtheunderlyingnucleoncongurationsandthusthemigrationofsingle-particlestates.Addi-tionally,E0transitionstrengthsfromtheory,reportedlycloseonthehorizon,wouldbeofinteresttofurtherinvestigateshapecoexistenceacrossthenuclearchart.Furtherexperimentalinvestigationofthe-decayingCoisomersisalsoimportant.Allattemptsthusfartoidentifytransitionsconnectingthepresumedprolateandspherical-decayingisomersin68;69;70Cohavebeenunsuccessful.Thustheenergyseparationsareunknownandeventheirorderingremainsunclear.Precisionmassmeasurementsareneededtodeterminethemassofeachisomer.Totalabsorptionspectroscopy(TAS)measurementsof68;69;70CodecaywouldallowexperimentaldeterminationoftheGamow-Tellerstrengthdistribution.Comparisonoflevelschemes,lifetimes,and-decaystrengthdistributionsbetweenexperimentandlargescaleshell-modelcalculationsfor68;69;70Cowouldprovidestringinttestsofcompetingtheoreticaldescriptions.212APPENDICES213AppendixA
IdenticationofAdditionalPeaks
ObservedinPulseShapeAnalysis
NotAliatedWiththe0+
2!0+
1Transitionin68NiInthisappendixthelow-energypeaksobservedinthepulse-shapeanalysisresultsfromtheGeDSSD,notaliatedwiththe0+
2!0+
1transitionin68Ni,arediscussed.The141.4-keVtransitioninFig.3.23comesfromthedecayofthe242.6-keVisomericstatein70Cuwhichhasahalf-lifeof6.6s[59].The185.0-keV,239.2-keV,and352.1-keVareroombackgroundlinesfrom226Ra,212Pb,and214Pb,respectively.Thepeakat92.6-keVisfromthedecayofthe93.3-keV1=2statein67Zn[79].Therstpulseenergiescoincidentwiththe92.6-keVsecondpulseenergypeakfromFig.3.28areshowninFig.A.1a.rays,detectedinSeGA,coincidentwiththe92.6-keVsecondpulseenergypeakfromFig.3.28arepresentedinFig.A.1b.21402004006008000100200300400500100.2308.3Counts / 2 keVFirst Pulse Energy (keV)Gated onSecond Pulse Energy92.6 keV010020030040050001020304050SeGAEnergy (keV)Counts / 1 keV91.4209.8300.0Gated onSecond Pulse Energy92.6 keV(a)(b)FigureA.1:(a)Coincidentrstriseenergiesofdoublepulseswitha92.6-keVsecondriseenergy.(b)GammaraysrecordedinSeGAcoincidentwithdoublepulsesrecordedintheGeDSSDwiththeenergyofthesecondriseinthe92.6-keVpeak.The92.6-keVtransitionobservedinFig.3.23wasplacedasthe(1=2!5=2)transitionin67Zn.The93-keVstate1=2statein67Znhasahalflifeof9.07(4)sandisfedbothdirectlyandindirectlythroughthedecayof67Cu[79].Thecoincidentrayswithenergiesof91.4,209.8,and300.0keV,showninFig.A.1b,areknowntofeed,directlyorindirectly,the93-keVstate[79].TheGeDSSDissensitivetobothelectronsandlow-energyraysandassuchbothwereobservedintherstriseenergyspectruminFig.A.1a.TheenergyrecordedinFig.215A.1acanbefromjustthe-decayelectron,justa-delayed-rayifthe-decayindirectlypopulatesthe93-keVstateandtheelectronand-raydepositenergyindierentstripsofthedetector,oracombinationofthesumofthe-decayelectronand-delayed-rayenergyifthedepositionsoccurinthesamestrip.Thebroadandcontinuousdistributionisfromthe-decayelectronsbothwithandwithoutsummingof-delayed-rays.Theisolated-rayeventsarethe100.2-and308.3-keVpeaksshiftedinenergybyˇ8.5keV.Theoriginofthisenergyshiftremainsunknown.Thepeakatˇ175keVisthedecayofthe174.9-keV5=2state[80]in71GepopulatedbysecondaryfragmentationoftheGeDSSDcrystalunderheavy-ionimplantation.TheraysdetectedinSeGAcoincidentwiththe175-keVsecondpulseenergypeakintheGeDSSDarepresentedFigureA.2.05001000150020000102030SeGAEnergy (keV)Counts / 1 keVGated onSecond Pulse Energy175 keV511**1139.2**806.2FigureA.2:GammaraysrecordedinSeGAcoincidentwithdoublepulsesrecordedintheGeDSSDwiththeenergyofthesecondriseinthe175-keVpeak.The511-and1139.2-keVpeaks,labeledwithtwoasterisks,arecoincidentwiththedecayofthe0+
2statein68Niduringeventswherethetherewasincompleteenergycollectionforthepair-productionorinternalconversiondecayprocesses.The806.2-keVpeakisnewandremainsunidentied.InFig.A.2,the511-and1139.2-keVpeaks,labeledwithtwoasterisks,arecoincidentwiththedecayofthe0+
2statein68Niduringeventswhereincompleteenergycollection216forthepair-productionorinternalconversiondecayprocessesoccurred.Thepeakat806.2keVisnewfromthisworkandremainsunidentied.The24-keVpeakobservedintherstriseenergyspectruminworkofRef.[81]duringthecommissioningoftheGeDSSDwasnotobservedinthepresentwork.Priorexperimentsdamagedthedetectorenoughtoprecludelowamplitudedoublepulsedetectionandhavedegradedtheenergyresolution.Theunresolvedhigh-energytailofthe175-keVpeakinFig.3.28bisfromthe190-keVtransitionwhichdepopulatesthe2742-keV(13/2+)statefeedingthe2552-keV(13/2+)statein69Cu[52],thegranddaughterof69CowhichwasimplantedintheGeDSSD.TheraysdetectedinSeGAcoincidentwiththe190-keVsecondpulseenergypeakintheGeDSSDarepresentedinFig.A.3.050010001500200005101520SeGAEnergy (keV)Counts / 1 keVGated onSecond Pulse Energy190 keV511**68118721357**1139.2**FigureA.3:GammaraysrecordedinSeGAcoincidentwithdoublepulsesrecordedintheGeDSSDwiththeenergyofthesecondriseinthe190-keVpeak.The511-keVpeak,labeledwithtwoasterisks,wascoincidentwiththedecayofthe0+
2statein68Niduringeventswherethetherewasincompleteenergycollectionforthepair-productionorinternalconversiondecayprocesses.The1357-keVpeakwascoincidentwithanunresolvedandunidentiedˇ200keVsecondpulseenergy.The681-and1870-keVtransitionsarefromthe680.6-1872.3-keV-raycascadethatdepopulatesthe2552-keVstatein69Cu[52].InFig.A.3,the511-keVpeak,labeledwithtwoasterisks,isagainfromthecoincidencewiththethedecayofthe0+
2statein68Niineventswithincompleteenergycollectionforthe217pair-productionorinternalconversiondecayprocesses.The1357-keVpeakwascoincidentwithanunresolvedandunidentiedˇ200keVsecondpulseenergy.The681-and1870-keVtransitionsarefromthe680.6-1872.3-keV-raycascadethatdepopulatesthe2552-keVstatein69Cu[52].218AppendixB
and-double-pulseCoincidencesObservedFollowingthe
-DecayoftheLong-Lived,Low-Spin,68CoIsomerInthisappendixtheand-double-pulsecoincidencesobservedduringthe-decayof68Cointo68Niarepresented.Thesecoincidenceswereusedtoidentifyandplacelevelsinthelow-energy68Nilevelscheme.CoincidencesWhileseveraltransitionsareobservedfollowingthe-decayof68Co,the2032.9-keV2+
1!0+
1transitionisthemostintensetransitionlistedinTable4.1.The2032.9-keVtransitioncollectssignicantintensityfromhigherlyingstates,andassuchseveralcoincidencesareobserved.Thecoincidencespectrumgatedonthe2032.9-keV2+
1!0+
1transitionareshowninFig.B.1.Astrongcoincidencewitha709.3-keVrayisshowninFig.B.1.The709.3-keVtransition,alongwiththe1139.2-keVand2742.2-keVtransitions,isknowntodepopulate219020040060080010000100200300400500786.6, 788.9477.7511662.5709.3862.8961.91000120014001600180020000501001502001104.21114.51268.41338.61421.31460**1514.31603.61610.51716.01898.31992.1200025003000350040000204060802130.52231.32231.32362.02457.12719.62728.32830.22968.33004.63031.93145.53230.43290.93378.63479.63515.43656.1, 3660.33741.53455.03533.03711.03944.24000450050005500600005105227.54224.94588.0(a)
