MASSMEASUREMENTSOFNEUTRON-RICHCOBALTISOTOPES BEYONDN=40ANDTHEDEVELOPMENTOFASINGLEION PENNINGTRAPMASSSPECTROMETERFORRAREISOTOPES By ChristopherJohnIzzo ADISSERTATION Submittedto MichiganStateUniversity inpartialentoftherequirements forthedegreeof Physics-DoctorofPhilosophy 2018 ABSTRACT MASSMEASUREMENTSOFNEUTRON-RICHCOBALTISOTOPESBEYONDN=40 ANDTHEDEVELOPMENTOFASINGLEIONPENNINGTRAPMASS SPECTROMETERFORRAREISOTOPES By ChristopherJohnIzzo Overthepastfewdecades,theuseofonlinePenningtrapmassspectrometry(PTMS)has enabledprecise,accuratemassmeasurementsofrareisotopesasaprobeofnuclearstructure farfromthevalleyofbetastability.AstheandonlyPenningtrapcoupledtoaprojectile fragmentationfacility,theLowEnergyBeamandIonTrap(LEBIT)facilityattheNational SuperconductingCyclotronLaboratoryallowsprecisionmassmeasurementsofexoticnuclei thatarenotavailableatotherPTMSfacilities. Thenuclearshellmodelprovidesarobustframeworkforunderstandingnuclearstructure Whilenuclearshellstructureiswellunderstoodforstableisotopes,theevolutionof nuclearstructureawayfromstabilityremainsanactiveareaofrareisotoperesearch.The regionnear Z =28and N =40isasubjectofgreatinterestfornuclearstructurestudies duetospectroscopicsignaturesin 68 Nisuggestingasubshellclosureat N =40.Trendsin nuclearmassesdonotappeartosupportthisconclusion,howeveracompletepictureofthe masssurfacesinthisregionhassofarbeenlimitedbythelargeuncertaintyremainingfor nucleiwith N> 40alongtheiron( Z =26)andcobalt( Z =27)chainsbecausethesespecies arenotavailableattraditionalisotopeseparatoronline(ISOL)facilities.RecentPenning trapmassmeasurementsof 68 ; 69 CoatLEBITprovidethepreciseexaminationofnuclear massesbeyond N =40intheCochain.Themotivation,procedure,andresultsofthese measurementsarepresentedinthisdissertation.Recenttheoreticalcalculationsforthese isotopesarealsopresented,andtheimportanceofthesemeasurementsandcalculationsfor understandingtheevolutionofnuclearstructurenear 68 Niisdiscussed. InordertoexpandthereachofLEBITtoisotopesveryfarawayfromstability,anewSin- gleIonPenningTrap(SIPT)hasbeendeveloped.Manyrareisotopesfarfromstabilitycan onlybeproducedatverylowratesincompatiblewiththecurrentdestructivemeasurement techniqueusedforonlinePTMS,whichrequires ˘ 100ionsormoretocompleteamassmea- surement.SIPTemploysanon-destructivemeasurementtechniquewhichenablescomplete massdeterminationswithasingleion.Thistechniquehasbeenusedsuccessfullyatotherfa- cilitiesforstableparticlemeasurementsbuthasneverbeforebeenextendedtomeasurements ofexoticradioisotopes.ThedesignandocommissioningtestsofSIPTarepresentedin thiswork,demonstratingpromisingoutlookforsingleionrareisotopemeasurementsinthe nearfuture. ACKNOWLEDGMENTS Graduateschoolhaspresentedmewithmanyofthemostchallengingandrewarding experiencesofmylifesofar,andIoweanenormousdebtofgratitudetoeveryonewho helpedmenavigatethisperiodofmylife.FirstIwouldliketothankmyadvisor,Georg Bollen,whoseenthusiasmforhisresearchconvincedmetojointheLEBITteam.Thank youtoGeorgforgivingmetheopportunitytotakepartinsuchexcitingandimportant projects,forallowingmetotraveltoconferencesandsummerschoolprogramstocontinue myprofessionaldevelopment,andforchallengingmetobecomeabetterscientist.Thank youaswelltotheothermembersofmycommittee,AlexandraGade,VladimirZelevinsky, DaveMorrissey,andStuartTessmer,fortakingthetimetoguidemethroughtheprocessof completingmyPhDandprovidinghelpfulfeedbackateachofourmeetings. IalsowanttosayahugethankyoutoRyanRingleforsupervisingmethroughoutmy graduateresearch.DespitehisfeelingstowardsHarryPotterandraspberrybeer,Ryanhas stillbeenthebestmentorIcouldhavehopedforduringthisformativeperiodofmycareer. Theworkofthisthesiswouldnothavebeenpossiblewithoutthesupportofmany collaboratorswhohelpedmealongtheway.Inparticular,IwanttothankMattRedshaw forteachingmetheartofFT-ICRdetection,JasonHoltforprovidingvaluabletheoryinput tohelpwiththeinterpretationofmythesisdata,andChandanaSumithrarachchiformany helpfuldiscussionsthattaughtmehowtobea\real"nuclearexperimentalist. IhavebeenextremelyfortunatetoworkwithanincredibleteamofLEBITpostdocsand students.Duringtheirtimeaspostdocs,KerimGulyuzandMartinEibachwereinvaluable resourcesformeasanewgradstudentwithamillionquestions.IwanttothankAdrian ValverdeandRachelSandler,theotherLEBITgraduatestudentsformyfewyearsin iv thegroup,fortheirsupportandfriendship.Ialsohavetoacknowledgethenewguardof LEBITstudents,AlecHamaker,IsaacYandow,DanielPuentes,and0.5*(JasonSurbrook), formakingthelastpartofmytimewithLEBITanabsoluteblast.Bestoflucktoyouguys, trynottodestroythelabonceI'mgoneandremembertostayclearofDanny's\sangria." Ican'tsaythankyouenoughtothemanywonderfulfriendsIhavemadeduringmytimeat MSU.Iamforevergratefulforeveryonewhotookpartinthemanyhallwaychats,lunches intheatrium,apartmenthangouts,winenights,studysessions,physicschoirrehearsals, boardgames,Lugnutsgames,karaokenights,movienights,trivianights,andcountlessother adventuresoverthelasteyears.AspecialthankyoutoWeiJiaOng,AmyLovell,and JoshBradtforprovidinganincrediblesupportsystemthroughoutgradschool(particularly duringthecoupleyearswhenIwasdrowninginproblemsets)andformanymuch-needed momentsoflevityandmomentsofsinceritythatalwayscameatjusttherighttime. ThankyouaswelltotheoldHFcrewforcontinuingtosupportmeevenasweallscatter aroundthecountryandsettleintoouradultlives.Christine,Emily,Lawrence,Rabia,Renee, Sam,andSteve,youallaremyrolemodels.IalsohavetothankLindseySteinberg,whose friendshipmeansmorethanIcanthewordstosay. ThankyoutotheChicagoCubsforwinningtheWorldSeries.Seriously,thatwas abigmomentforme. Finally,Iwanttoacknowledgemyincrediblefamily.Myparentshaveshownmesomuch loveandsupportineveryoneofmyendeavors,andthatmeanstheworldtome.Mysisters, BethandCindy,aretwoofthebestpeopleIknowandtheycontinuallyinspiremetobe abetterperson.Mostofall,Iwanttoacknowledgemygrandparents.Myhappinessand successaredirectproductsofthestheymadeandthelovingfamilystructuresthey workedtobuild.Iwillneverforgettheirmanystories,jokes,andlifelessons. v TABLEOFCONTENTS LISTOFTABLES .................................... viii LISTOFFIGURES ................................... ix Chapter1Introduction ............................... 1 1.1ImportanceofAtomicMassesforNuclearScience...............1 1.1.1EvolutionofNuclearStructureAwayFromStability.........2 1.2MassMeasurementsofRareIsotopes......................4 1.3MotivationforaNon-DestructiveMassMeasurementTechnique.......6 Chapter2PenningTrapMassSpectrometry .................. 9 2.1PenningTrapBasicConcepts..........................9 2.1.1TrappingFields..............................9 2.1.2IonMotioninaPenningTrap......................10 2.1.3ManipulationofIonMotionwithRFElectricFields..........12 2.2OverviewofPenningTrapMassSpectrometry.................14 2.3TOF-ICRTechnique...............................18 2.4FT-ICRTechnique................................21 Chapter3TheLEBITMassSpectrometerFacilityattheNSCL ..... 24 3.1BeamStoppingattheNSCL...........................26 3.2MajorComponentsoftheLEBITFacility...................28 3.2.1IonSources............................29 3.2.2Cooler/buncherandFastElectrostaticKicker.............30 3.2.3TOF-ICRPenningTrap.........................32 3.2.4SIPT....................................33 Chapter4MassMeasurementsofNeutron-RichCobaltIsotopesBeyond N=40 .................................... 34 4.1MotivationforMassMeasurementsof 68 ; 69 Co.................34 4.1.1EvidenceforaSubshellClosureat N =40...............34 4.1.2MassMeasurementsAround N =40..................36 4.2ExperimentalProcedure.............................40 4.2.1GasCellChemistry............................40 4.2.2SWIFTBeam........................43 4.2.3IsomerInvestigations...........................45 4.3ResultsandDiscussion..............................46 4.3.1MassMeasurementResults........................46 4.3.2LevelAssignment.............................48 4.3.3EvaluationofTwo-NeutronSeparationEnergyTrends........53 vi Chapter5DevelopmentofaSingleIonPenningTrapMassSpectrometer forRareIsotopes ............................ 58 5.1SIPTConceptandRequirements........................58 5.2TheSIPTBeamline................................62 5.3TheSIPTPenningTrap.............................65 5.3.1SpectrometerDesign...........................65 5.3.1.1TheSIPTMagnet.......................65 5.3.1.2PenningTrapElectrodeSystem................66 5.3.1.3CryogenicSystem........................69 5.3.1.4TOF-ICRDetection......................71 5.3.1.5FT-ICRDetectionCircuitDesign...............72 5.3.2ControlsandDataAcquisition......................76 5.4CommissioningoftheSingleIonPenningTrap.............78 5.4.1RoomTemperatureCommissioning...................78 5.4.2CryogenicCommissioning........................80 5.4.2.1Coolingto4K.........................80 5.4.2.2ResonatorCircuitResponse..................83 Chapter6SummaryandOutlook ......................... 88 APPENDICES ...................................... 90 AppendixACharacterizationoftheMiniTrapMagnetometer...........91 AppendixBEvaluationofSystematicFrequencyShiftsforSIPT..........98 AppendixCLimitingCaseRatioof 68 Co -DecayingStates............104 BIBLIOGRAPHY .................................... 109 vii LISTOFTABLES Table1.1:Areasofrare-isotoperesearchandtypicalprecisionsrequiredtoprobethe associatedphysicsusingmassmeasurements.................2 Table4.1:ComparisonofconditionsforRun1andRun2................44 Table4.2:Measuredfrequencyratios, c / c; ref ,calculatedatomicmassandmassex- cess(ME)values,andtheircomparisontothevaluesfrom2016Atomic MassEvaluation.inthemassexcessvalues,=ME LEBIT ME AME2016 ,arealsolisted...........................48 Table5.1:Parametersusedtoestimatetheachievable S=N fornarrowbandFT-ICR measurementswithasingleion........................61 Table5.2:Oxfordmagnetspasprovidedbythesupplier..........66 Table5.3:SIPTPenningtrapdimensions(seeFig.5.6.)................68 Table5.4:VendorspcationsforPT415cryorefrigeratorwithCP1110heliumcom- pressorfromCryomech,Inc..........................70 viii LISTOFFIGURES Figure1.1:Thechartofthenuclides,witheachnuclidecoloredaccordingtoitscur- rentlyknownmassprecision.Massprecisionscomefromthemostrecent AtomicMassEvaluation(AME2016)[1]...................2 Figure2.1:Threehyperbolictrapelectrodes(twoendcapelectrodesandonering electrode)usedtocreatethequadrupolarelectrostaticnecessaryfor axialionement.............................10 Figure2.2:IllustrationofthemotionofachargedparticleinaPenningtrap.This motionisacombinationofthreedistincteigenmotions:themagnetron motion(green)atfrequency ! ,themocyclotronmotion(red)at frequency ! + ,andtheaxialoscillations(blue)atfrequency ! z .Theblack pathillustratesthecombinationofthesethreemotions...........12 Figure2.3:AppliedRFgeometriesuesedtoobtaindipole(left)andquadrupole(right) excitationsoftheions'motioninthePenningtrap.AtLEBIT,thering electrodeissegmentedtoachievethesegeometries.Redandbluesegments representRFapplicationsofequalfrequencyandamplitude,180 ° outof phase......................................13 Figure2.4:Conversionbetweenthetworadialmodesofanion'smotioninaPenning trap.(a)Theionbeginswithpuremagnetronmotion(redcircle).When aquadrupoleRFdriveisappliedatthetruecyclotronfrequency c ,the mocyclotronradiusgrowsasseenbythegrowingblackcircles,and themagnetronradiusdecreasesasindicatedbythebluearrow.(b)When fullconversionofmagnetrontomocyclotronmotioniscomplete, themocyclotronradiusisequaltotheinitialmagnetronradius...14 Figure2.5:IonsejectedfromthePenningtrapmovethroughanaxialmagnetic gradientastheytraveltotheMCPdetector.Thisresultsinanaxialkick proportionaltotheions'radialenergy,asdemonstratedbyEq.(2.10)..19 Figure2.6:ExampleofaTOF-ICRresonanceobtainedbyscanningtheappliedRF quadrupoleexcitationfrequencyandmeasuringtheions'timeoftto anMCPdetector.Theredcurveisatheoreticalthecenterofwhich correspondsthecyclotronfrequency c ....................20 Figure2.7:SchematicillustrationofnarrowbandFT-ICRdetection..........23 ix Figure3.1:LayoutoftheNSCL.RareisotopebeamsfromtheA1900aredelivered eitherdirectlytofastbeamexperimentsortothebeamstoppingfacility, fromwhichstoppedbeamsaresenttolow-energyexperimentsincluding LEBITortothere-acceleratorfacilityforintermediateenergyexperi- ments.(Adaptedfrom http://nscl.msu.edu/public/virtual-tour. html .).....................................25 Figure3.2:PhotooftheANLgascellusedforbeamstoppingattheNSCL......27 Figure3.3:LayoutoftheLEBITfacility.Thefunctionsofeachmajorcomponentare describedinthetext.(Reproducedfrom https://groups.nscl.msu. edu/lebit/lebitfacility/index.html .).................28 Figure3.4:PhotooftheColutronionsourcewhichproducesstableandlong-lived ionsviaplasmaorsurfaceionization.....................29 Figure3.5:PhotoofthelaserablationionsourceatLEBIT..............30 Figure3.6:PhotosoftheLEBITcooler/buncherusedtopreparecooledionbunches fordeliverytothePenningtrap.Thepre-coolerandmicro-RFQareshown ontheleft,andthebuncherstageisshownontheright..........31 Figure3.7:The9.4-Tsuperconductingmagnet(left)andhyperbolicPenningtrap electrodestructure(right)usedforTOF-ICRmeasurementsatLEBIT..32 Figure3.8:Photooftherecently-commissionedSIPTbeamline,usedforiontransfer fromthecooler/bunchertothe7-TSIPTmagnetforFT-ICRmeasure- ments.Detailsonindividualcomponentsofthisbeamlinearepresented inSection5.2.................................33 Figure4.1:Single-particleshellmodelenergylevelsusingaharmonicoscillatorpo- tentialplusan l 2 interactionwithoutspin-orbitinteraction(left)andwith spin-orbitinteraction(right).........................35 Figure4.2:First-excited2 + stateenergiesE 2+ (top)and B ( E 2;0 + ! 2 + )transition strengths(bottom)intheeven-evennickelisotopes.Alldatatakenfrom Ref.[74].ThelargeE 2+ andthesmall B ( E 2)valuesat N =40suggest asubstantialshellgap.............................36 Figure4.3:Two-neutronseparationenergy S 2 n plottedasafunctionofneutronnum- ber N intheregionfrom Z =31to Z =50.Dataaretakenfromthe AME2016atomicmassevaluation[1].....................38 x Figure4.4:Two-neutronseparationenergy S 2 n plottedasafunctionofneutronnum- ber N intheregionaround 68 Ni.DataaretakenfromtheAME2016 atomicmassevaluation[1]..........................39 Figure4.5:Radioactivityobservedasafunctionofthe m=q valuetransmittedthrough thedipolemassseparatorforRuns1and2.TheofCIDisseenby comparingthecasewherethereisnobiasappliedtothegascellextraction tothecasewherea-150Visapplied.Notethat m=q wasscanned fromhighvaluestolowinRun1andfromlowvaluestohighinRun2, hencetheoppositedirectionsofthedecaytails...............42 Figure4.6:AttemptedTOF-ICRresonancesof 68 Co 2+ withSWIFT(left)and SWIFTon(right).Atamountofunidenstablecontam- inationfromthegascellarrivedat m=q =34,obscuringtheresonance beforeSWIFTwasturnedon.TheuseofSWIFTtocleanuniden contaminantsmadethismeasurementpossible...............45 Figure4.7:Schematicoverviewofthemajorexperimentalcomponentsusedforthis work......................................46 Figure4.8:The -delayed -rayspectrumdetectedfollowingthedecayof 68 Co.Dashed verticallinesmarktheenergiesof raysknowntofollowprimarilydecay fromonlyoneofthetwo -decayingstatesof 68 Co. raysat478keV followdecayfromthelow-spinstateand raysat324and595keVfollow decayfromthehigh-spinstate.Thepresenceofclearpeaksat324and 595keVandthelackofapeakat478keVsuggestthatthehigh-spin -decayingstateof 68 Cowasmeasuredinthisexperiment.Otherpeaks inthespectrumhaveallbeenidenfromeithernaturalbackground radiationor 68 Codecayscommontoboth -decayingstates........50 Figure4.9:Simlevelschemeshowingtherelevant -delayedgammaraysfor thetwo -decayingstatesof 68 Co.Circledgammaenergiesarethosethat signalthepresenceofonestateortheother,butnotboth.Energiesare allgiveninkeV.Basedondatafrom[88,94,95]...............50 Figure4.10:Two-neutronseparationenergies S 2 n plottedasafunctionofneutron number N forisotopesofiron,cobalt,nickel,andcopper.Greensquare pointscorrespondtonewcobaltvaluesfromthisworkandblackcircles correspondtodatafromAME2016[1].Pointsplottedwithanxmarker indicatevaluesderivednotfrompurelyexperimentaldataintheAME2016.54 xi Figure4.11:Neutronshellgap N plottedasafunctionofneutronnumber N for isotopesofiron,cobalt,nickel,andcopper.Thegreencurvecorresponds tonewcobaltvaluesfromthisworkandtheblackcurvescorrespond todatafromAME2016[1].Pointsplottedwithanxmarkerindicate valuesderivednotfrompurelyexperimentaldataintheAME2016.Inset: Neutronshellgapplottedasafunctionofprotonnumber Z forisotopes with N =40neutrons.............................56 Figure4.12:Two-neutronseparationenergies S 2 n plottedasafunctionofneutron number N forthenickelisotopicchain.Thesolidblackdataaretaken fromAME2016,andthedashedlinescorrespondtoIM-SRGtheoretical calculations.Bluetrianglesusea 40 Cacorefor N 40( pf neutron valencespace)anda 60 Cacorefor N> 40( sdg neutronvalencespace). Redsquaresusea pf 5 = 2 g 9 = 2 valencespaceforprotonsandneutronsfor theentirechainstartingfroma 56 Nicore..................57 Figure5.1:Frequencydomainprecisionasafunctionofsignal-to-noiseratiofor simulatedsingleionsignalsfrom 78 Ni + and 100 Sn + ............61 Figure5.2:LayoutofthemajorcomponentsofthenewSIPTbeamline........62 Figure5.3:115 ° cylindricalbender,withintegratedelectrostaticquadrupoledoublets oneachendandaquadrupolesingletinthemiddlefortransversebeam focusing.....................................63 Figure5.4:SimulatediontrajectoriesthroughtheSIPTbeamline,fromthekickerto the7-TSIPTmagnet.............................64 Figure5.5:Designdrawingandphotographofthedrifttubeassemblyusedforion injection/ejectionto/fromtheSIPTPenningtrap..............65 Figure5.6:DesigndrawingoftheSIPTPenningtrapcorrectedhyperbolicelectrode system.TrapdimensionsgiveninTable5.3.................68 Figure5.7:SIPTPenningtrapelectrodesbeforeassembly(left),partwaythrough assembly(middle)andafterassembly(right)................68 Figure5.8:OverviewoftheSIPTcryogenicsystemcomponents............71 Figure5.9:ConceptualoverviewofreverseionextractionforTOF-ICRmeasurements withSIPT...................................72 Figure5.10:SchematiccircuitdiagramoftheSIPTcryogenicanddetection electronics...................................73 xii Figure5.11:FlowchartsoutliningtheSIPTdataacquisitionprocesscurrentlyusedfor testing(left)andthatenvisionedforfutureonlineexperiments(right).77 Figure5.12:ScreenshotsoftheQt-baseduserinterfaceusedforcontrolofSIPThard- waredevicesincludingpowersupplies,AFGs,vacuumpumps,andgate valves......................................78 Figure5.13:10msTOF-ICRresonanceof c for 39 K + usingreverseionextraction fromtheSIPTPenningtraptotheSIPTDalyMCP............79 Figure5.14:DemonstrationofbroadbandFT-ICRdetectionwithSIPTatroomtem- perature.Theionpeakseeninthiscomesfrompickinguptheim- agecurrentgeneratedbythemocyclotronmotionofmany( ˘ 1000) 39 K + ions.Thedatapresentedhereistheaverageofeconsecutive shots,eachofwhichuseda256msacquisitiontime.............80 Figure5.15:SIPT4KstagewrappedinMylartoreduceradiativeheatingfromthe surrounding45Kstage.TwolayersofMylarwrappingwerenecessaryto reachtemperaturesof ˘ 4K..........................81 Figure5.16:600 HNbTiinductorcoil(left)andNbTiinductorcase(right)usedfor thehigh-QSIPTFT-ICRdetectioncircuit.Theinductorcoilconsists of194turnsof250 mNbTiwirewithtubularTcoatingwrapped aroundaTcore.Thewindingswerethencoveredbyanadditional layerofTntape,whichprovidesbothmechanicalsupportandsome additionalamountofthermalconductivity..................82 Figure5.17:SIPT4Kchamberwithallcomponentsmountedandwired(bottom). Thedesigndrawingofthisregionisincludedforreference(top)......83 Figure5.18:ResistanceacrosstheNbTiinductorcoilplottedovertimealongsidethe temperaturereadingsfromtheCernoxtemperaturesensorsmountedon thecoldheadandthebackoftheSIPTPenningtrap.Roughly12hours afterthetemperaturesensorsreachedtheirminimumvalues,theNbTi coilcooledbelowitscriticaltemperatureandenteredasuperconducting state,asevidencedbytheresistancedroptonearly0.........84 Figure5.19:FrequencydomainresponseoftheSIPTnarrowbandFT-ICRcryogenic detectioncircuitoperatingat ˘ 5.2K.Thisverynarrowfrequencyresponse correspondstoacircuitQfactorof2785,whichisgreaterthanwhatis requiredforsingleiondetection........................87 xiii FigureA.1:ALabVIEWscreenshotofFFTresonancesofbothmocyclotron motion(left)andtruecyclotronmotion(right)ofH 3 O + ionsmeasured withtheMiniTrapmagnetometerusingabroadbandFT-ICRquadrupole detection...........................93 FigureA.2:Resultsofthedipolecleaningscanusedtodeterminethemocy- clotronfrequency + ofionizedbackgroundgasmoleculesintheMini- Trapmagnetometerafteritwasmovedtoitscurrentlocationinthe9.4-T LEBITmagnet.................................94 FigureA.3:MiniTraptuningscansusedtodeterminetheoptimalratiobetweenthe endcapandringpotentials.Thetrapdepthwasheldconstantat10.4V. Aratioof9.15to-1.25betweentheendcapandringpotentialswasfound toproducethebestapproximationofaquadrupolarelectrostaticpotential because,atthesesettings,themeasuredionfrequencyvariedtheleastas theionsweredriventoincreasinglylargeradii...............94 FigureA.4:Amplitude(top)andcenterfrequency(bottom)ofthe + peakinthe FFTspectrumasafunctionoftheappliedRFexcitationfrequency.The plotsontheleftwereobtainedwitha200mVppRFexcitationandthe plotsontherightwereobtainedwitha150mVppRFexcitation.The observedbehaviorisdiscussedinthetext..................95 FigureA.5:FrequencydomainresponseoftheMiniTraproomtemperatureresonant circuitusedfornarrowbandFT-ICRdetectionofthetruecyclotronmotion oftrappedH 3 O + ions.............................96 FigureB.1:Illustrationofthemisalignmentangle betweenthemagneticand thePenningtrapaxis.............................99 FigureB.2:FrequencyratioshiftsduetomisalignmentbetweenthePenningtrapaxis andthemagneticasafunctionofionmass,assuminga6umass betweentheionofinterestandthereferenceion.........100 FigureB.3:RadarplotsofthemagneticstrengthintheSIPTmagnetdetermined fromNMRmeasurementsafterthemagnetwasenergized.........102 FigureB.4:Relativemocyclotronfrequencyshiftsduetospecialrelativityplot- tedasafunctionofmocyclotronradius ˆ + forionsofvariousmasses ina7-Tmagnetic...........................103 xiv Chapter1 Introduction 1.1ImportanceofAtomicMassesforNuclearScience Oneofthemostimportantconceptsgoverningthepropertiesandprocessesstudiedacross manyareasofnuclearscienceresearchisthebindingenergywhichholdsprotonsandneutrons togetherinanatomicnucleus.Owingtothewell-knownmass-energyequivalencegivenby Einstein'sfamousequation E = mc 2 ,thebindingenergyofanucleusisdirectlyre inthemassofthenucleus,asthetotalnuclearmassisthesumoftheconstituentnucleon massesminusthebindingenergy.Massmeasurementsthereforepresentacriticaltoolfor probingawidevarietyofnuclearBycomparingatomicmasssbetween variousisotopesandlookingatmasstrendsacrossthenuclearchart,muchinformation canbeobtainedforanumberofresearchapplicationsincludingnuclearstructure,nuclear astrophysics,andfundamentalinteractionstudies. Fig.1.1showsthechartofthenuclides,witheachnuclidecoloredbyitscurrentlyknown massprecisionaccordingtothemostrecentAtomicMassEvaluation(AME2016)[1].As seeninthischart,atomicmassesaregenerallyknowntoaveryhighdegreeofprecisionfor moststableisotopes.Thefurtheronegetsfromstability,however,thelesspreciselythemass isgenerallyknown,owingtotheyofproducingandstudyingsuchexoticisotopes. Table1.1showstypicalmassprecisionsrequiredfortareasofrare-isotoperesearch[2]. 