(b)
(c)
(d)Single Escape
Double EscapeEnergy (keV)Counts / 2 keVCounts / 2 keVCounts / 2 keVCounts / 2 keVGated2032.9 keVGated2032.9 keVGated2032.9 keVGated2032.9 keVFigureB.1:Background-subtractedcoincidencespectragatedonthe2032.9-keV2+
1!0+
1transitionin68Ni.Thebackgroundwastakensymmetricallyeithersideofthe2032.9-keVpeak.Coincidenttransitionsarelabeledwiththeirenergiesand,whenapplicable,singleanddouble-escapepeaksaredenotedwithoneortwostars,respectively,inadditiontotheenergyofthepeak.220the2742-keV2+
2state.Thecoincidencespectragatedonthe709.3-keV,1139.2-keV,and2742.2-keVtransitionsareshowninFigs.B.2a,B.2b,andB.2c,respectivelywhilethesumofthecoincidencespectrafromallthreegatesispresentedinFig.B.2d.22105010002040608002040010002000300040000100200300Energy (keV)2032.93031.93031.93031.92032.9Counts / 2 keVCounts / 2 keVCounts / 2 keVCounts / 2 keV1603.6, 1610.51282.61521.5Single Escape
Double Escape1603.6, 1610.51603.6, 1610.51603.6, 1610.51521.51421.3, 1428.3662.5511511662.51282.61421.3, 1428.3511662.51282.61421.3, 1428.3511662.51282.61421.3, 1428.3Gated709.3 keVGated1139.2keVGated2742.2 keVGated709.3+1139.2+2742.2 keV500520010020051120002030010020020602032.9(a)
(b)
(c)(d)FigureB.2:Background-subtractedcoincidencespectragatedonthe(a)709.3-keV,(b)1139.2-keV,(c)2742.2-keV,and(d)sumofthe709.3-,1139.2-,and2742.2-keVtransitions.Thebackgroundwastakensymmetricallyeithersideofeachrespectivepeakregion.Coinci-denttransitionsarelabeledwiththeirenergiesand,whenapplicable,single-escapepeaksaredenotedwithonestarinadditiontotheenergyofthepeak.Theinsetsin(a)and(b)showthefullheightsofthe2032.9-keVand511-keVpeakstruncatedin(a)and(b),respectively.Together,thecoincidencespresentinFigs.B.1andB.2verifymostofthe68Nilowenergylevel-schemeinFig.4.1.Inaddition,severalnewraysareobservedinFigs.4.2,222B.1,andB.2.Usingthecoincidences,presentedinFig.B.3manyoftheserayswereplacedinthe68Nilevelscheme.223-100Counts / 2 keV0100200Gated323.5 keV271.7649.2Counts / 2 keV(c)Counts / 2 keV-1000100200300Gated477.7keV1514.32032.93054.93265.2(d)477.7
5110100200Gated271.7keV323.5511-50050100Counts / 2 keVGated258.3 keV(a)(b)02040602032.91139.2709.3Gated662.5 keV511Counts / 2 keV10260028003000052742.23002.63092.8300032003400-505-100-50050100Counts / 2 keV2032.9Gated786.6 keV & 788.9 keV(e)(f)-4004080-20020402032.9Gated862.8 keVCounts / 2 keVCounts / 2 keVGated961.9 keV1114.52032.9(g)(h)05001000150020002500-20020Energy (keV)Gated1104.2 keV2032.91268.405001000150020002500050100150Energy (keV)Gated1114.5 keV2032.9961.95112800300032003400010202830.23358.23508.8Counts / 2 keVCounts / 2 keV(i)(j)68Co1114.52032.9FigureB.3:Background-subtractedcoincidencespectra.Coincidenttransitionsarelabeledwiththeirenergies.Allinsetsdisplayadditionalrangesoftheirrespectivespectra.Theopensquaresymbolusedon(c)representsacontaminating649.2-327.0-keVcoincidencefrom68Co.Asingleasteriskafteranenergylabelsigniesthetransitionwasobservedexclusivelyincoincidence,andtwoasterisksfollowinganenergylabelidentiesacoincidencewithcontaminatingtransition.224FigureB.3:(cont'd)020406080Counts / 2 keV2032.91104.2Gated1268.4 keV(k)-20020406080Counts / 2 keV2032.930003200053095.3Gated1338.6 keV(m)Single Escape0500100015002000250005001000150020002500Energy (keV)Energy (keV)50100Counts / 2 keV-10010201245.4**Gated1428.3 keV1603.61002003000204026002700280029000510Counts / 2 keVCounts / 2 keVCounts / 2 keV2032.9Gated1603.6 keV5111428.31139.2709.31344.02742.22040Counts / 2 keV-1001020Counts / 2 keVGated1668.4 keV2032.92422.01514.31282.6477.7511(p)
(r)0260027002800290001020Gated1421.3 keV2742.22032.91610.52231.71245.4**1139.2709.35110150016001700180001020Gated1514.3 keV477.72032.91668.61717.81521.80-20242032.92600270028002900709.32742.2Gated1610.5 keV1421.3511(o)
(q)
(s)(t)02040Counts / 2 keVGated1282.6 keV2600270028002900051015709.31139.22032.9(l)2742.22231.7-10010Gated1344.0 keV1603.6Counts / 2 keV(n)2032.9225FigureB.3:(cont'd)020402032.91514.31282.6477.7511Gated1717.8 keV1421.3**020402032.9Gated1898.3 keV(u)(v)Counts / 2 keVCounts / 2 keV-1001020Counts / 2 keV-10Counts / 2 keV2032.9Gated1992.1 keV(w)02040Gated2231.3 keV511**2032.91421.3**-5051015Counts / 2 keVCounts / 2 keVGated2362.0 keV2032.90204060Counts / 2 keV511511150017001900051668.6
1717.8Gated2422.0 keV-1001020Counts / 2 keV2032.9Gated2573.9 keV(y)(z)01020302032.9Gated2130.5 keV(x)(aa)(ab)05001000150020002500-10-505101505001000150020002500-100102030Counts / 2 keVGated2728.3 keV2032.9Gated2830.2 keV2032.9Counts / 2 keV2032.91114.5Energy (keV)Energy (keV)(ac)(ad)226FigureB.3:(cont'd)0204026002750290005Counts / 2 keV2742.22032.9Gated3031.9 keV5111139.2709.3-5051015Counts / 2 keVGated2989.9 keV2032.91338.6280031003400-31353371.82859.3(ae)(af)-50510-1001020Counts / 2 keVCounts / 2 keV1338.62032.9Gated3095.3 keVGated3290.9 keV2032.9(ag)(ah)01020Counts / 2 keVGated3371.8 keV2950305031500243095.32989.92032.9**-10-505101114.5Counts / 2 keVGated3358.2 keV(ai)(aj)-5051015-100102030Counts / 2 keVGated3378.6 keVGated3456.5 keV2032.92032.9(ak)(al)0500100015002000250002040608005001000150020002500-50510Counts / 2 keVEnergy (keV)Gated3479.6 keV2032.91300155018000510151554.91554.9*Gated3496.5 keVEnergy (keV)2032.9(am)(an)Counts / 2 keVCounts / 2 keV227FigureB.3:(cont'd)228FigureB.3:(cont'd)-50510010203040Counts / 2 keVCounts / 2 keVGated3944.2 keVGated3962.6 keV(ay)(az)-5051015-50510Counts / 2 keVCounts / 2 keVGated4224.9 keVGated4239.5 keV5115112032.92032.9(ba)(bb)-50510-20246Counts / 2 keVGated4255.9 keVGated4328.5 keV(bc)(bd)-505-505Counts / 2 keVGated4374.0 keVGated4424.9 keV05001000150020002500-50505001000150020002500-50510Gated5227.6 keVCounts / 2 keVCounts / 2 keVCounts / 2 keVCounts / 2 keVEnergy (keV)Energy (keV)(be)(bf)
(bh)2032.92032.910Gated4588.0 keV(bg)2032.92032.92032.92032.9229The258.3-keVtransitionwasrstidentiedintheworkofRef.[20]andwasplaceddepopulatinga3405-keVlevel.The258.3-keVtransitionwasalsoobservedinlaterworkandthe3405-keVstatewasassignedatentative(4+)spinandparity[82].FigureB.3ashowsthe258.3-1114.5-keVand258.3-2032.9-keVcoincidencestherebysupportingtheplacementofthe258.3-keVdepopulatingthe3405-keV(4+)state[82]feedingthe3147-keV4+state[12].The271.7-and323.5-keVtransitionswererstidentiedfollowingthedecayoftheshort-lived,high-spin,68Coisomer[12].Theformerdepopulatesa3444-keV(6;7)statefeedinga3120-keV(5)statewhilethelatterdepopulatesthe3120-keVstatefeedingtheiso-meric2847-keV5state[83].TheworkofRef.[82]alsoobservedthesetransitions,updatedtheenergiesofthetwohigher-lyingstatesto3442.6-keVand3118.9-keV,andpostulated(5)and(4)spinsandparitiesforthetwo,respectively.Recentlythe271.7-keVtransitionwasalsoobservedfollowingdecayof68Coselectivelypopulatedbythedecayof68Fe[21].Inthepresentworkastrong271.7-323.5-keVcoincidenceisobservedinFigs.B.3bandB.3c.Basedontheabsoluteintensitiesandtheobservedcoincidencestheplacementofthesetwotransitionissupported.The595.5-keVtransition[12,82],paralleltothe271.7-323.5-keVcascade,isobscuredinFig.4.2bythe594.3-keVtransitionfrom69Ni[84]populatedinthedecayof69Co,arandomlycorrelatedbeamcontaminant.Thethe814.5-keV5!2+
1transitionisnotobservedcoincidentwiththedecayinFig.4.2duetothe0.86(5)mshalflifeoftheisomeric2847-keV5state[83]butisobservedin-raysingles.Theabsoluteintensitiesofthe814.5-keVand271.7-keVtransitionsmatchwithinerrorsuggestingthatthe595.5-keVtransitionisweakcomparedtothe323.5-keVtransitionconsistentwiththeresultsofRef.[82].The477.7-keVtransition[12]isknowntodepopulatethe2511-keV0+
3state[20]feedingthe2032.9-keV2+
1state.TheworkofRef.[12]alsoidentieda1515-keVtransitionfeeding2302511-keV0+
3statefroma4025-keV(2+)state.The4024.6-keVground-statetransitionisalsoobservedinFig.4.2.Inthepresentworkstrong477.7-2032.9-keV,477.7-1514.3-keV,and1514.3-2032.9-keVcoincidencesareobservedinFigs.B.3dandB.3qconsistentwiththecurrentplacementofthe477.7-keVand1514.3-keVtransitions.Aweak477.7-511-keVcoincidenceisobservedinFig.B.3dmostlikelyfrompairproductionoriginatingfromhigh-energy-raysfeedingthe2511-keV0+
3state.The477.7-477.7-selfcoincidenceobservedinFig.B.3disnewtothisworkandremainsunexplained.Twoweakercoincidencesbetweenthe477.7-keVand3054.9-keVand3265.2-keVtran-sitionsarepresentintheinsetofFig.B.3d.Ifplacedabovethe1514.3-keVtransition8(2)3054.9-1514.3-keVand5(2)3265.9-1514.3-keVcoincidenceswouldbeexpectedofwhichzeroareobservedineachcase.Therefore,the3054.9-keVand3265.2-keVtransitionsareplacedfeedingthe2511-keVstatedirectly,depopulatinganewstateat5566keV,forwhichthegroundstatetransitionisobservedinFig.4.2,andapreviouslyidentied5774-keVstate[21],respectively.Twoadditionaltransitionsarealsoplaceddepopulatingthenew5566-keVlevel.The3533.0-keVtransition,observedincoincidencewiththe2032.9-keVtransitioninFigs.B.1andB.3aq,wasplacedfeedingthe2033-keV2+
1statefromthe5566-keVlevel.Anew3962.6-keVtransitionobservedincoincidencewith511-keVraysinFig.B.3az,andthe0+
2!0+
1E0transitioninFig.4.4andwasplacedfeedingthe1603-keV0+
2statefromthe5566-keVlevel.Inadditiontothestrong1514.3-477.7-keVcoincidence,threeadditional-raycoinci-denceswiththe1514.3-keVtransitionarealsopresentinFig.B.3q.Thecoincidenceat1521.8keVisfromthesingle-escapepeakofthe2032.9-keVtransition.Theothertwotran-sitionsat1668.6keVand1717.8keVwereplacedfeedingthe4025-keV(2+)statefromtwo231levelsat5693and5744keV,respectively.A3660.3-keVtransition,observedincoincidencewiththe2032.9-keVtransitioninFigs.B.1andB.3at,isalsoplaceddepopulatingthenew5693-keVlevelfeedingthe2033-keV2+
1state.Forthe1668.6-keVtransition,the1514.3-1668.6-keVcoincidenceisseeninFig.B.3tanda1668.6-2422.0-keVcoincidenceobservedinFigs.B.5q,andB.3aa.A1668.6-1282.6-keVcoincidenceisalsoobservedinFigs.B.5landB.5t,whichisexpectedsincethe1282.6-keVtransition[21]feedsthe2742-keV2+
2statefromthe4025-keV(2+)state.The1717.8-1514.3-keVcoincidenceisseeninFig.B.3t.The1717.8-2422.0-keVcoinci-denceisobservedinFigs.B.3uandB.3Ac.Additionalcoincidencesbetweenthe1717.8-keVtransitionandthe1282.6-keV,1514.3,and477.7-keVtransitionsinFig.B.3ufurthersupporttheplacementofthe1717.8-keVtransitionfeedingthe4025-keV(2+)state.Thecoincidencewiththe2032.9-keVtransitioninFig.B.3uispredominatelycontaminationfromtheunre-solved1716.0-keVtransitionseenincoincidencewiththe2032.9-keVtransitioninFig.B.1.The1716.0-keVtransitionwasplacedfeedingthe2033-keV2+
1statefromanew3749-keVlevel.Thepeakat1421.3-keVinFig.B.3u,denotedwithtwoasterisks,isthe1421.3-keVtransitionthatfeedsthe2742-keV2+
2statefromthe4163-keV(2+)statedetectedincoin-cidencewiththe1720-keVdoubleescapepeakfromthe2742.2-keVtransitionthatisalsounresolvedfromthe1717.8-keVtransition.The1992.1-2032.9-keVcoincidencepresentinFigs.B.3wandB.1placesthenew1992.1-keVtransitionfeedingthe2033-keV2+
1statefromtheknown4025-keV(2+)state.Inthepresentwork,vetransitionshavebeenplaceddepopulatingthe4025-keV(2+)statewithenergiesof4024.6-keV,2422.0-keV,1992.1-keV,1514.3-keVand1282.6-keV.Thebackground-subtractedcoincidencespectrumgatedonthesumofthosevetransitionsispresentedinFig.B.4.InthesummedcoincidencespectrumpresentedinFig.B.4the2321668.6-keVand1717.8-keVtransitionsareclearlyobservedandthereforecondentlyplacedfeedingthe4025-keV(2+)stateinthe68Nilevelscheme.01000200030000100200300Counts / 2 keVEnergy (keV)477.7Gated1282.6+1514.3+1992.1+2422.0+4024.6 keV2032.92742.2709.35111717.81668.6150017001900020401717.81668.6FigureB.4:Background-subtractedcoincidencespectragatedonthesumofthe1282.6-keV,1514.3-keV,1992.1-keV,2422.0-keV,and4024.6-keVtransitions.Thebackgroundwastakensymmetricallyeithersideofeachrespectivepeakregion.Coincidenttransitionsarelabeledwiththeirenergies.Theinsetshowsazoomed-inviewofthe1500to1900keVregionofthespectrum.The662.5-keVtransitionisknowntodepopulatethe3405-keV(4+)state[20,82]feedingthe2742-keV2+
2state.Twocoincidencesbetweenthe662.5-keVraywithnew3002.6-keVand3092.8-keVraysarepresentintheinsetofFig.B.3e.Thesetransitionsareplacedfeedingthe3405-keV(4+)statefromtwonewlevelsat6407keVand6498keV.Anewdoubletaroundˇ787keVwasobservedincoincidencewiththe2032.9-keVtran-sitioninFig.B.3f.Thoughunresolved,atcomprisedoftwoGaussiansplusalinearbackgroundwasperformedextractingtwopeakswithenergiesof786.6(4)and788.9(2)keV.Gatingeithersideofthedoubletrevealedexclusivecoincidencewiththe2032.9-keVsug-gestingthatbothtransitionsdirectlyfeedthe2032.9-keV2+
1statefromtwonewlevelsat2820and2822keV.Thestrongcoincidencebetweenthedoubletand2032.9-keVtransitionisshowninFigureB.3f.Acoincidencebetweenanew862.8-keV-rayandthe2032.9-keVtransitionisshowninFig.B.3g,placinganewlevelat2896keV.The961.9-keVtransitionisalsonewtothiswork233andisobservedincoincidencewiththe1114.5-keVand2032.9-keVtransitionsinFig.B.3h.Basedonthecoincidencerelationshipsthe961.9-keVtransitiondepopulatesanew4109-keVlevelfeedingthefeedingthe3147-keV4+state[12].The1114.5-keVtransition,rstobservedintheworkofRef.[12],feedsthe2032.9-keV2+