1 ResearchArea m=m NuclearStructure 10 6 NuclearAstrophysics 10 7 NuclearModelsandFormulae 10 7 WeakInteraction 10 8 Table1.1:Areasofrare-isotoperesearchandtypicalprecisionsrequiredtoprobetheasso- ciatedphysicsusingmassmeasurements. Figure1.1:Thechartofthenuclides,witheachnuclidecoloredaccordingtoitscurrently knownmassprecision.MassprecisionscomefromthemostrecentAtomicMassEvaluation (AME2016)[1]. ComparingTable1.1withFig.1.1,itisclearthatanabundanceofscienmotivation remainstocompleteprecisemassmeasurementsofrareisotopesawayfromstability. 1.1.1EvolutionofNuclearStructureAwayFromStability Thenuclearshellmodelplaysacentralroleinunderstandingnuclearstructure.Aquantum- mechanicaltreatmentoftheprotonsandneutronsinanuclearpotentialrevealsthediscrete quantumstatesthatanucleuscanoccupy.Largeenergygaps,knownasshellgaps,exist betweencertainclustersoforbitals,knownasshells.Theseareanalogoustotheatomic 2 shellsoccupiedbyelectronsinanatom.Justasclosed-shellatoms(theinertgases)exhibit ahighdegreeofchemicalstability,closed-shellnucleiaresimilarlystable,andtheproperties ofnucleiwithnearlyclosedshellscantypicallybeexplainedsimplybythepropertiesofa fewvalencenucleonsorholes.Thetotalnumberofnucleonsneededtocompleteaproton orneutronshellisreferredtoa\magicnumber,"andnucleiwithamagicnumberofboth protonsandneutronsareknownas\doubly-magic"nuclei.TheNobelPrizewasawarded in1963toMariaGoeppert-MayerandJ.HansD.Jensenfortheirworkonthenuclear shellmodel,demonstratingthattheinclusionofaspin-orbitinteractioncouldbeusedto reproducetheexperimentallyobservedmagicnumbers[3,4]. Amajorareaofinterestincurrentnuclearstructureresearchistheevolutionofshell structureawayfromstability.Asearlyas1960,TalmiandUnnademonstratedthatthe N =8shellgapislostinneutron-richberylliumisotopes[5].In1975,onlinemassspec- trometryexperimentssuggestedthatthe N =20neutronshellclosure,well-establishedfor stableisotopesaround 40 Ca,maynotpersistforunstableisotopeswithrelativelylarge N=Z ratios[6].Thiswaslaterbyadditionalexperimentalstudies[7{9]. Itisworthemphasizingtheofthisrealizationthatthemagicnumbers,which providesuchanimportantfoundationforourunderstandingofnuclearstructure,arenot immutableaswaspreviouslybelieved.Thissparkedarushofexperimentalandtheoretical toidentifyandexplainfurtherexamplesofevolvingshellstructureawayfromstability. tprogresshasbeenmadeinthisregardoverthelastfewdecades.Developments inrareisotopeproductionhavevastlyexpandedtherangeofexoticnucleiavailableforstudy, whiledevelopmentsindetectionandmeasurementtechniqueshaveimprovedtheaccuracy andsensitivityofexperimentalstudies.Onthetheoreticalside,theoftensor[10]and three-bodyinteractions[11{13]arenowunderstoodtoplayanimportantroleinshiftingthe 3 relativespacingofshellmodelenergylevelsinregionsofthenuclearchartfarfromstability, resultinginthedisappearanceofsomemagicnumbersandtheappearanceofnewones. Anareaofparticularinterestoverthelastfewdecadesistheregionaround N =40, Z =28duetoexperimentalsignaturessuggestingthearrivalofamagicnumberat N =40 inthe 28 Nichain.ThisexampleisexploredinChapter4,presentingnewresultsfromprecise massmeasurementsof 27 Coisotopesbeyond N =40whichexpandtheunderstandingof nuclearstructureinthisregion. 1.2MassMeasurementsofRareIsotopes TherelationbetweenatomicmassesandbindingenergydiscussedinSection1.1makes massesimportantprobesforinvestigatingnucleartrendsawayfromstability.Massde- terminationsaregenerallycategorizedaseitherindirectordirectmeasurements.Indirect measurementsrelyonnuclearreactionorradioactivedecaystudiestodeterminemass ences,knownas Q -values,betweenparentanddaughternuclei.Chainsof Q -valuescanthen beusedtodeterminemassesofisotopesfarfromstability.Uncertaintiesfromeach Q -value measurementaccumulateinthemassdetermination,withtheresultthatindirectmass measurementsofrareisotopesfarfromstabilityfrequentlycomewitharelativelyhighdegree ofuncertainty. Directmassmeasurementsincludethosebasedont,frequency,magnetic rigidity,orsomecombinationofthesetechniques.Time-otmeasurementswithmass spectrometersallowfastandhighlysensitivemeasurements,whichareimportantproperties formeasuringradioactiveisotopesfarfromstabilityassuchisotopesareoftenproducedat lowratesanddecayinshorttimespans.ExperimentssuchasSPEGatGANIL[14],TOFI 4 atLANL[15],andtheS800spectrographattheNSCL[16]havesuccessfullyemployedsuch methodsfordirectmassmeasurementsofrareisotopes.AttheRIKENRadioactiveIsotope BeamFactory,thetimetmagnetic-rigiditytechniquewasusedrecentlytoperform thedirectmassmeasurementsoftheneutron-richisotopes 55 57 Ca[17]. Theobtainableprecisionofsuchmeasurementsislimitedbytheions'totalght, soavarietyofstrategieshavebeendevelopedtoextendtheions'pathlengthandthusthe traveltime.TheCSS2cyclotronatGANIL[18]andSARAatGrenoble[19]usedcyclotrons tosendionsalongaspiralpath.StorageringsincludingtheExperimentalStorageRing (ESR)atGSI[20]andtheHeavyIonCooler-Storage-Ring(HIRFL-CSR)atLanzhou[21] usemanypassesaroundalargecircularringtoextendthepathlength.time- t(MR-TOF)devicesuseelectrostatictobounceionsbackandforthwithina smallchamberforasetnumberofpasses.MR-TOFdeviceshavebecomeverypopularinthe lastfewyearsbecausetheyarerelativelycompactandinexpensivetobuild,andcanachieve veryhighmassresolutionswhenalargenumberofareused[22{25].Suchdevices areoftenusedforbeambuthavealsodemonstratedtheabilitytoachievehigh precisiondirectmassmeasurementsofrareisotopes.Forinstance,theMR-TOFdeviceat ISOLDEwasusedtoexplorenuclearstructuretrendsfarfromstabilityalongtheCachain outto 54 Cawithsub-ppmmassprecision[26]. ThehighestdegreeofmassprecisionandaccuracyisachievedusingPenningtrapsto measurethecyclotronfrequencyofionsnedinastrongmagneticThesetechniques arediscussedindetailinChapter2.Penningtrapmassspectrometry(PTMS)hasbeen usedtomeasurestableionsatmassprecisions m=m< 10 10 [27]andunstableionsat precisions < 10 8 [28].ThedemonstrationthatPenningtrapscouldbeimplemented forprecisionmassmeasurementsatarareisotopefacilitywasISOLTRAPattheISOLDE 5 facility[29].ThesuccessofISOLTRAPpromptedthedevelopmentofseveralotherPTMS programsatvariousrareisotopefacilities,includingJYFLTRAPata[30],CPTat ArgonneNationalLab[31],SHIPTRAPatGSI[32],LEBITatNSCL[33],andTITANat TRIUMF[34]. Amongthesefacilities,theLow-EnergyBeamandIonTrap(LEBIT)facilityatthe NationalSuperconductingCyclotronLaboratory(NSCL)istheandonlyPenningtrap massspectrometercoupledtoaprojectilefragmentationfacility,allowinghigh-precisionmass measurementsofrareisotopesthatareunavailableatotherPenningtrapfacilities.Since itscommissioningin2005,LEBIThassuccessfullymeasuredthemassesofmorethan65 tspecies,achievingmassprecisionsaslowas ˘ 2ppb[28]andmeasuringspecieswith half-livesbelow100ms[35].TheworkdiscussedinthisthesiswascarriedoutatLEBIT, andtheLEBITfacilityisdiscussedindetailinChapter3. 1.3MotivationforaNon-DestructiveMassMeasure- mentTechnique OneofthemostsigtassociatedwithPenningtrapmassmeasurementsof isotopesfarfromstabilityistheextremelylowproductionratesforsuchspecies.Much ofthemostgroundbreakingrare-isotoperesearchoccursattheedgesofthenuclearchart, exploringthelimitsofnuclearbindingandthechangesinnuclearinteractionsthatoccur insuchexoticnuclei.Rare-isotope-beamfacilitiesarebeginningtoachievetheabilityto producethesenuclei,howeverproductionratesareoftenextremelylow. ThePTMStechniquescurrentlyusedforrareisotopemeasurementsaredestructivetech- niques,meaningthattheionsbeingmeasuredarelostduringthemeasurementprocess.Asa 6 result,ionsmustbecontinuouslyre-loadedintothePenningtrap.Acompletemassdetermi- nationrequiresaminimumof ˘ 100detectedionswithsuchdestructivetechniques(details onPTMStechniquesarepresentedinChapter2).Forextremelyexoticisotopesfarfrom stability,whereproductionratesmayby ˘ afewperdayorless,itisthereforeimpossibleto useadestructivetechniquetocompleteaPenningtrapmassmeasurementsimplybecause thetimerequiredtodetect ˘ 100ionsfarexceedsthetimeavailablefortypicalonlinebeam experiment(typicallyaweekortwo). At,non-destructivePTMStechniqueknownasnarrowbandFourierTransform IonCyclotronResonance(FT-ICR)hasbeenusedforextremelyhigh-precisionmassmea- surementsofstableionswithsingle-ionsensitivity.Inantoextendthistechnique toshort-livedradioisotopesfarfromstability,anewPenningtrapknownastheSingleIon PenningTrap(SIPT)hasrecentlybeendevelopedatLEBIT.Thedesignandcommis- sioningofSIPTarepresentedindetailinChapter5.Usingthenon-destructivenarrowband FT-ICRtechnique,SIPTwillallowcompletemassdeterminationswithasingletrappedion, therebyextendingLEBIT'sreachtothefarlimitsofthenuclearchartwhereproduction ratesareextremelylow. Ingeneral,shorthalf-livespresentanadditionalyformeasuringnucleifarfrom stability.SIPTisexpectedtorequirehalf-livessimilartothosecurrentlymeasurableat LEBIT( ˘ tensofmsorlonger).However,theadditionalstabilitybyshellclosures meansthatisotopesinthevicinityofmagicordoubly-magicnucleioftenhavesurprisingly longhalf-lives,evenfarfromstability.Thesearetheregionsofmostinterestforstudywith SIPT. Forexample,thedoubly-magicnuclei 78 Niand 100 Snareoftenconsidered\holygrails" fornuclearstructurestudiesfarfromstability.With28protonsand50neutrons, 78 Niis 7 themostneutron-richdoubly-magicnucleus.Ontheoppositesideofthevalleyofstability, 100 Snhas50protonsand50neutronsandistheheaviest N = Z nucleus.Thesenucleiand thoseintheirvicinitythereforeprovidevaluableinsightintotheroleofmagicnumbersfar fromstability.Withhalf-livesof122msand1.16srespectively, 78 Niand 100 Snbothlive longenoughforPenningtrapmassmeasurements.However,currentproductionratesfor thesetwonucleiareonly ˘ afewperdayattheNSCL,sodestructivePTMStechniques arenotanoptionformeasuringthesenuclei.Non-destructivemeasurementswithSIPTwill provideapathtowardsprecisemassmeasurementsofthesehighly-exoticnuclei,allowing carefulstudiesofnuclearbindingenergytrendsfarfromstability. AdiscussionofPTMS,includingdetaileddescriptionsofTOF-ICRandFT-ICRdetec- tion,ispresentedinChapter2.Chapter3describestheLEBITfacilityattheNSCL.The precisionmassmeasurementsofcobaltisotopesbeyond N =40,introducedattheendof Section1.1,arepresentedindetailinChapter4.Finally,thedevelopmentandthe commissioningtestsofSIPTarediscussedinChapter5. 