1statefroma3148-keV4+state[12,19{21,82].Coincidenceisobservedbetweenanew961.9-keVrayandthe1114.5-keVtransitioninFigs.B.3handB.3jandwiththe2032.9-keVtransitioninFigs.B.3handB.1.Anew2830.2-keVtransitionisalsoseenincoincidencewiththe1114.5-keVtransitioninFigs.B.3jandB.3adandalsowiththe2032.9-keVtransitioninFigs.B.3jandB.1.The961.9-keVtransitionwasplacedfeedingthe3148-keV4+statefromanew4109-keVlevelwhilethe2830.2-keVtransitionisalsoplacedfeedingthe3148-keV4+statefromthe5977-keVlevelalsonewtothiswork.A3944.2-keVtransition,observedincoincidencewiththe2032.9-keVtransitioninFig.B.3ay,isalsoplaceddepopulatingthe5977-keVlevel.Twoweakercoincidencesbetweenthe1114.5-keVtransitionandnew3358.2-keVand3508.8-keVtransitionsareshownintheinsetofFig.B.3jandFigs.B.3aiandB.3ao,respectively.Thesetwotransitionsareplacedfeedingthe3148-keV4+statedirectlyfromtwonewlevelsat6506keVand6656keV.Thecoincidencesbetweenthe3508.8-keVtransitionandthe2032.9-keVand511-keV-raysareduetocontaminationinthegatefromthe3515.4-keVtransition(seeFig.B.3ap)andthe3514-keVsingle-escapepeakofthe4024.6-keVtransition,respectively.Coincidencesbetweenthenew1104.2-keVrayandthe1268.4-keVtransitionareob-servedinFigs.B.3iandB.3k.A1104.2-2032.9-keVcoincidenceisalsopresentinFigs.B.3iandB.1alongwithastrong1268.4-2032.9-keVcoincidenceinFigs.B.3kandB.1.The1268.4-keVtransitionwasrstobservedintheRef.[20]andplacedfeedingthe2032.9-keV2+
1234statefromanewlevelat3301keV.Subsequentstudies[21,82]alsoobservedthe1268.4-keVtransitionandconrmeditsplacement.Thepresentworkplacesthe1104.2-keVtransitiondepopulatinganewlevelat4405keVfeedingthe3301-keVlevelwhichinturndecaysbythe1268.4-keVtransitiontothe2032.9-keV2+
1state.The1338.6-keVtransition,observedincoincidencewiththe2032.9-keVtransitioninFigs.B.3landB.1,isnewtothiswork.Thereisalsocoincidencebetweenthe1338.6-keVtransitionandanothernewrayat3095.3keV.Basedontheabsoluteintensitiesandtheobservedcoincidencesthe1338.6-keVtransitionwasplacedfeedingthe2033-keV2+
2statefromanew3372-keVlevel,whichisfedbythe3095.3-keVtransitionfromanothernewlevelat6467keV.The3371.8-keVground-statetransitionisobservedinthe-delayed-rayspectrumshowninFig.4.2.The1421.3-keVtransitionisknowntofeedthe2742-keV2+
2statefromthe4163-keV(2+)state[21].The1610.5-keVtransitionisnewtothisworkandplacedfeedingthe4163-keV(2+)statefromthe5774-keVlevel[21]basedonthe1421.3-1610.5-keVcoincidenceobservedinFigs.B.3oandB.3s.The1610.5-709.3-keVcoincidencesdisplayedinFigs.B.2a,B.2d,andB.3sandthe1610.5-2032.9-keVcoincidencespresentinFigs.B.3sandB.1originatefromthe1610.5-1421.3-709.3-2032.9-keV-raycascade.The1610.5-2742.2-keVcoincidenceisalsopresentinFigs.B.2c,B.2d,andB.3sfromthe1610.5-1421.3-2742.2-keV-raycascade.Thecoincidencewiththe1245.4-keVtransition,denotedwithtwoasterisks,presentinbothFigs.B.3oandB.3pisfromacoincidencewitha1424.0-keVtransitionfromanunknownsourcethatcontaminateseachrespectivegate.The1603.6-keVand1428.3-keVtransitionsarebothnewtothiswork.The1603.6-keVtransitionisobservedincoincidencewiththe709.3-keV,1139.2-keV,and2742.2-keVtransitionsinFigs.B.3randB.2d,andFigs.B.2a,B.2b,andB.2c,respectively.A1603.6-2351428.3-keVcoincidenceisalsoobservedinFigs.B.3randB.3p.Basedontheabsoluteintensitiesandcoincidencerelationshipsthe1603.6-keVtransitionwasplacedfeedingthe2742-keV2+
2statefromanewlevelat4346-keV,whichisfedbythe1428.3-keVtransitionfromtheknown5774-keVlevel[21].The1603.6-511-keVcoincidenceobservedinFig.B.3rispredominantlyduetothepair-productiondecaymodeofthecoincident0+
2!0+
1E0transition.Onceagainthecoincidencewiththe1245.4-keV,denotedwithtwoasterisks,presentinbothFigs.B.3oandB.3pisfromacoincidencewitha1424.0-keVtransitionthatcontaminateseachrespectivegate.Anadditionalcoincidencebetweenthe1603.6-keVtransitionandanew1344.0-keVrayispresentinFigs.B.3nandB.3r.Astrongcoincidencebetweenanew3656.1-keVrayandthe2032.9-keVtransitionispresentinFigs.B.3asandB.1.Bothcoincidencerelationshipsplaceanewlevelat5689keV.The1898.3-2032.9-keVcoincidenceobservedinFig.B.3visalsopresentinFig.B.1placinganewlevelat3931keVdepopulatedbythenew1898.3-keVtransitionfeedingthe2033-keV2+
1state.Thenew2130.5-keVtransitionisseenincoincidencewiththe2032.9-keVrayinFigs.B.3xandB.1andwasplacedfeedingthe2033-keV2+
1statefromtheknown4163-keV(2+)state.The2032.9-2231.3-keVcoincidenceobservedinFigs.B.3yandB.1placesanewlevelat4264keVdepopulatedbythenew2231.3-keVtransitionwhichfeedsthe2033-keV2+
1state.Thecoincidencesbetweenthe2231.3-keVwiththe511-keVand1421.3-keVrays,denotedwithtwoasterisksinFig.B.3y,arisefromcoincidenceswiththesingleescapepeakfromthe2742.2-keVtransitionwhichisunresolvedwiththe2231.3-keVtransition.Acoincidencebetweenanew2362.0-keVrayandthe2032.9-keVtransitionisobservedinFigs.B.3yandB.1.The2362.0-keVtransitionwasplacedfeedingthe2033-keV2+
1state236fromanew4394keVlevel.Anew2573.9-keVisshownincoincidencewiththe2032.9-keVtransitioninFigs.B.3abandB.1.The2573.9-keVtransitionwasplacedfeedingthe2033-keV2+
1statefromanewlevelat4607keV.The4607.2(5)-keVground-statetransitionisobservedinFig.4.2).Thecoincidencebetweenanew2728.3-keVraywiththe2032.9-keVtransitionisshowninFigs.B.3abandB.1.The2728.3-keVtransitionwasplacedfeedingthe2033-keV2+
1statefromanewlevelat4761keV.Thenew2989.9-keVrayisobservedincoincidencewiththe3371.8-keVray,andassociated2859.3-keVsingleescapepeak,inFig.B.3ae.Inaddition,coincidencesbetweenthe2989.9-keVrayandthe1338.6-keVand2032.9-keVtransitionsarealsopresentinFig.B.3ae.Whengatingonthe3371.8-keVtransition,showninFig.B.3aj,the2989.9-keVand3095.3-keVtransitionsareobservedincoincidence.Coincidencesbetweenthe3095.3-keVtransitionandthe1338.6-keVand2032.9-keVraysareshowninFig.B.3ag.The3371.8-keVtransitionwasplacedasthegroundstatetransitionforthe3372-keVlevelfedbythe2989.9-keVand3095.3-keVtransitionsfromtwonewlevelsat6361and6467keV,respectively.Thecoincidencewiththe2032.9-keVtransitioninFig.B.3aj,labeledwithtwoasterisks,resultsfromcontaminationofthegatefromthe3378.6-keVtransition.The3378.6-2032.9-keVcoincidenceisshowninFig.B.3akandthe3378.6-keVwasplacedfeedingthe2033-keV2+
1statefromanewlevelat5411keV.The3031.9-keVtransitionwasplacedfeedingthe2742-keV2+
2state.Strong3031.9-1139.2-keVcoincidencesareseeninFigs.B.2b,B.2d,andB.3af.Inadditionthe3031.9-709.3-keVcoincidencesobservedinFigs.B.2a,B.2d,andB.3af,3031.9-2032.9-keVcoin-cidencesseeninFigs.B.1andB.3af,and3031.9-2742.2-keVcoincidencespresentinFigs.237B.2c,B.2d,andB.3afallsupporttheplacementofthe3031.9-keVtransitionfeedingthe2742-keV2+
2statefromtheknown5774-keVlevel[21].The3290.9-keVand3456.5-keVraysarebothnewtothisworkandareobservedincoincidencewiththe2032.9-keVtransition,exclusively,inFig.B.1andFigs.B.3ahandB.3al,respectively.The3290.9-keVand3456.5-keVtransitionsareplaceddirectlyfeedingthe2033-keV2+
1statefromtwonewlevelsat5243keVand5489keV,respectively.The3479.6-keVtransition,rstobservedintheworkofRef.[12],wasplacedfeedingthe2033-keV2+
1statefroma5513-keVlevel[12].Thestrong3479.6-2032.9-keVcoincidenceisobservedinFigs.B.1andB.3amconrmsthisplacement.Asecondcoincidencebetweenthe3479.6-keVtransitionandanew1554.9-keVtransitionisalsopresentinFig.B.3am.The1554.9-keV-rayistooweaktoseeinthe-gated-raysinglesspectrumshowninFig.4.2andplacedabovethe3479.6-keVtransitioninthe-raycascadefeedingthe5513-keVlevelfromanewlevelat7067-keV.Acoincidencebetweenanew3496.5-keVrayandthe2032.9-keVtransitionisobservedinFig.B.3an,placinganewlevelat5529keVforwhichthe5528.7-keVground-statetransitionisobservedinFig.4.2.Anew3925.9-keVtransitionobservedincoincidencewith511-keVraysinFig.B.3ax,andthe0+
2!0+
1E0transitioninFig.4.4andwasplacedfeedingthe1603-keV0+
2statefromthe5529-keVlevel.Astrongcoincidencebetweenthe3515.4-keVand2032.9-keVtransitionsisobservedinFigs.B.1andB.3ap.The3515.4-keVtransitionwasrstobservedintheworkofRef.[12]andsubsequentlybyRef.[21]andwasplacedfeedingthe2033-keV2+
1statefroma5549-keVlevel[12,21].Thepresentworkconrmsthisplacement.The3515.4-511-keVcoincidence,denotedwithtwoasterisksinFig.B.3aq,resultsfromthe3513.6-keVsingleescapepeakfromthe4024.6-keVtransitionthatunresolvedfromthe3515.4-keVtransition.238The3608.5-keVraywasobservedincoincidencewiththe2032.9-keVtransitioninFig.B.3arplacinganewlevelat5641keV.The3711.0-keVtransitionwasplacedfeedingthe2033-keV2+
1statefromthe5743-keVlevel,discussedearlierinthissection,basedonthe3711.0-2032.9-keVcoincidencesobservedinFigs.B.1andB.3au.The3711.0-511-keVcoincidenceobservedinFig.B.3auisfromthe3713.9-keVsingleescapepeakofthe4224.9-keVtransition.Theabsoluteintensityofthe3711.0-keVadjustedaccordinglytocorrectforthiscontamination.Astrongcoincidencebetweenthe3741.5-keVand2032.9-keVtransitionsisobservedinFigs.B.1andB.3av.The3741.5-keVtransitionwasrstobservedintheworkofRef.[12]andsubsequentlybyRef.[21]andwasplacedfeedingthe2033-keV2+
1statefroma5774-keVlevel[12,21].Thepresentworkconrmsthisplacement.Thenew3872.3-keVtransitionwascoincidentwiththe2032.9-keVtransitioninFig.B.3awandwasplacedfeedingthe2033-keV2+
1statefromanewlevelat5905keV.The4224.9-keVlevelisalsonewtothisworkandisshownincoincidencewiththe2032.9-keVtransitioninFigs.B.1andB.3baplacinganewlevelat6258keV.Anew4239.5-keVtransitionisshownincoincidencewith511-keVraysandthe0+
2!0+
1E0transitioninFigs.B.3bband4.4andwasplacedfeedingthe1603-keV0+
2statefromanewlevelat5843keV.The4255.9-keV,4328.5-keV,4374.0-keV,4424.9-keV,4588.0-keV,and5227.6-keVtran-sitionsareallnewtothepresentworkandobservedincoincidencewiththe2032.9-keVtransitioninFigs.B.3bc,B.3bd,B.3be,B.3bf,Figs.B.3bgandB.1,andFigs.B.3bhandB.1,respectively,andareplacedfeedingthe2033-keV2+
2statefromnewlevelsat6289,6361,6407,6458,6621,and7260keV.ThesecoincidencesaresummarizedinTable4.2.239-double-pulseCoincidencesTheunambiguousidenticationofthe0+
2!0+
1E0transitioncoupledwiththehighstatisticsinthepresentworkpermitsexaminationof-double-pulsequadruplecoincidences.ThebackgroundsubtractedquadruplecoincidencespectraarepresentedinFig.B.5andallowplacementofseveraltransitionslistedinTable4.3.Ineachcasethebackgroundwastakensymmetrically,directlyaboveandbelow,thepeakofinterest.The-double-pulsecoincidencesinFig.B.5allowidenticationandplacementofweaktransitions.StrongertransitionsobservedearlierinthissectionalsoshowcoincidencesinFig.B.5butwillnotbediscussedanyfurther.Anew1579.2-keV-rayisobservedincoincidencewithboththe1421.3-and1139.2-keVtransitionsinFig.B.5g.Theweakintensityofthe1579.2-keVtransitionprecludesobservationof1421.3-1579.2-keVand1139.2-1579.2-keVcoincidencesinFigs.B.5dandB.5a,respectively.The1579.2-keVtransitionwasplacedfeedingthe4164-keV(2+)statefromthe5743-keVlevelidentiedearlierinthissection.The1540.7-keVtransitionisalsonewtothisworkandobservedincoincidencewiththe1139.2-keVtransitioninFig.B.5f.The1540.7-keVtransitionwasplacedfeedingthe2742-keV2+
2statefromanewlevelat4283keV.Acoincidencebetweenanew1631.2-keVrayandthe1139.2-keVtransitionisobservedinFig.B.5j,placinganewlevelat4373keV.InFigs.B.5kandB.5pacoincidencebetweenanew1641.3-keVand2529.8-keVtransitions.Basedontheabsoluteintensitiesandthelackofanyothercoincidencesthe2529.8-keVtransitionwasplacedfeedingthe1603.5-keV0+
2statefromanewlevelat4132keVandthe1641.3-keVtransitionwasplacedfeedingthatnew4132-keVlevelfromtheknown5774-keVlevel[12].240InFig.B.5macoincidenceispresentbetweenanew1713.3-keV-rayandthe1139.2-keVtransition.The1713.3-keVtransitionwasplacedfeedingthe2742-keV2+
2statefromanew4456-keVlevel.Theweakintensityofthe1713.3-keVtransitionprecludesobservationofthe1139.2-1713.3-keVcoincidenceinFig.B.5a.ThesecoincidencesaresummarizedinTable4.2.TheremainderofthetransitionslistedinTable4.3displayednocoincidences(otherthanwith511-keVrays)andassucharehardtoplacepreciselyinthe68Nilevelscheme.However,thecoincidencewiththe0+
2!0+
1E0transitionrequiresthattheyfeedthe1603-keV0+
2stateeitherdirectlyorindirectly.Anattemptwasmadetomatchenergysumsofunplacedtransitionswithobservedlevelswithotherobservedlevelsorenergysums.Severaltransitionswereplacedusingthistech-nique.The1366.4-keVand1400.3-keVtransitionswereplacedfeedingthe4164-keVleveldepopulatingthenew5530-keVand5565-keVlevelsdiscussedpreviouslyinthissection.Thesumofthe1705.3-keVtransitionwiththe2742-keVlevelandthesumofthe2860.8-keVtransitionwiththe1603-keVlevelbothsumtoanewlevelat4448keV.Furthermore,ifthe2860.8-keVtransitionwerelocatedabovethe1139.2-keV,1421.3-keV,or2422.0-keV(oranytransitionlowerinenergy)theexpectednumberofcoincidenceswouldbereadilyobserved,supportingthisplacement.Thetwoenergysumsmatcheachotherwithin0.05keVlendingfurthercredibility.Thesumofthe2947.1-keV-raywiththe2742-keVstategivesastatewithanenergyof5689keVandthesumofthe3235.0-keV-raywiththe2742-keVstategivesastatewithanenergyof5977keV.The5689-keVand5977-keVlevelswerealreadymentionedearlierinthissection.Thesumofthe3218.4(11)-keVtransitionwiththe4025-keVstate,4500.1(3)-keVtran-241sitionwiththe2742-keVstate,andthe5639.8(8)-keVtransitionwiththe1603-keVstateallyieldanenergyofˇ7242-keVandareconsistentwithina1˙error.Examiningthe-gated-raysinglesspectrum,showninFig.B.1,a7240.5(10)keVtransitionisobservedwhichinthelimitof2˙isconsistentwiththeweightedaverageenergyofthethreesumenergiesmentionedabove.Thereforethe3218.4-keV,4500.1-keV,and5639.8-keVtransitionsareallplaceddepopulatinganew7242-keVstate.Thesumofthe4198.7.1-keV-raywiththe2742-keVstateandthesumofthe5337.7-keV-raywiththe1603-keVbothgiveanenergyof6941keV.Sincethetwosumsmatcheachotherwithin0.25keVtheplacementofanewlevelat6941-keV,depopulatedbythosetwotransitions,canbemadewithreasonablecondence.The5395.8-keV,5978.0-keV,and6178.6-keVtransitionswereplacedfeedingthe1603-keV0+