8 Chapter2 PenningTrapMassSpectrometry 2.1PenningTrapBasicConcepts 2.1.1TrappingFields APenningtrapisanionstoragedevicewhichusesacombinationofauniformmagnetic andaquadrupolarelectrostatictocaptureachargedparticleinthreedimensions. Themagneticprovidesradialt,aschargedparticlesinamagneticare boundtoorbitaboutthemagneticlinesatthecyclotronfrequency ! c =2 ˇ c = qB m (2.1) whichdependsonlyontheions'charge q ,mass m ,andthemagneticstrength B .A magneticalonedoesnottrapionsinthedirectionalongtheaxis,sotoobtain three-dimensionaltanelectrostaticpotentialissuperposed.AtLEBIT,thisis accomplishedusingasystemofthreehyperbolictrappingelectrodes:twoendcapsanda ring,asshowninFig.2.1.Thesethreeelectrodesarehyperboloidsofrevolutiondby z 2 ˆ 2 = z 2 0 (2.2) 9 Figure2.1:Threehyperbolictrapelectrodes(twoendcapelectrodesandoneringelectrode) usedtocreatethequadrupolarelectrostaticnecessaryforaxialiont. andcreateanelectrostaticquadrupolepotentialwhichcanbegivenincylindricalcoordinates ( ˆ;z )by V ( ˆ;z )= U 0 4 d 2 (2 z 2 ˆ 2 ) ; (2.3) where U 0 isthepotentialbetweentheendcapandringelectrodes,and d isa characteristictrapparameteras d = q ˆ 2 0 = 4+ z 2 0 = 2.Thequantities z 0 and ˆ 0 refer tohalfoftheminimumdistancebetweenendcapelectrodesandtheminimumradiusofthe ringelectrode,respectively,asshowninFig.2.1.OtherPenningtrapelectrodegeometries, suchascylindricaltraps,canbeusedtotlyapproximateaquadrupolarelectric [36],howeversuchgeometriesintroducehigher-orderelectriccontributionswhich mustbecompensatedtominimizeuncertaintiesfromfrequencyshiftsifthetrapistobe usedforhigh-precisionfrequencymeasurements[37]. 2.1.2IonMotioninaPenningTrap AderivationofthemotionofachargedparticleinaPenningtrapcanbefoundinRef.[38], andtherelevantresultsaresummarizedhere.Theadditionofaquadrupolarelectrostatic 10 toauniformmagneticresultsinthreedistincteigenmotions.Inthe z -direction, asthedirectionoftheuniformmagnetic ~ B ,ionswillundergosimpleharmonic motionatthefrequency ! z =2 ˇ z = r qU 0 md 2 : (2.4) Intheradialplane,thepresenceofthequadrupolarelectrostatic ~ E splitsthetrue cyclotronmotionatfrequency ! c intotwodistinctradialmotions:aslow ~ E ~ B driftknown asthemagnetronmotionatfrequency ! andamuchfastermocyclotronmotionat frequency ! + ,withtheradialfrequenciesas ! =2 ˇ = ! c 2 r ! 2 c 4 ! 2 z 2 : (2.5) AnillustrationofthesethreeeigenmotionsispresentedinFig.2.2.Thetruecyclotron frequencyissimplythesumofthetworadialfrequencies ! c = ! + + ! (2.6) andthethreeeigenfrequenciesarerelatedtothecyclotronfrequencyby ! c = q ! 2 + + ! 2 + ! 2 z : (2.7) Infact,Eq.(2.6)asderivedinRef.[38]onlyholdstrueforaperfectPenningtrap.The non-trivialdemonstrationthatthisrelationcanstillbeusedforhigh-precisionmeasurements inarealPenningtrapwithoutintroducingadditionalsystematicuncertaintiescanbefound inRef.[39]. 11 Figure2.2:IllustrationofthemotionofachargedparticleinaPenningtrap.Thismotion isacombinationofthreedistincteigenmotions:themagnetronmotion(green)atfrequency ! ,themocyclotronmotion(red)atfrequency ! + ,andtheaxialoscillations(blue) atfrequency ! z .Theblackpathillustratesthecombinationofthesethreemotions. InatypicalPenningtrapenvironmentwithastrongmagnetic( ˘ T)andarelatively weakelectric( ˘ V/mm), ! + ˛ ! z ˛ ! . 2.1.3ManipulationofIonMotionwithRFElectricFields OnceinaPenningtrap,ions'motioncanbemanipulatedinvariouswaysusing multipolarRFelectric[40].AtLEBIT,theseRFeldsareappliedtotheringelec- trode,whichissegmentedintoeightequalpartstoallowfordipole,quadrupole,oroctupole excitations[41],thoughcurrentlyonlydipoleandquadrupoleexcitationsareregularlyem- ployed. AnillustrationofthedipoleandquadrupoleRFispresentedinFig.2.3. InthedipoletheappliedRFis180 ° outofphasebetweenoppositehalves oftheringelectrode.Dipoleexcitationsappliedtotheringelectrodecandriveeitherofthe tworadialmotionswhenappliedattheirrespectivefrequencies,increasingtheradius ˆ + or ˆ oftheselectedmotion.Unlikethemagnetronfrequency,whichisweaklymass-dependent, 12 Figure2.3:AppliedRFgeometriesuesedtoobtaindipole(left)andquadrupole(right)exci- tationsoftheions'motioninthePenningtrap.AtLEBIT,theringelectrodeissegmented toachievethesegeometries.RedandbluesegmentsrepresentRFapplicationsofequal frequencyandamplitude,180 ° outofphase. themocyclotronfrequencyisstronglymass-dependent,anddipoleexcitationatthe mocyclotronfrequencyisthereforecommonlyusedatLEBITtoremoveunwantedion speciesfromthePenningtrapbydrivingtheirmocyclotronmotiontoalargeradius wheretheionsarelostfromthetrap.UnknowncontaminantsinthePenningtraparealso ideninthismannerbyscanningtheapplieddipoleRFfrequencyandlookingfora reductioninthenumberofionsextractedfromthetrap. InthequadrupoleRFtheappliedRFisthesameonoppositequarters oftheringsegmentandadjacentquartersare180 ° outofphase,asshowninFig.2.3.This isusedtocouplethetrappedions'tworadialmotions.Whenaquadrupole RFdriveisappliedatthetruecyclotronfrequency c = + + ,aperiodicbeatingoccurs betweenthemagnetronandmocyclotronmotions,asdemonstratedinFig.2.4.Be- cause + ˛ ,asubstantialchangeintheions'radialenergyoccursduringtheconversion betweenradialmotions.Thischangeinenergyisthendetectedinamannerdiscussedin Section2.3andusedtomeasurethetruecyclotronfrequency c ofthetrappedions,which 13 Figure2.4:Conversionbetweenthetworadialmodesofanion'smotioninaPenningtrap. (a)Theionbeginswithpuremagnetronmotion(redcircle).WhenaquadrupoleRFdrive isappliedatthetruecyclotronfrequency c ,themocyclotronradiusgrowsasseen bythegrowingblackcircles,andthemagnetronradiusdecreasesasindicatedbytheblue arrow.(b)Whenfullconversionofmagnetrontomocyclotronmotioniscomplete,the mocyclotronradiusisequaltotheinitialmagnetronradius. isthenusedtodeterminetheions'massaccordingtoEq.(2.1). 2.2OverviewofPenningTrapMassSpectrometry Penningtrapsprovideanexcellentenvironmentforprecisionstudiesofchargedparticles, tinasmallvolume,well-controlledelectromagneticandtheability tomanipulateparticles'motionasdescribedintheprevioussection.Whileseveralareasof activeresearchmakeuseofPenningtrapsforthesereasons,theapplicationofparticular interestforthisthesisistheuseofPenningtrapstoperformprecisemassmeasurements ofchargedparticles.TwotmethodsofPenningTrapMassSpectrometry(PTMS) arenowwellestablishedandwidelyused:Time-of-FlightIonCyclotronResonance(TOF- ICR)[40]andFourierTransformIonCyclotronResonance(FT-ICR)[42]detection.Both 14 ofthesemethodsarenowemployedatLEBIT.Theyarediscussedindetailinthenext twosectionsandarecomparedatahighlevelinthissection.AthirdPTMStechnique knownasPhaseImagingIonCyclotronResonance(PI-ICR)waspioneeredbytheSHIP- TRAPexperimentatGSIinrecentyears[43].Severalothermassmeasurementexperiments, includingLEBIT,havenowtakenstepstowardsincorporatingPI-ICRdetectionaswell.A briefdiscussionofPI-ICRdetectionisincludedattheendofthissection. TOF-ICRdetectioniscurrentlytheprimarytechniqueusedforPenningtrapmassmea- surementsofrareisotopes.Itisadestructivemeasurementtechnique,meaningthations mustbeejectedfromthetrapfordetectionandnewionsloadedintothetraprepeatedlyto completeasinglemassdetermination,asdescribedinthenextsection.Themassprecision ofaTOF-ICRmeasurementisgivenapproximatelyby m m ˇ c T RF p N (2.8) [40],where c = qB= 2 ˇm isthecyclotronfrequencyofanionwithmass-to-chargeratio m=q inaPenningtrapwithmagneticstrength B , T RF isthemeasurementtimeofions inthePenningtrap, N isthetotalnumberofionsdetected,and isaunitlessparameter dependentontheparticularexperimentalsetup.AtLEBIT,thevalueof is ˇ 0 : 3[44]. Assumingthatradioactiveionscanbeobservedforaboutonehalf-life,thismeansthations withhalf-livesontheorderoftensofmillisecondscanbemeasuredtoprecisionsrequired fornuclearstructureorastrophysicsstudies(seediscussioninSection1.1)inthetimespan ofatypicalonlinebeamexperiment.Forexample,asingly-chargedspeciesofmass50u withahalf-lifeof50mscouldbemeasuredintheLEBIT9.4-TPenningtraptoanexpected precisionof ˘ 2 10 7 withonly1000detectedions.ItfollowsfromEq.(2.8)thateven 15 higherprecisionscanbereachedforlonger-livedspecies.Forinstance, 14 O( T 1 = 2 =71s) wasmeasuredatLEBITtoamassprecisionof ˘ 2 10 9 [28].Thismeasurementuseda 250-msmeasurementtime,andalsoemployedaRamseyexcitationschemeforanadditional improvementinprecision[45]. TOF-ICRdetectionalsotheadvantageofhighversatility.Measuringtions overawidemassrangerequiresonlyafewparameterchangeswhichcanbeimplemented quickly.NomajorchangesintheLEBITsetuparerequiredbetweenmeasurements,leaving alargeamountofyinpreparationandschedulingforbeamtime. FT-ICRdetectionisusedforawidevarietyofPTMSexperiments.BroadbandFT-ICR detectioniswidelyusedinanalyticalchemistrybecauseitallowsforsimultaneousiden cationofnumerousspeciesheldinthePenningtrap.WhilebroadbandFT-ICRdetection providesexcellentresolutionforspeciesidention( m=m ˘ 10 6 ),high-precisionmass measurementsforfundamentalstudiesrequiremuchhigherprecision.Thisisaccomplished usingnarrowbandFT-ICRdetection,whichusesaresonatingdetectioncircuitthatistuned toresonatenearthefrequencyoftheparticularspeciesbeingmeasured.Detailsofthis detectiontechniquearediscussedinSection2.4. AsinTOF-ICRdetection,themassprecisionachievablewithFT-ICRdetectionisin- verselyrelatedtotheobservationtime.Themassesofstablechargedparticlescanthere- forebemeasuredtoextremelyhighprecisionsbyobservingtheirmotioninthetrapfor verylongtimeperiods.NarrowbandFT-ICRdetectionhasbeenusedinthismannerfor someofthemostprecisedeterminationsoffundamentalphysicalproperties[2,27],including particle/anti-particlesymmetriesfortestsoftheCPTtheorem[46{48]andelectrong-factors fortestsofQEDanddeterminationoffundamentalconstants[48,49],reachingfractionalpre- cisionsbelow10 10 . 16 TheprimarydistinctionofFT-ICRdetectionisthatitisanon-destructivetechnique, meaningthationsarenotlostduringthedetectionprocess.Thenon-destructivenatureof FT-ICRdetectioniscentraltotheSIPTprojectintroducedinChapter1anddiscussedin detailinChapter5,asthiswillenablecompletemassdeterminationswithasingledetected ion.SIPTwillbeusedforradioactiveionmeasurements,limitingtheobservationtimeand thereforetheprecision.However,asshowninSection5.1,precisionscomparabletothose obtainedwithTOF-ICRdetectionareexpectedwithawell-designeddetectioncircuit.This comesinexchangefortheversatilitybyTOF-ICRdetection,however,asagiven resonatorcircuitwillonlybeusableoverasmallmassrange. PI-ICRdetectionusesaposition-sensitivemicrochannelplate(MCP)detector.Ions ejectedfromthePenningtrapattpointsalongtheirorbitwillthereforeshowup attlocationsontheposition-sensitivedetector.Byvaryingthetimeforwhichions areheldinthetrapandthentrackingthechangeinlocationontheMCP,thefrequencyof theions'motioncanbedeterminedfromtheaccumulatedphase.IncontrasttotheTOF- ICRtechnique,theresolutionofaPI-ICRmeasurementthereforedependsnotonlyonthe measurementtimebutalsoontheresolutionofthephaseimaging.Thisinclusionofphase informationhasbeenshowntoallowafactorof40improvementinmassresolutionover TOF-ICRdetection[43].AtLEBIT,aposition-sensitiveMCPhasbeenpurchasedand stepshavebeenmadetoadapttheionejectionopticstoallowforcommissioningofPI-ICR detection. 