2statesinceitisunlikelythattheyoriginatefromstatesabovethe7792(4)-keV[56]neutronseparationenergy,placingnewlevelsat6999,7581,and7782keV,respectively.2420102030Counts / 2 keVGated662.5 keV5111139.202040Gated1421.3 keV5111139.2Counts / 2 keV-2024Counts / 2 keV5111139.2Gated1540.7 keV0510Counts / 2 keVGated1282.6 keV5111139.205105111139.21603.6Gated1428.3 keV-2024Counts / 2 keVCounts / 2 keV5111139.21421.3Gated1579.2 keV0500100015002000250030003500400045000204060Counts / 2 keVGated1139.2 keV511662.51421.3, 1428.31603.6, 1610.51282.63031.9x505001000150020000510Counts / 2 keVEnergy (keV)5111139.2Gated1603.6 keV0500100015002000-2024Energy (keV)1139.21421.31428.3Gated1610.5 keV(a)
(b)(d)
(f)(h)(c)
(e)(g)(i)4805105400100200x1x5511Counts / 2 keV511FigureB.5:Background-subtracted-double-pulsecoincidencespectrarecordedincoin-cidencewiththedetectionofthe0+
2!0+
1E0transitionin68Ni.Thebackgroundwastakensymmetricallyeithersideofthepeakexcept.Theinsetin(a)showsthefullheightofthe511-keVpeakcutointhespectrumdisplayedin(a).Theinsetinpanel(k)showstheregionbetween2510and2550keVforthespectrumin(k).Theinsetsinpanels(l)and(n)showtheregionbetween2400and2440-keVforthesamespectrumineachpanel.Theinsetin(o)showsthefullheightofthe511-keVpeakcutointhespectrumdisplayedin(o).243FigureB.5:(cont'd)0510Gated1717.8 keV511240024202440022422.0Counts / 2 keV051015511Gated2422.0 keVCounts / 2 keV480510540020401668.61717.851105001000150020000510Counts / 2 keVEnergy (keV)Gated3031.9 keV5111139.205001000150020000510Counts / 2 keVEnergy (keV)-2024Counts / 2 keV1139.2Gated1713.3 keV0510Counts / 2 keV511Gated2529.8 keV1641.351102Gated1668.6 keV2422.024002420244005Counts / 2 keVGated1631.2 keV5111139.2024Gated1641.3 keV251025302550022529.8(j)
(l)(n)(p)(k)
(m)(o)(q)511244AppendixC
CoincidencesObservedFollowingthe-DecayoftheShort-Lived,High-Spin,70CoIsomer.Inthisappendixthecoincidencesobservedfollowingthe-decayoftheshort-lived,high-spin,70Coisomerarepresented.Thesecoincidenceswereusedtoidentifyandplacelevelsinthelow-energy70Nilevelscheme.coincidencespectraareshowninFig.C.1foralltentransitionslistedinTable4.9.InFig.C.1allcoincidencesbelongingto70Nialiatedwiththeshort-lived,high-spin,70Coisomerarelabeledwithanenergywhiletransitionsaliatedwiththelong-lived,low-spin,70Coisomeraredenotedwithblacksquares.2450200400600Counts / 2 keV0200400600Counts / 2 keV234.7448.4680.3, 683.3915.3969.61641.61392.91080.0845.4234.7448.4680.3, 683.31641.6915.3845.41392.91080.01259.10200400600-1000100200Counts / 2 keVCounts / 2 keV234.7680.3845.4915.3969.61259.11641.61080.01259.11392.9969.6680.3448.4845.40100200300Counts / 2 keV234.7680.3, 683.3969.61259.11392.9845.4448.40200400-2002040Counts / 2 keV1259.1969.6683.3448.4234.7448.4969.61259.1Counts / 2 keV02040448.4969.61259.1Counts / 2 keV06001200180002040Counts / 2 keVEnergy (keV)1259.1969.6683.3060012001800-101030Energy (keV)1259.1969.6448.4Counts / 2 keVGated1259.1 keVGated448.4 keVGated680.3 keV&683.3 keVGated845.4 keVGated1392.9 keVGated969.6 keVGated235.7 keVGated915.3 keVGated1080.0 keVGated1641.6 keV(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)FigureC.1:Seriesofbackgroundsubtractedcoincidencespectracorrelatedtothedecayoftheshort-lived,high-spin,70Coisomer.Thebackgroundwastakensymmetricallyeithersideofthepeakexceptwhereotherraysinterfered,inwhichcasethebackgroundwastakenaboveascloseaspossibletothepeakofinterest.Transitionsaliatedwiththelong-lived,low-spin,70Coisomeraredenotedwithblacksquares.246Therayscoincidentwiththe1259.1-keV(2+
1!0+
1)transitionareshowninFig.C.1a.Sincethe1259.1-keVtransitioncollectsintensityfromthedecayofboth70Coisomers,transitionsaliatedwiththedecayofthelong-lived,low-spin,isomer,denotedbyblacksquaresinFig.C.1a,arepresentanddiscussedinthenextsection.Basedontheexistingknowledgeofthe70Nilevelschemethestrong1259.1-969.6-keVcoincidencesobservedinFigs.C.1aandC.1b,1259.1-448.5-keVcoincidencesobservedinFigs.C.1aandC.1c,and448.5-969.6-keVcoincidencesobservedinFigs.C.1bandC.1careexpected.Inthepresentwork1030(60)1259.1-969.6-keVcoincidencesand1277(65)448.4-969.6-keVcoincidencesareexpectedofwhich1085(50)and1337(65)areobserved,respectively,therebyvalidatingthecoincidencespectroscopytechniquesusedherein.Allothercoinci-dencespresentedinthisworkwereveriedinthissamemanner.Coincidencewitha234.7-keVtransitionisobservedinFigs.C.1a,C.1b,andC.1c.InturnFig.C.1d,gatedonthe234.7-keVtransition,showsstrongcoincidenceswiththe448.4-keV,969.6-keV,and1259.1-keVtransitions.Basedontheabsoluteintensities,andtherecordednumberof234.7-448.4-keVcoincidences,the234.7-keVtransitionwasplacedfeedingthe2677-keV6+
1statefromthe2912-keV(5)stateasreportedbyRef.[23].InFig.C.1ftherayscoincidentwiththe915.3-keVtransitionarepresented.Thespectrumisverycleanandstrongcoincidenceswiththe448.4-keV,969.6-keV,and1259.1-keVtransitionsareobservedwithnoothercoincidencespresent.Theproposedplacementofthe915.3-keVtransitiondepopulatingastateat3592keVfeedingthe2677-keV6+
1state[23]iscertainlycorrect.Thecoincidencespectraforthe845.4-keVand1080.0-keVtransitionsareshowninFigs.C.1gandC.1h.InFig.C.1gtherearecoincidenceswithbetweenthe845.4-keVtransitionandthe234.7-keV,448.4-keV,969.6-keV,and1259.1-keVtransitions.Basedontherecorded247coincidencesandtheabsoluteintensitieswesupporttheplacementofthe845.4-keVtran-sitiondepopulatingthenew3757-keV(7)sateandfeedingtheproposed2912-keV(5)state.InFig.C.1hthe1080.0-keVtransitionisobservedincoincidencewiththe448.5-keV,969.6-keV,and1259.1-keVtransitions.Furthermore,the1080.0-keVtransitionisnotincoincidencewitheitherthe234.7-keVorthe683.3-keVtransitionssuggestingthatitrunsinparallelwiththem.ThecurrentresultssupporttheconclusionofRef.[23]thatthe1080.0depopulatesthe3757-keV(7)stateandfeedsthe2677-keV6+