17 2.3TOF-ICRTechnique TOF-ICRdetectionisatechniqueformeasuringthecyclotronfrequencyofchargedparticles inaPenningtrapbydetectingtheenergygainedwhenmagnetronmotionisconvertedinto mocyclotronmotion.AsdiscussedinSection2.1.3,thisconversioncanbeachieved byapplyingaquadrupolarRFatafrequency RF thatmatchesthetrappedions'true cyclotronfrequency c . Because ! + ˛ ! ,maximumenergygainisachievedwithafullconversionfrompure magnetronmotiontopuremocyclotronmotion.Topreparetheionsinaninitial stateofmagnetronmotion,LEBITpioneeredtheuseofaLorentzsteerer[50],whichuses atransverseelectricimmediatelybeforeinjectionintothePenningtrapinconjunction withthe9.4-Tmagneticdtocreatean ~ E ~ B force,steeringtheionsslightlyof thecentralbeamaxisastheyenterthePenningtrap.Beforeameasurement,theelectric oftheLorentzsteererisscannedtodeterminehowfartheionscanbedriven withoutreducing.Thefurthertheionsareinjected,thelargertheirinitial magnetronradius ˆ andthusthegreatertheradialenergygainwhenthemagnetronmotion isconvertedtomocyclotronmotion.Thiscanbeseensimplyfromthein rotationalkineticenergy E r = 1 2 m ( ! 2 + ! 2 ) ˆ 2 : (2.9) Completeconversionfrommagnetrontomocyclotronmotionusingaquadrupolar RFexcitationrequirestheproperproductofRFdurationandamplitude,knownasa ˇ - pulse[40].AtLEBIT,theamplituderequiredfora ˇ -pulseatagivenRFdurationhas beencalibratedbyscanningtheRFamplitudeforaparticularRFdurationtothe maximumkineticenergygain.Thiscalibrationisstoredinthecontrolsystem,sotheuser 18 Figure2.5:IonsejectedfromthePenningtrapmovethroughanaxialmagneticgradient astheytraveltotheMCPdetector.Thisresultsinanaxialkickproportionaltotheions' radialenergy,asdemonstratedbyEq.(2.10). cannowsetthedesiredRFduration(basedonconsiderationssuchasionhalf-lifeanddesired precision),andthecontrolsystemusesthestoredcalibrationtoautomaticallycalculatethe RFamplitudeneededfora ˇ -pulse. Todetectthechangeinradialenergy,ionsareejectedfromthePenningtrapandtravel toanMCPdetectorjustoutsideofthemagneticAsshowninFig.2.5,ionsmoving fromthestrongmagneticatthecenterofthemagnettotheMCPoutsidethemagnet willencounteranegativemagneticgradientintheaxialdirection.Achargedparticle orbitingintheradialplanewillthereforeexperienceaforceintheaxialdirectiongivenby F z = @B @z = E r B 0 @B @z ; (2.10) where isthedipolemomentoftheorbitingchargedparticlewithradialenergy E r ina centralmagneticstrength B 0 [2].Thisaxialforcecausesionswithmoreradialenergyto reachtheMCPinlesstime,sothegaininradialenergyisultimatelydetectedasareduction intimeoftfromthePenningtraptotheMCP. 19 Figure2.6:ExampleofaTOF-ICRresonanceobtainedbyscanningtheappliedRF quadrupoleexcitationfrequencyandmeasuringtheions'timeofttoanMCPdetector. Theredcurveisatheoreticalthecenterofwhichcorrespondsthecyclotronfrequency c . TodeterminethecyclotronfrequencyofachargedparticleinaPenningtrap,thefre- quency RF oftheappliedquadrupoleRFelectricisscannedaroundtheions'expected cyclotronfrequency c .AftereachRFexcitationisapplied,ionsareejectedfromthePen- ningtrapandthetimeofttotheMCPismeasured.Thenanotherionorsmallbunch ofionsisinjectedintothetrapandthenext RF stepisapplied.When RF = c ,theinitial magnetronmotionwillbeconvertedtomocyclotronmotion,andthisgaininenergy willbedetectedasareductioninthetimeoft.Plottingtimeoftasafunction oftheapplied RF thenrevealsasubstantialdipat c ,whichiswithatheoreticalline shape[40]todeterminethecenter.AnexampleofsucharesonanceplotisshowninFig2.6. AsseeninEq.(2.1),thecyclotronfrequencydependsonlyontheions'mass,charge state,andthestrengthofthemagneticThechargestateoftheionsisknownpriorto trapping,howeverthemagneticatLEBITisknowntodecayovertimeatarateof ˘ 10 20 ppb/hr.Tomonitorthestrengthofthemagneticatahighlevelofprecision,eachionof interestmeasurementisimmediatelyprecededandfollowedbymeasurementsofareference ionwithawell-knownmass.Thereferenceionfrequenciesarethenlinearlyinterpolatedto determinethecyclotronfrequency c; ref ofthereferenceionatthetimetheionofinterest wasmeasured.Themagneticstrengththencancelsoutwhentakingtheratioofthe referenceionandionofinterestfrequencies,andthemassoftheionofinterestisdetermined fromthisratioas m = m ref c; ref c q q ref : (2.11) NotethatthemassesinEq.(2.12)refertothemassesofthemeasuredions;todetermine theatomicmassoftheionofinterest,themassofmissingelectronsmustbeaccountedfor. Inveryhigh-precisionmeasurements,theelectronbindingenergiesmustalsobeaccounted for,thoughthesearetypicallyonly ˘ 10eVandcanthereforeoftenbeneglected. 2.4FT-ICRTechnique TheFT-ICRtechniquereliesonpickinguptheimagecurrentcreatedwhenionsoscillate insideaPenningtrap,generatingsometime-varyingimagechargeonthetrapelectrodes[42]. Whilethetime-domainsignalgeneratedinthismannermaylookquitecomplicated,particu- larlyifmultipleionspeciesarepresentorifthereisasubstantialamountofnoise,thissignal canbeconvertedtoafrequency-domainspectrumviaFastFourierTransform(FFT)[51].In thefrequencydomain,thedetectedionfrequencieswillbeplainlyvisibleasdistinctpeaks, whichcanbetodeterminethefrequencyoftheions'motion. Forprecisionmeasurements,thenumberofionsinthetraptypicallymustbelimitedtoa fewatatimeorlessinordertoavoidsystematicfrequencyshiftsfromioninteractions[52]. 21 Also,whileitisdesirabletoexcitetheions'motiontolargeradiitoincreasetheimagecharge detectedonthetrapelectrodes,ionsbecomemoresensitivetoimperfectionsasthey getclosertothetrapelectrodes,whichwillleadtofrequencyshiftsaswellandtherefore limitshowclosetheionscangettotheelectrodes[2,38,53].Thismeansthatprecision measurementswithFT-ICRdetectionrequireahighdegreeofsensitivitysothattheimage chargefromveryfew(orevensingle)ionscanbedetected. Theneededgaininsensitivityforprecisionmeasurementsisaccomplishedusingwhatis knownasnarrowbandFT-ICRdetection[2].TheprincipleofnarrowbandFT-ICRdetection isillustratedinFig.2.7.ThePenningtrapelectrodesusedforimagecurrentpickupare connectedinparallelwithaninductorofinductance L tocreateanRLCresonatorcircuit, wheretheresistance R istheeparallelresistanceofthecircuitandthecapacitance C isacombinationofthecapacitancebetweenthepickupelectrodesandotherparasitic capacitancesfromthewires,etc.ThisRLCcircuitwillresonateatafrequency circ = 1 2 ˇ p LC ; (2.12) sobychoosingpropervaluesof L and C thecircuitcanbetunedsothat circ isapproximately equaltothefrequencyoftheions'motiontobedetected.Thistunedresonancecircuitwill enhancetheionsignal,whichisthenfurtheramplandprocessedwithanFFTalgorithm foranalysis. Thedetectedionmotiondependsonthemultipolarofthepickupelectrodes inthesamewayasthedrivenionmotionsdescribedinSection2.1.3.Dipolepickup,which istosay,tialimagecurrentpickupbetweenoppositehalvesoftheringelectrode, isshowninFig.2.7andisusedtodetectthemagnetronandmocyclotronmotions. 22 Figure2.7:SchematicillustrationofnarrowbandFT-ICRdetection. Quadrupolepickupbetweenadjacentquartersoftheringelectrodeisusedtodetectthe sumfrequency c = + + whentheions'motionisamixedstateofmocyclotron andmagnetronmotions.Inrealisticcases,suchpuremultipoleareoften onlyapproximated,forinstanceifsomeringsegmentelectrodesareneededtodrivethe ions'motionratherthanforimagecurrentpickuporifanimperfecttrapgeometryisused. Thismeansthatthetotalimagecurrentsignalmaybedividedbetweenmultiplefrequency peaksincludingcomponentsfromtmultipolarities.Anexampleofasinglefrequency spectrumincludingpeaksat + and c ispresentedwiththediscussioninAppendixAon characterizingtheMiniTrapmagnetometerdevelopedatLEBIT. 23 Chapter3 TheLEBITMassSpectrometer FacilityattheNSCL TheNationalSuperconductingCyclotronLaboratory(NSCL)isaworld-classfacilityforrare isotoperesearchlocatedonthecampusofMichiganStateUniversity(MSU).Rareisotope beamsattheNSCLareproducedbyprojectilefragmentation.Naturallyabundantheavy ionprimarybeamsareacceleratedbytwocoupledsuperconductingcyclotronstoenergies ontheorderof100MeVpernucleon.Thesefastprimarybeamsarethenimpingedona light,thin 9 Betarget.Protonsandneutronsareknockedoftheprimarybeamnucleiin theresultingnuclearcollisions,producingacocktailbeamcontainingavarietyoft nuclides.ThedesiredrareisotopespeciesisthenselectedhtusingtheA1900fragment separator[54],whichusesasystemofmagnetsanddegraderstoouttheunwanted species. Theprojectilefragmentationmethodhasafewimportantadvantagescomparedtoother rareisotopeproductionmethods.Onesuchadvantageisthatthisisauniversaltechnique, equallyapplicableacrossthenuclearchart.Anotheradvantageofprojectilefragmentation isthatitisaveryfastprocess.Becauseafast,heavyprimarybeamisusedwithalight,thin productiontarget,thereactionproductsretainnearlyalloftheirinitialforwardmomentum. Beamisthenperformedt,andasaresultrareisotopescanbedelivered 24 Figure3.1:LayoutoftheNSCL.RareisotopebeamsfromtheA1900aredeliveredeither directlytofastbeamexperimentsortothebeamstoppingfacility,fromwhichstopped beamsaresenttolow-energyexperimentsincludingLEBITortothere-acceleratorfacil- ityforintermediateenergyexperiments.(Adaptedfrom http://nscl.msu.edu/public/ virtual-tour.html .) toexperimentalareaspromptlyfromthetimetheyareproduced. Fastbeamsareexcellentforstudiesofveryshort-livednucleiorformanyreactionstudies, howevertheyarenotidealforallexperiments.Precisionmeasurementssuchascollinearlaser spectroscopyatBECOLA[55]orPenningtrapmassmeasurementsatLEBITrequirestopped beams,andmanyreactionstudiesrelevantfornuclearastrophysicsorstructurerequirerare isotopebeamsatloworintermediateenergies.Theseenergyregimesarealsoavailableat theNSCLthankstothebeamstoppingfacilitydescribedinthenextsection,whichslows thefastbeamsdeliveredfromtheA1900tothermalenergies.Thesestoppedbeamscan theneitherbedeliveredtothelow-energyareaincludingLEBITandBECOLAortothere- acceleraterfacilityReA3[56],whichacceleratesbeamstointermediateenergies.Thelayout oftheNSCL,includingfastbeam,stoppedbeam,andre-acceleratedbeamexperiments,is presentedinFig.3.1. 25 Thenext-generationupgradeforrareisotopeproductionatMSU,knownastheFacility forRareIsotopeBeams(FRIB),isnowwellonitswaytocompletion.FRIBwillprovide anenormousgaininbeampower,increasingproductionratesacrossthenuclearchartand allowingaccesstoalargenumberofrareisotopesfarfromstabilitythatarecurrentlyun- availableanywhereelseintheworld.Thiswillpresenttheopportunityforgroundbreaking newrareisotoperesearchandnewdiscoveries.ThecurrentexperimentalareasattheNSCL, includingLEBIT,willremaininusewhenFRIBcomesonline,simplytakingbeamfromthe newFRIBacceleratorratherthanfromthecurrentcyclotronfacility.Thusallofthepast andcurrentdevelopmentsthathavemadeLEBITaworld-classfacilityforprecise,accurate massmeasurementsofrareisotopeswillmakeLEBITwell-preparedtotakefulladvantage ofthenewscienopportunitiespresentedbyFRIB. 