1state.Theobservationofthe1392.9-keVisnewtothiswork.InFig.C.1istrongcoinci-dencesareobservedwith683.3-keV,969.6-keV,and1259.1-keVtransitionswithnoothercoincidencesobserved.Basedontherecordedcoincidencesandlackofcoincidenceswithtransitionshigherinthelevelschemethe1392.9-keVisproposedtodepopulateanewstateat4305keVfeedingthe2912-keV(5)state.Inthepresentworkthe683.3-keVtransitionisobservedtobeselfcoincident.Inthe-gated-raysinglesspectrum,showninFig4.22b,apeakwithananomalouslargewidthandacentroidofˇ682keVisobserved.InFig.C.1etherayscoincidentwiththewideˇ682-keVpeakarepresented.Inadditiontoastrongselfcoincidence,strongcoincidenceswith969.6-keVand1259.1-keVareobservedalongwithweakercoincidenceswith234.7-keV,448.4-keV,845.4-keV,and1392.9-keV.Lookingcloselyattheothercoincidencespectraforcoincidencesbetweenonlyoneofthetransitionsinthedoubletweobservefoursuchcases.InFigs.C.1candC.1d,448.4-680.3-keVand234.7-680.3-keVcoincidencesareobserved,respectively.Thiswouldplacethe845.4-keVand1392.9-keVtransitionsparalleltothenew680.3-keVtransition,whichissupportedbythe845.4-683.3-keVand1392.9-683.3-keVcoincidencesobservedinFigs.C.1gandC.1i,respectively.Thissuggeststhata680.3-keV248transitionfeedsthe2912-keV(5)statefromthe3592-keV(6)state.Theintensityofthe680.3-keVand683.3-keVtransitionswerededucedfromtherecordedcoincidences.Therewere402(30)countsintheselfcoincidencethatwhendividedbytwoandcorrectedforeciencygives4660(415)counts.Thisishowmanyeventsinsinglesowthroughthe680.3-683.3-keV-raycascade.Howeverthereisalsothe680.3-234.7-keV-raycascade.Thereare139(25)countsinthe680.3-234.7-keVcoincidence,andcorrectedforthe234.7-keV-rayeciencygives1910(350)counts.Thesumofthosetwocascadesisthenumberofcountsinthedoubletthatbelongtothe680.3-keVtransitionwhiletheremainderareattributedtothe683.3-keVtransition.Usingthisinformationcoupledwiththenumberofcountsinthedoublet,obtainedfromthe-delayed-raysingles,theabsoluteintensities,reportedinTable4.9,werededuced.Thelasttransitionnewtothisworkisthe1641.6-keVray.InFig.C.1jstrongco-incidencesbetween1641.6-keVtransitionandthe448.4-keV,969.6-keV,and1259.1-keVtransitionsareobserved.The1641.6-keVtransitionisalsoadoubletevidencedbythewidthofthepeakinFig.4.22dandtheresultsoftheisomerseparationinFig.4.35e.Thankfullythetwotransitionscomposingtheˇ1642-keVdoubletarealiatedexclusivelywiththedecayofdierent70Coisomersmakingtheanalysismorestraightforwardthanthatoftheˇ682-keVdoublet.Thecontaminating1643.5-607.5-keVcoincidence,denotedbytheblacksquareinC.1jwillbediscussedinthenextsection.Basedontheobservedcoincidencesthe1641.6-keVtransitionmostlikelyfeedsthe2677-keV6+
1stateplacinganewlevelat4319keV.AsummaryofallobservedcoincidencesisshowninTable4.10249AppendixD
CoincidencesObservedFollowingthe-DecayoftheLong-Lived,Low-Spin,70CoIsomer.Inthisappendixthecoincidencesobservedfollowingthe-decayofthelong-lived,low-spin,70Coisomerarepresented.Thesecoincidenceswereusedtoidentifyandplacelevelsinthelow-energy70Nilevelscheme.FigureD.1presentsaseriesofcoincidencespectraforraysobservedfollowingthedecayofthelong-lived,low-spin70Coisomer.InFig.D.1atherayscoincidentwithanew1037.5-keVrayareshown.The1259.1-1037.5-keVcoincidenceobservedinFig.D.1aisalsoobservedinFig.4.37a.The1037.5-keVtransitionwasplacedfeedingthe1259.1-keV2+
1statefromanewlevelat2296keV.Insinglesthereisa2294.3-keVtransitionnotincoincidencewithanyotherrayswhich,despitetheˇ2keVenergydierence,isproposedtobetheground-statetransitionforthisnewstate.InFigs.D.1band4.37aacoincidencebetweenanew1441.2-keVtransitionandthe1259.1-keVrayisobserved,whichplacesanewlevelat2700keV.Furthermore,arelativelyintensetransitionisobservedin-gated-raysinglesat2700.3keV,notincoincidencewithanyotherrays,andispresumedtobetheground-statetransitionforthenewlevel.Astrongcoincidencebetweenanew1676.3-keV-raywiththe1259.1-keVtransitionis250Counts / 2 keV-20020401259.1010Gated1037.5 keV1259.1Gated1441.2 keV-10010201259.1Gated1676.3 keV-5051015Counts / 2 keVCounts / 2 keVCounts / 2 keV1259.1Gated1952.3 keV0102030-505101259.1607.61866.5Gated1644.5 keV1259.1Gated2104.8 keV-10010-505Counts / 2 keVCounts / 2 keVCounts / 2 keVCounts / 2 keVGated2252.0 keVGated2531.0 keV1259.11259.1010002000-50510Energy (keV)Counts / 2 keVCounts / 2 keVGated2614.5 keV1259.1010002000-505607.6Gated3845.5 keV(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)Energy (keV)FigureD.1:Seriesofbackgroundsubtractedcoincidencespectracorrelatedtothedecayofthelong-lived,low-spin,70Coisomer.Thebackgroundwastakensymmetricallyeithersideofthepeakexceptwhereotherraysinterfered,inwhichcasethebackgroundwastakenaboveascloseaspossibletothepeakofinterest.Transitionsaliatedwiththeshort-lived,high-spin,70Coisomeraredenotedwithblacksquares.Transitionsobservedincoincidencebutnotinsinglesaredenotedwithasterisks.Theinsetsin(l)and(m)showthecoincidencespectragatedonthe1626-keVand771.9-keVtransitions.251FigureD.1:(cont'd)05Counts / 2 keV05Counts / 2 keVGated3853.4 keVGated3861.5 keV05-505Counts / 2 keVCounts / 2 keVGated4479.3 keV1259.11259.11259.1607.6607.61866.51866.5771.9*44604480450020-2Gated 771.9 keV-505-505Counts / 2 keVCounts / 2 keV010002000010002000Energy (keV)Energy (keV)Gated4132.4 keVGated4165.3 keV(k)(l)(m)(n)(o)(p)384038603880-202Gated1626 keV1259.11626*1259.1607.61866.51259.1607.61866.5Gated3984.6 keV-2024-5051015Counts / 2 keVCounts / 2 keV1259.11259.1607.61866.5Gated4822.5 keVGated4215.0 keV(q)(r)showninFigs.D.1mandFig.4.37a,placinganewlevelat2935keV.InFig.D.1dtherayscoincidentwiththe1952.3-keVray,rstidentiedbyRef.[23],areshown.ThecoincidenceisalsoobservedinFig.Fig.4.37a.InRef.[23]a1950-keVtransitionwasobservedincoincidencewiththe1259.1-keVtransitionandplacedfeedingthe1259-keV2+
1statefromanewlevelat3209.Thepresentresultssupportthisplacementandupdatestheenergyto3211keVforthenewlevel.Therayscoincidentwithanew1644.5-keVtransitionareshowninFig.D.1e.This252FigureD.1:(cont'd)-20246Counts / 2 keV607.6-20241259.1Gated4272.5 keVGated4880.5 keVCounts / 2 keV(s)(t)010002000-2024Counts / 4 keVGated4379.3 keV1259.1607.61866.5010002000-202Energy (keV)Energy (keV)(v)Counts / 2 keV4(u)Gated4901.2 keV1259.1rayisunresolvedfromthe1641.6-keVtransition,aliatedwiththedecayoftheshort-lived,high-spin,70Coisomer,andassuchthecoincidencespectrumiscontaminatedwiththe448.4-,969.6,and1259.1-keVtransitions,identiedbyblacksquaresinFig.D.1e.However,somecoincidenceswiththe1259.1-keVtransitionarenotcontaminants,andastrongcoincidencewiththe607.6-keV(2+
2!2+