3.1BeamStoppingattheNSCL InordertoperformPenningtrapmassmeasurementsofrareisotopesfromprojectilefrag- mentation,thefastrareisotopebeamsdeliveredfromtheA1900mustbestoppedso thattheionscanbecapturedinthePenningtrap.Mostofthebeamenergyisinitially lostbysendingthebeamthroughasystemofsoliddegraders.Theremainingenergyislost throughcollisionswithneutralheliumatomsinahgaschamberdevelopedat ArgonneNationalLaboratory(ANL)andcommissionedattheNSCLin2014[57].Apic- tureoftheANLgascellispresentedinFig.3.2.Radiofrequencyelectricareusedto repelionsfromthewallsofthegaschamber,andacombinationofDCelectricandgas wareusedtotransporttheionsthroughthegascell.Thelow-energyrareisotopebeam isthenextractedthrougharadiofrequencyquadrupole(RFQ)ionguideanddeliveredeither 26 Figure3.2:PhotooftheANLgascellusedforbeamstoppingattheNSCL. tolow-energyexperimentssuchasLEBITortoReA3forintermediate-energyexperiments. Twomajorprojectsarecurrentlyunderwaytoexpandbeamstoppingcapabilitiesatthe NSCL.TheAdvancedCryogenicGasStopper(ACGS)willoperateatcryogenictemperatures of ˘ 40Kinordertofreezeoutmuchofthestablecontaminationpresentinthegascell. Thiswillprovidemuchpurerlow-energybeams,alleviatingmuchofthecurrentdiy associatedwithchemistryinthegascellasdiscussedinSection4.2.1.TheACGSisalso designedtooptimizeevenwithveryhighincomingrates,inpreparationforthe highbeamratesexpectedwhenFRIBcomesonline.ACGSiscurrentlybeingcommissioned andisexpectedtobeoperationalforonlinebeamexperimentsinthenearfuture. TheothermajorbeamstoppingprojectcurrentlyunderwayattheNSCListhecyclotron gasstopper[58].Thecyclotrongasstopperalsooperatesatcryogenictemperatures,but unliketheACGS,ionsinthecyclotrongasstoppermovealongacirculartrajectory,spiraling inwardsastheyloseenergyviacollisionswithneutralheliumatoms.Thisspiralpath providesanextendedstoppingdistance,whichwillbeespeciallyusefulfortlystopping lightionspecies.ThecyclotrongasstopperwillbeinstalledintheNSCLbeamlineparallel totheACGSsothateitherdevicemaybeuseddependingonwhichwouldbeoptimalfora 27 Figure3.3:LayoutoftheLEBITfacility.Thefunctionsofeachmajorcomponent aredescribedinthetext.(Reproducedfrom https://groups.nscl.msu.edu/lebit/ lebitfacility/index.html .) givenexperiment. 3.2MajorComponentsoftheLEBITFacility AschematicoverviewoftheLEBITfacilityispresentedinFig.3.3.Ionsaredelivered fromthebeamstoppingfacilityorfromeitheroftwoionsources.A90 ° electrostatic benderisusedtodirectionsfromthedesiredsourcetotheLEBITcooler/buncher,which preparesshort,low-emittanceionbunchesfordeliverytooneofthePenningtraps.Ion bunchesaretheneithersenttothe9.4-TPenningtrapforTOF-ICRmeasurementsorto the7-TSingleIonPenningTrapcurrentlybeingcommissionedforultra-highsensitivityFT- ICRmeasurements.Eachofthemajorcomponentsisdiscussedindetailinthefollowing subsections. 28 Figure3.4:PhotooftheColutronionsourcewhichproducesstableandlong-livedionsvia plasmaorsurfaceionization. 3.2.1IonSources LEBIThastwoineionsources:aColutronplasmaionsourceandalaserablationsource (LAS)[59].Thesesourcesprovidestableorverylong-livedionstoLEBITwhenrare-isotope beamisnotbeingdeliveredfromthegasstoppingfacility.Inadditiontobeingextremely valuableforsystemdiagnosticsandcalibrations,thesesourceshavealsonowbeen usedforanumberofhigh-precisioninemeasurementsofscienimportance[60{67]. ApictureoftheColutronionsourceispresentedinFig.3.4.Atungstentisheated toproduceelectronsandisnegativelybiasedtosparkadischarge,ionizinggasatomsofthe desiredspecieswhichareintroducedtothechamberwithaleakvalve.Thetcan alsobepositivelybiasedtoprovidealkalimetalionsviasurfaceionizationfromimpurities inthet. ApictureoftheLASispresentedinFig.3.5.Thelaserablationsourceusesapulsed Nd:YAGQuantelBrilliantlasertoproduce4nslightpulses,whicharethenguidedtoa solidtargetofthedesiredsourcematerial.Thelaserirradiationresultsintheemissionof 29 Figure3.5:PhotoofthelaserablationionsourceatLEBIT. positiveionsfromthesurfaceofthetarget,whicharethenelectrostaticallytransportedto themainLEBITbeamline. 3.2.2Cooler/buncherandFastElectrostaticKicker TheLEBITcooler/buncherisa3-stagelinearPaultrapusedforbeampreparation beforedeliverytothePenningtrap.Detailscanbefoundin[68],andapictureispresented inFig.3.6.Inallthreestages,radiofrequencyquadrupole(RFQ)electricareused toionsinthetransversedirections,andagas(typicallyhelium)isusedto cooltheionstothermalequilibriumwiththegas.Someamountofaheaviergas,suchas neon,issometimesintroducedthroughaseparateleakvalvetopromotecollision-induced dissociationofmoleculestoimprovebeampurity[69].Thestage,thepre-cooler,hasthe highestgaspressure( ˘ 0.03mbar)forfastioncoolingandusesanaxialDCto guideionsthrough.Thesecondstageisreferredtoasthemicro-RFQandactsasabarrier betweentheandthirdstagestoallowerentialpumping.Thisisasmall-scaleversion 30 Figure3.6:PhotosoftheLEBITcooler/buncherusedtopreparecooledionbunchesfor deliverytothePenningtrap.Thepre-coolerandmicro-RFQareshownontheleft,andthe buncherstageisshownontheright. ofthepre-coolerandalsousesanaxialDCtoguideionsthroughtothenextstage. Thestageisthebuncherstage.Inthebuncherstage,aseriesofelectrodesisusedto shapetheaxialpotentialintoapotentialwelltotraptheions.Thecontinuousincoming beamiscollectedinthebuncherforasetamountoftime,andthenthepotential isswitchedtoejectthecollectedionsinashort,sub- spulse.Inthismanner,theLEBIT cooler/buncherprovidesshort,low-emittanceionbunchestothePenningtrapforcapture andmeasurement. Betweenthecooler/buncherandthePenningtrap,afast-switchingelectrostatickicker isusedtoseparateionsoftmassesbytheirtimeoft.Ionsareejectedfrom thecooler/buncherwiththesamekineticenergy E kin = 1 2 mv 2 ,soheavierionswilltravelat slowerspeedsandthuswillreachagivenlocationatalatertimethanlighterions.Thekicker isgenerallyheldatahighpotentialtopreventionsfromreachingthePenningtrap.When ionsofthedesiredmassreachthekicker,thepotentialisswitchedforashortperiodoftime toallowtheseionstopass,thenswitchesbacktohighpotential.Thefastelectrostatickicker hasaresolvingpower m m > 400,whichisttopreventnon-isobariccontaminants fromreachingthePenningtrap. 31 Figure3.7:The9.4-Tsuperconductingmagnet(left)andhyperbolicPenningtrapelectrode structure(right)usedforTOF-ICRmeasurementsatLEBIT. 3.2.3TOF-ICRPenningTrap TOF-ICRmassmeasurements,discussedindetailinSection2.3,arecarriedoutinthe LEBITPenningtrap,whichishousedina9.4-Tsuperconductingmagnet.Picturesofthe TOF-ICRPenningtrapelectrodesandmagnetarepresentedinFig.3.7.Aseriesofdrift tubesusedforioninjectionandejectionaremountedoneithersideofthePenningtrapand sitinsidethemagnetbore.Oneoftheinjectiondrifttubesissegmentedtoforma Lorentzsteerertopreparetheioninaninitialstateofmagnetronmotion,asdescribedin Section2.3. TheLEBITPenningtrapusesahyperbolicelectrodegeometrywithadditionalcompen- sationelectrodesforidealapproximationofatruequadrupolarelectrostaticpotential[41]. Thesecompensationelectrodesminimizefrequencyshiftsduetothefactthatthehyperbolic electrodesareinsizeandthatholesintheendcapelectrodesarerequiredtoallowthe ionstoenterandexitthePenningtrap.Thecoppertrapelectrodesareplatedwithgoldto minimizepatchduetooxidation. AnMCPdetectorismountedinaDaly[70]outsidethe9.4-Tmagnet. Ionsareguidedtowardsacollectorplateandcreateacascadeofelectronswhicharethen 32 Figure3.8:Photooftherecently-commissionedSIPTbeamline,usedforiontransferfrom thecooler/bunchertothe7-TSIPTmagnetforFT-ICRmeasurements.Detailsonindividual componentsofthisbeamlinearepresentedinSection5.2 detectedontheMCP.Aposition-sensitiveMCPwasalsorecentlyinstalleddownstreamof theDalyrationtobegintestingofPI-ICRdetectiondiscussedinSection2.2. 3.2.4SIPT Apictureoftherecently-addedSIPTbeamlineispresentedinFig.3.8.Thisbranchofthe LEBITbeamlineislocatedafterthecooler/bunchersothatrareisotopesfromthebeam stoppingfacilityorstableionsfromeitherofthetwooionsourcescanbeusedwith SIPT.Cooledandbunchedionsfromanyofthesesourcesarethendirectedtoeitherthe 9.4-TPenningtrapforTOF-ICRmeasurementsorthe7-TSIPTPenningtrapforhigh- sensitivityFT-ICRmeasurements.ThedesignandcommissioningofSIPTarediscussedin detailinChapter5. 33 Chapter4 MassMeasurementsofNeutron-Rich CobaltIsotopesBeyondN=40 TheresultspresentedinthischapterwererecentlypublishedinPhysicalReviewC[71]. Portionsofthetextinthischapterandseveralofthepresentedherearereproduced fromthisreference.Additionaldetailsanddiscussionareincludedhereaswell. 4.1MotivationforMassMeasurementsof 68 ; 69 Co 4.1.1EvidenceforaSubshellClosureat N =40 Theregionofthenuclearchartnear N =40, Z =28hasdrawnmuchattentiondueto experimentalsignaturessuggestingthearrivalofaneutronshellclosureat N =40in 68 Ni. Tounderstandandevaluatethemeaningofthesesignatures,thequantumstatespredicted bytheshellmodelinthisregionmustbeconsidered.Aharmonicoscillatormean alonepredictsthat40wouldbeamagicnumber,completingthefourmajorharmonic oscillatorshells.Theinclusionofthespin-orbitinteractionsplitstheenergydegeneracy oforbitalswithineachshellandshiftsthespacingbetweentheseorbitals.Ofparticular relevancehereistheshiftingofthe g 9 = 2 orbital,thelowest-energyleveloftheharmonic oscillatorshell,whichcomesdowninenergyfarenoughtojointhe pf -shell.Thiseis 34 Figure4.1:Single-particleshellmodelenergylevelsusingaharmonicoscillatorpotential plusan l 2 interactionwithoutspin-orbitinteraction(left)andwithspin-orbitinteraction (right). depictedinFig.4.1.Theadditional10particlesaccommodatedbythe g 9 = 2 orbitalexplains why50,not40,isthewell-establishedmagicnumber.Thequestionofapotentialshellor subshellclosureat N =40isthereforeaquestionofthespacingbetweenthis g 9 = 2 orbital andthe pf -shell. Theevidencesupportingashellclosureat N =40in 68 NiispresentedinFig.4.2.A large2 + stateenergyE 2+ andasmalltransitionstrength B ( E 2;0 + ! 2 + )are clearlyapparentat N =40inthenickelchain[72{74].Thesequicklydisappearwhen movingawayfromnickel.Suchevidencepresentsacompellingcaseforasubstantialshellgap at N =40in 68 Ni.However,asGraweandLewitowiczhavepointedout[75],itispossibleto accountforthespectroscopicsignaturespresentedinFig.4.2purelybecauseofthechangein paritybetweenthe pf orbitalsandthe g 9 = 2 orbital,evenwithnoenergygapbetweenthem. Furthermore,Langanke etal. demonstratedthatmuchofthelow-lying B ( E 2)strengthin 68 Nicomesfromexcitedstatesabove4MeV,andthereforethesmall B ( E 2 ; 0 + g.s. ! 2 + 1 ) valuedoesnotnecessarilyrequireatenergygapacross N =40[76].Totruly 35 Figure4.2:First-excited2 + stateenergiesE 2+ (top)and B ( E 2;0 + ! 2 + )transition strengths(bottom)intheeven-evennickelisotopes.AlldatatakenfromRef.[74].Thelarge E 2+ andthesmall B ( E 2)valuesat N =40suggestasubstantialshellgap. examinewhetheranenergygapdoesariseat N =40inthenickelregion,theadditional probeofmassmeasurementsmustbeconsidered. 