1)transitionisobservedbothinFigs.D.1eand4.38a.Aweakercoincidenceisobservedwiththe1866.5-keVtransitionaswellinFigs.D.1eand4.38c.Thisplacesthe1644.5-keVrayfeedingthe1867-keV2+
2statefromthesame3511-keVlevelidentiedabove.Athirdtransitionwithanenergyof2252.0-keV,observedincoincidencewiththe1259.1-keVtransitioninFig.D.1g,wasplaceddepopulatingthesame3511-keVlevelandisbelievedtofeedthe1259.1-keV2+
1state.InFig.D.1fastrongcoincidencebetweenanew2104.8-keV-rayandthe1259.1-keVtransitionisobserved,placinganewlevelat3364keV.The2104.8-1259.1-keVcoincidenceisalsopresentinFig.4.37a.InFig.D.1hanew2531.0-keVrayisshownincoincidencewiththe1259.1-keVtran-253sitionplacinganewlevelat3790keV.Acoincidencebetweenanew2614.5-keV-rayandthe1259.1-keVtransitionispresentinFigs.D.1iand4.37b,placinganewlevelat3874keV.In-gated-raysinglesthereisacontaminanttransitioninthe2614-keVregionsotheintensityofthetransitionwasdeterminedusingtheeciency-corrected15(4)1259.1-2614.5-keVcoincidences.InFig.D.1ithe-rayscoincidentwithanew3845.5-keV-rayareshown.FiguresD.1iand4.37ashowacoincidencewith607.6-keVplacinganewlevelat5712keV.Fur-thermore,anew5711.4-keV-raywasidentiedin-gated-raysingles,andisassumedtobetheground-statetransitionforthisnewlevel.Anew2777.4-keV-raywasalsoplaceddepopulatingthenew5712-keVlevelandfeedingthenew2935-keVlevelbasedoenergydierences,butnocoincidenceswereobservedtosupportthisplacement.rayscoincidentwithanew3853.4-keV-rayareshowninFig.D.1k.Astrongcoinci-dencewiththe1259.1-keVtransitionisobserved,placingannewlevelat5112keV.InFig.D.1lcoincidencesbetweenanew3861.5-keVrayandthe607.6-keV,1259.1-keV,and1866.5-keVtransitionsareobserved,placinganewlevelat5728keV.Thereisanadditionalcoincidencewitha1626-keVray,whichisalsoobservedintheinsetinFig.D.1lobtainedbygatingonthe1626-keVregion.However,withoutthe-gateddecaycurvetoconrmthealiationofthe1626-keVraywiththedecayofthelong-lived70Coisomer,itcannotbecondentlyplacedinthedecayscheme.FigureD.1macoincidencebetweenanew4479.3-keVrayandthe1259.1-keVtransitionisobserved,placinganewlevelat5738keV.Therewere5(1)4479.3-1259.1-keVcoincidencesexpectedand6(2)arerecorded.Additionallytwoothertransitionswereplaceddepopulatingthislevelbasedonenergydierences.A3871.7-keVtransitionwasplacedfeedingthe1867-keV2+
2stateanda2803.4-keVtransitionwasplacedfeedingthe2935-keVlevel.These254placementsarenotbasedoanyrecordedcoincidencesanditisalsopossiblethatthe3871.7-keVtransitioncoulddepopulatea5130-keVlevel,forwhichtheunplaced5130-keVtransitioncouldbetheground-statetransition.Asecondcoincidencewitha772.0-keVrayisalsoobservedinFig.D.1mwhichinturnisseenintheinsetobtainedbygatingonthe772-keVregion.Howeverwithouta-gateddecaycurvetoconrmthe772.0-keVtransition'saliationwiththedecayofeither70Coisomeritcannotbeplacedinthedecayscheme.InFig.D.1ncoincidencesbetweenanew3984.6-keVrayandthe607.6-keV,1259.1-keV,and1866.5-keVtransitionsareobserved,placinganewlevelat5850keV.FiguresD.1oandD.1pshowcoincidencesbetweennew4132.4-keVand4165.3-keV-rays,respectively,withthe607.6-keV,1259.1-keV,and1866.5-keVtransitions.Thesecoincidencesplacenewlevelsat5999keVand6032keV.A4771.6-keVraywasalsoplaceddepopulatingthenew6032-keVlevel,feedingthe1259.1-keV2+
1state,basedoenergydierencesbutnocoincidenceswereobservedtosupportthisplacement.rayscoincidentwithanew4822.5-keV-rayareshowninFig.D.1q.Acoincidencewiththe1259.1-keVtransitionisobserved,placingannewlevelat6082keV.InFig.D.1rcoincidencesbetweenanew4215.0-keVrayandthe607.6-keV,1259.1-keV,and1866.5-keVtransitionsareobserved,andthereforethe4215.0-keVtransitionmostlikelydepopulatesthesamenew6082-keVlevel.A6081.9-keVraywasobservedin-delayed-raysinglesandwasplacedasthegroundstatetransitionforthenew6082-keVlevel.InFig.D.1sanew4272.5-keVrayisshownincoincidencewiththe607.6-keVtransition,placinganewlevelat6139-keV.Anothernewrayat4800.5-keVinobservedincoincidencewiththe1259.1-keVtransitioninFigureD.1t,whichplacesitdepopulatingthissamenew6139-keVlevel.255InFig.D.1uacoincidencebetweenanew4901.2-keVraywiththe1259.1-keVtransitionisobserved,placinganewlevelat6160keV.Basedoncalculatedenergydierencesbetweenlevelsthe2950.7-keVtransitionhasalsobeenplaceddepopulatingthisnew6160-keVlevelandfeedingthenew3211-keVlevel.However,nocoincidencesarepresenttoverifythatplacement.InFig.D.1vanew4379.9-keVrayisshownincoincidencewiththe607.6-keV,1259.1-keV,and1866.5-keVtransitions,placinganewlevelat6246keV.Alsoplacedinthedecayschemeforthelong-lived,low-spin,70Coisomeraretwonewlevelsat6284keVand6340keVforwhichonlythe6283.8-keVand6339.9-keVground-statetransitionsareobserved.Nocoincidenceswitheither607.6-keVor1259.1-keVtransitionswereobserved.256BIBLIOGRAPHY257BIBLIOGRAPHY[1]ProfessorE.RutherfordF.R.S.Lxxix.thescatteringofandparticlesbymatterandthestructureoftheatom.PhilosophicalMagazineSeries6,21(125):669{688,1911.[2]Crchandbookofchemistryandphysics,94thed.http://www.hbcpnetbase.com/,2013.[3]B.A.Brown.LectureNotesinNuclearStructurePhysics.MichiganStateUniversity,2010.[4]TakaharuOtsuka,ToshioSuzuki,RintaroFujimoto,HubertGrawe,andYoshinoriAkaishi.Evolutionofnuclearshellsduetothetensorforce.Phys.Rev.Lett.,95:232502,Nov2005.[5]S.M.Lenzi,F.Nowacki,A.Poves,andK.Sieja.Islandofinversionaround64Cr.Phys.Rev.C,82:054301,Nov2010.[6]KrisHeydeandJohnL.Wood.Shapecoexistenceinatomicnuclei.Rev.Mod.Phys.,83:1467{1521,Nov2011.[7]YusukeTsunoda,TakaharuOtsuka,NoritakaShimizu,MichioHonma,andYutakaUtsuno.Novelshapeevolutioninexoticniisotopesandconguration-dependentshellstructure.Phys.Rev.C,89:031301,Mar2014.[8]APoves.Shapecoexistence:theshellmodelview.JournalofPhysicsG:NuclearandParticlePhysics,43(2):024010,2016.[9]TOtsukaandYTsunoda.Theroleofshellevolutioninshapecoexistence.JournalofPhysicsG:NuclearandParticlePhysics,43(2):024009,2016.[10]JLWoodandKHeyde.Afocusonshapecoexistenceinnuclei.JournalofPhysicsG:NuclearandParticlePhysics,43(2):020402,2016.[11]J.Elseviers,A.N.Andreyev,S.Antalic,A.Barzakh,N.Bree,T.E.Cocolios,V.F.Comas,J.Diriken,D.Fedorov,V.N.Fedosseyev,S.Franchoo,J.A.Heredia,M.Huyse,O.Ivanov,U.Koster,B.A.Marsh,R.D.Page,N.Patronis,M.Seliver-stov,I.Tsekhanovich,P.VandenBergh,J.VanDeWalle,P.VanDuppen,M.Venhart,258S.Vermote,M.Veselsky,andC.Wagemans.Shapecoexistencein180hgstudiedthroughthedecayof180tl.Phys.Rev.C,84:034307,Sep2011.[12]W.F.Mueller,B.Bruyneel,S.Franchoo,M.Huyse,J.Kurpeta,K.Kruglov,Y.Kudryavtsev,N.V.S.V.Prasad,R.Raabe,I.Reusen,P.VanDuppen,J.VanRoos-broeck,L.Vermeeren,L.Weissman,Z.Janas,M.Karny,T.Kszczot,A.P 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