4.1.2MassMeasurementsAround N =40 Fornuclearstructureinvestigations,trendsinnuclearbindingarestudiedusingprotonand neutronseparationenergies( S p and S n )[77],asthedbetweenthebinding energiesofagivennucleusandthenucleuswithonefewerprotonorneutron(or,equivalently, theamountofenergyrequiredtoremoveasingleprotonorasingleneutronfromagiven 36 nucleus).Thisisthenuclearanalogofionizationenergiesinatomicscience. Toinvestigateapotentialneutron(sub)shellclosureat N =40,neutronseparation energiesmustbeconsidered.Nuclearpairing[78,79]createanodd-evenstaggering whenplotting S n asafunctionofneutronnumber,becauseremovinganeutronfroma nucleuswithanevennumberofneutronsrequiresadditionalenergytobreakapairof neutronsbeforeonecanberemoved.Inmanycases,thisstaggeringobscuresthe trendsbeinginvestigated.Itisthereforecommoninsteadtoconsidertwo-neutronseparation energies( S 2 n ),eliminatingtheodd-evenstaggering. Two-neutronseparationenergiescanbeexpressedasafunctionofatomicmasses: S 2 n ( N;Z )=[ m ( N 2 ;Z ) m ( N;Z )+2 m n ] c 2 ; (4.1) where m n isthemassofafreeneutronand c isthespeedoflight. Asimpleliquid-dropmodelofthenucleuswouldsuggestthat,foragivenprotonnumber Z , S 2 n steadilydeclinesasafunctionofneutronnumber N .Thiscanbefoundfromthe semi-empiricalmassformulapresentedbyvonWackerin1935[80].Inreality,this generalsteadydeclineencountersnumerousdeviations,indicatingthepresenceofadditional structureForexample,thetwo-neutronseparationenergiesareplottedasafunction ofneutronnumberforisotopicchainsintheregionfrom Z =31to Z =50inFig.4.3.In thisgure,theneutronshellclosureat N =50canclearlybeidenfromthefactthat the S 2 n valuesdropverysuddenlyat N =50relativetothegeneraldecline.Thisisaresult ofthefactthataddingneutronsbeyond N =50resultsinahigher-lyingneutron shell,fromwhichtheenergycosttoremovetwoneutronsistlylowerthanthe energyneededtoremoveneutronsfromthelowershell.Otherstructurearevisiblein 37 Figure4.3:Two-neutronseparationenergy S 2 n plottedasafunctionofneutronnumber N intheregionfrom Z =31to Z =50.DataaretakenfromtheAME2016atomicmass evaluation[1]. Fig.4.3aswell,suchastheonsetofdeformationbetween N =56and61fortheelements Rb( Z =37)toRu( Z =44)[77]. Thistoolofseparationenergiesdeterminedfrommassmeasurementsservesasanim- portantprobetoexaminethestructureintheregionof 68 Ni. S 2 n isplottedasafunction ofneutronnumberfortheelementsiron( Z =26)tocopper( Z =29)intheregionaround N =40inFig.4.4.Whileanasdramaticasthemajor N =50shellclosureseenin Fig.4.3isnotexpected,asmallersubshellclosureat N =40shouldbeindicatedsimilarly byasuddenin S 2 n whencrossing N =40.Theobservationofsuchanrequires arelativelyhighdegreeofprecision,withuncertainties ˘ 10keVorbetterinthisregionto ensurethatthetrendsarenotobscuredbytheerrorbars. Inrecentyears,onlinePenningtrapmassspectrometryhasprovidedsuchprecisedata extendingbeyond N =40inthenickel,copper,zinc,andgalliumchains( Z =28 31), 38 Figure4.4:Two-neutronseparationenergy S 2 n plottedasafunctionofneutronnumber N intheregionaround 68 Ni.DataaretakenfromtheAME2016atomicmassevaluation[1]. revealingnosignofasubshellclosureacross N =40[81,82].Anoddkinkisobserved inthenickelchainat N =39,whichisnotcurrentlyunderstood[81].Measurements southof Z =28havesofarbeenlimited,however,duetothefactthatiron( Z =26) andcobalt( Z =27)isotopesinthisregionarenotavailablefromISOLfacilities.Asthe onlyPenningtrapmassspectrometercoupledtoafragmentationfacility,LEBITpresents theuniqueopportunitytoperformprecisemassmeasurementsoftheseelusiveisotopes. ApreviousLEBITcampaignprovidedhigh-precisionmassmeasurementsof 63 66 Feand 64 67 Co,extendinguptobutnotbeyond N =40[83].AscanbeseeninFig.4.4,the relativelylargeerrorbarsbeyond N =40intheironandcobaltchainsobscurethetrendsat thecriticalpointofcrossing N =40.ThePenningtrapmassmeasurementsof 68 ; 69 Co wererecentlycompletedatLEBIT,substantiallyreducingtheerrorbarsfromtheAME2016 valuesandenhancingtheunderstandingofnuclearstructurechangesacross N =40inthe regionnear 68 Ni. 39 4.2ExperimentalProcedure 68 Coand 69 CowereproducedattheNSCLbythefastfragmentationprocessdescribedin Chapter3.Thecoupledcyclotronswereusedtoaccelerateastableprimarybeamof 76 Geto anenergyof130MeV/u,whichthenimpingedonathinBetargettoinducefragmentation. UnwantedfragmentswereoutusingtheA1900fragmentseparator,andthedesired cobaltionsweredeliveredtothebeamstoppingfacility.Thisexperimentwascarriedouton twoseparateoccasionsapproximatelyoneyearapart(hereafterreferredtoas\Run1"and \Run2")duetopoorthroughthegascellduringRun1( < 1%total thecauseofwhichwaslatertracedtoaelectrodeinthegascell. Chemicalinteractionsinthegascellpresentedtchallengeswhichrequireda largeamountoftomitigateinordertosuccessfullycompletethemassmeasurements. Thesechallengesandthemethodsusedtoworkpastthemarediscussedindetailinthe followingsubsection. 4.2.1GasCellChemistry Highpurityheliumgas(99.999%)waspassedthroughaMonotorrbeforeuseinthe gascelltominimizetheamountofstablecontaminationpresent.Additionally,allelements insidethegascellwerepreparedunderultra-highvacuumstandardsforthispurpose.Still, somelevelofimpurityhasalwaysbeenobservedfromthegascell[57],presentingtwo importantchallengesforthe 68 ; 69 Coexperiment.First,astheradioactivebeampassed throughthegascell,manyoftheionsofinterestchemicallybondedtostablecontaminants, formingseveralmoleculeswithtmass-to-charge( m=q )values(knownas\molecular sidebands").Followingthegascell,adipolemagneticseparatorwasusedtoselectthe 40 desired m=q ,sowiththedesiredcobaltisotopesspreadovermultiplemolecularsidebands, atportionofthealreadylowbeamratewaslostatanyselected m=q value. Thesecondchallengepresentedbycontaminationinthegascellwasthatstablespecies at m=q =68and69cameattlyhigherratesthanthe 68 ; 69 Co + ionsofinterest, arrivingatthePenningtrapataratioofmorethan100:1.Thedipolecleaningmethod describedinSection2.1.3wasnotttothoroughlyremovecontaminantsatsuch highrates,soisobariccontaminantsinitiallyoverpoweredthesignalfromthecobaltions. Forreasonsnotcurrentlyunderstood,thestablecontaminantsidenfromthegascell changedbetweenRun1andRun2.Table4.1summarizesthebetweenRuns1 and2,includingthestablecontaminantsidenineachcase. Themolecularsidebandswereinvestigatedbymeasuringradioactivityonasiliconbeta- detectorimmediatelyafterthedipolemagneticseparatorandscanningthestrengthofthe magneticintheseparatortodeterminethepresenceofradioactiveionsasafunction of m=q .TheresultsofthesescansforbothRun1andRun2whilesending 68 Cointothe gascellarepresentedinFig.4.5.Inantobreakupstablemolecularcontaminants, a-150Vsetbiaswasappliedtothegascellextraction.Thisisawidelyusedtechnique knownascollisioninduceddissociation(CID)[84{86],wherebyenergeticcollisionswitha gasareusedtoinducefragmentationofmolecularions.ItisclearfromFig.4.5that, duringRun2,asignitamountof 68 Co 2+ waspresentathighermolecularsidebands whichbrokeupafterthebiaswasapplied.Therelativeamountof 68 Co 2+ extractedinRun 1wasmuchlowerthaninRun2,howeverasmallpeakat m=q =34wasapparentafter thebiaswasapplied.Thoughthispeakwasmuchsmallerthanthepeakat m=q =68,the amountofstablecontaminationat m=q =34wasalsomuchless,sothelowerrateof 68 Co 2+ wasacceptableinexchangeformanageablelevelsofisobariccontamination. 41 Figure4.5:Radioactivityobservedasafunctionofthe m=q valuetransmittedthroughthe dipolemassseparatorforRuns1and2.TheofCIDisseenbycomparingthecase wherethereisnobiasappliedtothegascellextractiontothecasewherea-150Vis applied.Notethat m=q wasscannedfromhighvaluestolowinRun1andfromlowvalues tohighinRun2,hencetheoppositedirectionsofthedecaytails. Thoughthecontaminationat m=q =34wasmuchlowerthanat m=q =68,some wasstillrequiredtoreducethecontaminationsothataTOF-ICRresonanceof 68 Co 2+ couldbeachieved.Asetofslitswasusedtocutoutaportionofthebeamimmediately afterthedipolemagnet.Theslitwidthandpositionwereadjustedwhilemonitoringthe radioactivityobservedonthesiliconbeta-detectorinordertocutasmuchofthebeamas possiblewithoutreducingtheamountof 68 Co 2+ .Thedipolecleaningmethoddescribedin Section2.1.3wasusedtoremoveknowncontaminantsfromthePenningtrap.DuringRun1, theadditionalstepofSWIFTcleaning(describedinthenextsubsection)wasalsorequired. Incombination,thesewerettoobtainaTOF-ICRresonanceof 68 Co 2+ . Thechemistryfor 69 Cowasthesameasfor 68 Co,sothedipolemagnetwassetto m=q = 34 : 5when 69 CowasdeliveredfromtheA1900.Forodd-massisotopeslike 69 Co,measuring 42 doubly-chargedionsisparticularlyhelpfulforreducingstablecontaminationbecauseno singly-chargedcontaminantswillarriveathalf-integermassvalues.Inthismeasurement, theonlycontaminantideninthePenningtrapwasthedoubly-chargeddaughter 69 Ni 2+ , whichcouldeasilybecleaned.Thoughtherateof 69 Co 2+ arrivingatthePenningtrapwas extremelylow( < 0.5ions/s),a 69 Co 2+ TOF-ICRresonancecouldstillbeachievedthanks tothelowlevelofcontamination. 4.2.2SWIFTBeam DuringRun1,additionalwasneededtoremoveiosobariccontaminantsfromthe Penningtrapinordertoobtaina 68 Co 2+ TOF-ICRresonance.Majorbeamcomponents, suchas 16 O 18 O + ,couldbeidendandremovedfromthePenningtrapwiththedipole cleaningmethoddescribedinSection2.1.3.However,anumberofadditionalcontaminants werepresentataleveltoolowtoidentifyinthetimeallotted.Toremovesuchcontaminants, theStoredWaveformInverseFourierTransform(SWIFT)techniqueisusedatLEBIT[87]. Thistechniqueemploysabroadbandexcitationwithatailoredwaveformtodriveallions withinanedmassbandwithoutdrivingtheionofinterest.Unlikethedipole cleaningmethod,whichrequiresspidenofeachcontaminantinordertodrive itatthecorrectfrequency + ,SWIFTwillcleanallcontaminantswithinthesetbandand doesnotrequireidenofeachone.TheofSWIFTcleaningforthisexperiment isdemonstratedinFig.4.6. 43 Run1 Run2 SpeciesMeasured 68 Co 2+ , 69 Co 2+ 68 Co 2+ 68 Co 2+ ReferenceIon 16 O 18 O + 34 S + 69 Co 2+ ReferenceIon 39 K + N/A 68 Co 2+ DetectedRateonMCP 0.2counts/s 0.6counts/s 69 Co 2+ DetectedRateonMCP 0.2counts/s N/A Total 68 Co 2+ IonsDetected 4779 23129 Total 69 Co 2+ IonsDetected 4275 N/A CIDUsed? Yes Yes SWIFTUsed? 68 Co 2+ :Yes 68 Co 2+ :No 69 Co 2+ :No 69 Co 2+ :N/A Numberof 68 Co 2+ Resonances 7 10 Numberof 69 Co 2+ Resonances 5 N/A BeamContaminants m=q =68: m=q =68: 40 Ar 12 C 16 O + Uniden 40 Ar 14 N + 2 12 C 4 1 H 4 16 O + 12 C 3 1 H 2 14 N 16 O + +Uniden m=q =34: m=q =34: 16 O 18 O + 34 S + +Uniden 1 H 2 32 S + 1 H 33 S + m=q =69: Uniden m=q =34 : 5: 69 Ni 2+ (daughter) Table4.1:ComparisonofconditionsforRun1andRun2. 44 Figure4.6:AttemptedTOF-ICRresonancesof 68 Co 2+ withSWIFT(left)andSWIFTon (right).Atamountofunidenstablecontaminationfromthegascellarrived at m=q =34,obscuringtheresonancebeforeSWIFTwasturnedon.TheuseofSWIFTto cleanunidencontaminantsmadethismeasurementpossible. 4.2.3IsomerInvestigations -decayexperimentshavereportedtheexistenceoftwo -decayingstatesin 68 Co[88]and recentlyasecond -decayingstatein 69 Coaswell[89].Inthepast,LEBIThasonseveral occasionsdemonstratedtheabilitytoresolvegroundandisomericstateswhenthestates arepopulatedatroughlyequalproportionsinthefragmentationprocess[83,90,91].Thisis markedbyasignaturedoublepeakintheTOF-ICRresonance,asseeninFig.2ofRef.[91]. BecauseonlyasinglepeakintheTOF-ICRresonancewasobservedforboth 68 Coand 69 Co, anadditionalstepwasimplementedtoexaminewhichstatewaspresentintherareisotope beamdeliveredtoLEBIT. BeforethecobaltionsfromthegascellweredeliveredtoLEBIT,theywerecollected infrontofahigh-puritygermanium(HPGe)detector.Aschematicoverviewofthemajor experimentalcomponentsfromthisexperiment,includingtheHPGedetector,ispresented 45 Figure4.7:Schematicoverviewofthemajorexperimentalcomponentsusedforthiswork. inFig.4.7.Asthecobaltdecayed, -delayed raysweredetectedwiththeHPGedetector. Thepresenceorabsenceofparticular rayscouldthenprovideanindicationofwhich -decayingstatewasobserved,asdiscussedingreatdetailintheanalysissectionofthis chapter.GammaspectrawereattemptedinthismannerduringRun1,howevertherates weretoolowtoobserveanyofthepeaksofinterest(seeTable4.1forratesobservedinthe Penningtrap).TheimprovedratesduringRun2yieldedausefulgammaspectrumfor 68 Co whichisanalyzedinSection4.3.2. 69 Cowasnotre-measuredinRun2duetolimitedbeam time. 4.3ResultsandDiscussion 4.3.1MassMeasurementResults Toaccountformagneticdrifts,eachcobaltmeasurementwasprecededandfollowed byareferencemeasurementofastablespecieswithawell-knownmass.Thereference measurementfrequencieswerethenlinearlyinterpolatedtodeterminethereferencefrequency atthetimetheionofinterestwasmeasured.Theofnon-linearchangesinthemagnetic 46 werepreviouslystudiedatLEBITandshowntocontributetotheoverallsystematic uncertaintyonlyatalevelof ˘ 10 10 [63],whichisnegligibleforthismeasurement.To minimizesystematicfrequencyshifts,itisbesttochooseareferencespecieswithamass- to-chargeratiosimilartothatoftheionofinterest[39].InRun1,thestablecontaminant 16 O 18 O + arrivingfromthegascellwasusedasareferencefor 68 Co 2+ ,and 39 Kfromthe LEBITthermalionsourcewasusedasareferencefor 69 Co 2+ .InRun2,highlevelsof sulfurwereobservedfromthegascell,representingthepredominantsourceofcontamination. Theoriginofthissulfurisunknown. 34 S + wasthereforereadilyavailableasareferenceion for 68 Co 2+ onthatoccasion. Afterlinearinterpolationofthereferenceionfrequencies,theatomicmassoftheionof interestwasthencalculatedfromtheratioofthecyclotronfrequenciesofthetwospecies usingtheequation m = h m ref q ref e m e i q q ref 1 r +2 m e (4.2) where r istheratio c c; ref and e istheelementarycharge.Theionizationpotentialsofall speciesandthemolecularbindingof 16 O 18 O + arenotincludedinthesecalculationsasthey areall < 20eVanddonotcontributeatthelevelofuncertaintyforthismeasurement[92]. InRun1,seven 68 Cofrequencyratioscontainingatotalof4779 68 Co 2+ ionswererecorded withaweightedaverage r 1 =1 : 000641552(70).Twooftheseseven 68 Co 2+ measurements useda25msRFexcitationtime,oneuseda50msRFexcitationtime,andfouruseda 100msRFexcitationtime.Anear-unityBirgeratio[93]of0.93(18)indicatesthatadditional statisticalareunlikely.InRun2,ten 68 Cofrequencyratioscontainingatotalof23129 68 Co 2+ ions,allexcitedwitha100msRFexcitationtime,wererecordedwithaweighted average r 2 =0 : 99987011(12).OnthisoccasiontheBirgeratiowas1.96(15),sothestatistical 47 IonRunNumberReferenceFrequencyRatioMass(u)ME(keV)AME2016(keV)(keV) 68 Co 2+ 1 16 O 18 O + 1 : 000641552(70)67 : 9445592(48) 51642 : 8(4 : 4) 51930(190) 290(190) 2 34 S + 0 : 99987011(12)67 : 9445593(82) 51642 : 6(7 : 6)290(190) Average67 : 9445592(41) 51642 : 7(3 : 8)290(190) 69 Co 2+ 1 39 K + 1 : 13026790(24)68 : 946093(15) 50214(14) 50280(140)66(140) Table4.2:Measuredfrequencyratios, c / c; ref ,calculatedatomicmassandmassexcess (ME)values,andtheircomparisontothevaluesfrom2016AtomicMassEvaluation.Dif- ferencesinthemassexcessvalues,=ME LEBIT ME AME2016 ,arealsolisted. uncertaintywasbymultiplicationwiththeBirgeratio.Thiscommonly-usedBirge adjustmentisvalidinthecasewherealluncertaintiesareunderratedbythesamecommon factor,whichistakentobetrueformeasurementsofequalreliability.Fivefrequencyratios wererecordedfor 69 Co,eachusinga50msRFexcitationtime,withaweightedaverage r =1 : 13026790(24)andaBirgeratioof1.22(21).Thisstatisticaluncertaintyhasalso beenbymultiplicationwiththeBirgeratio.Systematicesuchasminortrap misalignmentinthemagneticanddeviationsfromapurelyquadrupoleelectricpotential resultinsmallfrequencyshiftsdependentonthemass-to-chargefromthereference ion.TheseshiftshavepreviouslybeenevaluatedatLEBITandcontributeonlyatalevelof 2 : 0 10 10 = ( q=u )[62],whichisnegligibleforallfrequencyratiosconsideredhere.Takinga weightedaverageoftheresultsfromthetwoindependentmeasurementsof 68 Coyieldsamass excessofME( 68 Co)= 51642 : 7(3 : 8)keV,andthemassexcessof 69 Cowasdeterminedto beME( 69 Co)= 50214(14)keV.AsummaryoftheseresultsfromLEBITandcomparison withtheAME2016values[1]ispresentedinTable4.2. 4.3.2LevelAssignment Beforedrawingconclusionsfromtheseresults,thepossiblepresenceofisomersmustbe considered.AspreviouslydiscussedinSection4.2.3,aHPGedetectorwasusedtoobtain 48 aspectrumof -delayed raysfromthedecayof 68 CoduringRun2.Thisspectrumis presentedinFig.4.8.The raysfromthisspectrumwerethencomparedwiththecurrent literatureavailablefor 68 Co decay[88,94,95].Whilethereisdisagreementintheliterature regardingtherelativegammaintensities,thereisagreementthatdecayfromthelow-spin stateproducesa478keVgammarayandanyproductionof595keVor324keVgammarays areatverylowintensities( < 1%).Decayfromthehigh-spinstateof 68 Co,ontheother hand,isassociatedwithhigherintensityproductionofthe595keVand324keVgammas ( ˘ 32%and ˘ 38%,respectively)andnoproductionofthe478keVgammaray.A levelschemeshowingtherelevant -delayedgammaraysforthetwo -decayingstatesof 68 CoispresentedinFig.4.9.AsshowninFig.4.8,thegammaspectrumcollectedaspartof thisworkshowsclearpeaksat595keVand324keV,whilenoevidenceofapeakat478keV ispresent.Thisdemonstratesthepresenceofthehigh-spinbeta-decayingstatein 68 Co,and doesnotsupportthepresenceofanyofthelow-spinbeta-decayingstate. Itisworthnotingthattheabsoluteintensityofthe478keVgammainthelow-spinstate decay( ˘ 6%)issubstantiallylowerthanthereportedintensitiesofthe595keVand324keV gammasinthehigh-spinstatedecay( ˘ 32%and ˘ 38%,respectively).Additionally,the high-spinstatehasashorterhalf-lifethanthelow-spinstate(0.23(3)sascomparedto 1.6(3)s)[88].Accountingforthesizeofthepeaksinthegammaspectrum,thedetector ateachenergy,therelativeintensitiesofeachpeak,andtheexpecteddecaylosses fromthegammadetectortothePenningtrap,itwascalculatedthatthelow-spinstatecould havebeenpresentataleveljustbelowdetectabilityattheGedetectorandstillbeenthe dominatingbeamcomponentatthePenningtrap.Thesecalculationsarepresentedindetail inAppendixC.However,giventhatthereisnopositiveevidenceofasecondstateinthe gammaspectrumorintheTOF-ICRresonanceandthegammaspectrumshowscompelling 49 Figure4.8:The -delayed -rayspectrumdetectedfollowingthedecayof 68 Co.Dashed verticallinesmarktheenergiesof raysknowntofollowprimarilydecayfromonlyoneof thetwo -decayingstatesof 68 Co. raysat478keVfollowdecayfromthelow-spinstate and raysat324and595keVfollowdecayfromthehigh-spinstate.Thepresenceofclear peaksat324and595keVandthelackofapeakat478keVsuggestthatthehigh-spin -decayingstateof 68 Cowasmeasuredinthisexperiment.Otherpeaksinthespectrum haveallbeenidenfromeithernaturalbackgroundradiationor 68 Codecayscommon toboth -decayingstates. Figure4.9:levelschemeshowingtherelevant -delayedgammaraysforthetwo -decayingstatesof 68 Co.Circledgammaenergiesarethosethatsignalthepresenceofone stateortheother,butnotboth.EnergiesareallgiveninkeV.Basedondatafrom[88,94,95]. 50 evidenceforthepresenceofthehigh-spinstate,weassumethatthiswasinfactthestate measuredinthePenningtrap. No 69 Co 2+ gammaspectrawereobtainedinthiswork.However,the(1/2 )beta- decayingstateproposedbyLiddick etal. [89]wasonlyobservedin 69 Cowhenproduced bybetadecayfrom 69 Fe.Inthatsameexperiment, 69 Cowasalsoproduceddirectlyby projectilefragmentation,andthereonlytheshorter-lived7/2 statewasobserved.As 69 Co wasonlyproduceddirectlybyprojectilefragmentationinthiswork(albeitwithat primarybeam)andonlyonestatewasobservedhereaswell,weassumethatthe 69 Comass determinationreportedherecorrespondstothe7/2 state. Withtheseassumptions,weconcludethat,inboth 68 Coand 69 Cotheonestatemeasured inthePenningtrapwasthebeta-decayingstatewiththehigherspin.However,inboth cases,theorderingofthebeta-decayingstatesisstillunknown.Mueller etal. proposedspin andparityassignmentsforthetwostatesin 68 Cobasedonangularmomentumcoupling ofthetwobeta-decayingin 69 Niwithan f 7 = 2 protonhole[88],whichwould suggestahigh-spin(7 )groundstateandalow-spin(3 + )isomer.Thisargumentfollows therulesforangularmomentumcouplingofparticle-holeinodd-oddnuclei laidoutbyBrennanandBernstein[96].Whileothershavesuggestedalternatespinand parityassignmentsforthelow-spinstate[94,97],nonehaveyetanycontradictionto thisordering. Inthecaseof 69 Co,oneofthebeta-decayingstatesisbelievedtobe7/2 basedonthe ˇf 1 7 = 2 observedinallotherodd- A cobaltisotopes,andtheotherbeta-decaying stateproposedbyLiddick etal. isdescribedasa(1/2 )prolate-deformedintruderstate attributedtoprotonexcitationsacrosstheZ=28shellashasbeensuggestedfor 65 Coand 67 Co[98].The(1/2 )stateapproachesthe7/2 groundstatenear N =40andbecomes 51 isomeric,possiblyevencrossingthegroundstate,at 69 Co.Nocommentontheorderingof thesetwostatescanbemadein[89],buttheirseparationislimitedto < 467keVor < 661keV dependingontheassumedstrengthoftheunobservedM3 -raytransition. Toshedlightontheorderingofthe -decayingstatesin 68 Coand 69 Co,ateamof many-bodynuclearstructuretheoristswasconsultedtoperform abinitio calculationsus- ingthevalence-spacein-mediumsimilarityrenormalizationgroup(VS-IMSRG)[99{103] frameworkbasedontwo-nucleon(NN)andthree-nucleon(3N)forcesfromchirale theory[104,105].Inparticular,theSRG-evolved[106]1.8/2.0(EM)interactionfrom Refs.[107,108]wasused,whichpredictsrealisticsaturationpropertiesofmatter andhasbeenshowntoreproducewellground-stateandseparationenergiesfromthe p - shelltothetinisotopes[109,110].TheMagnusformulationoftheIMSRG[111]wasthen usedtoconstructanapproximateunitarytransformationtodecoupleagivenvalencespace Hamiltonian(andcoreenergy)tobediagonalizedwithastandardshell-modelcode[112]. Twotvalencespacestrategiesforcobaltisotopeswereconsidered.The usedstandard h! spacesforbothprotonsandneutrons:forprotons,the pf shell;for neutrons,the pf shellabovea 40 Cacorefor N< 40,andthe sdg shellabovea 60 Cacore for N> 40.Thesespacesallowfornoneutronexcitationsat N =40,soweknow apriori thatcalculationsinthisvicinitywillbeunreliable.Sincethisisalsotheregionofinterest forthecurrentmeasurements,across-shell p 1 = 2 f 5 = 2 g 9 = 2 neutronspacewasalsodecoupled usinga 52 Cacore. Withthe p 1 = 2 f 5 = 2 g 9 = 2 space,thegroundstatein 68 Cowasfoundtobea2 ,which agreeswiththespin-parityofthelow-spinbeta-decayingstatesuggestedbyFlavigny et al. [94],thoughFlavigny etal. makenocommentonwhetherthisisthegroundstate.The calculationspredictalargenumberofstatesbelow1MeV,soanitivepredictionofthe 52 ground-stateisnotpossiblegivenpresenttheoreticaluncertainties.Inthecaseof 69 Co,the groundstatewascalculatedtobe7/2 ,consistentwiththesurroundingodd-masscobalt isotopes. Itisclearthatadditionalworkisneededtoclarifytheorderingsofthetwobeta-decaying statesin 68 Co.Mueller etal. suggestahigh-spingroundstate[88]whiletheVS-IMSRG calculationssuggestalow-spingroundstate,asisthecaseforthetwoodd- N cobaltisotopes justbelow N =40.However,withthelargenumberofcloselyingstates,neitherproposalis presentedwithahighdegreeofForthepurposeofexaminingmasssurfacesinthe regionsof 68 Ni,thehigh-spinstateof 68 Comeasuredinthisworkistreatedastheground state.Shouldfutureworkchallengethisassignment,itisworthnotingthattheresults presentedinthisworkwillstillbevaluableforaprecisedeterminationoftheground-state massiftheexcitationenergyoftheisomericstatehasbeenmeasured. 4.3.3EvaluationofTwo-NeutronSeparationEnergyTrends Thetrendsin S 2 n arepresentedinFig.4.10,showingtheAME2016dataandresultsfrom thiswork.WhiletheAME2016datashowsafairlylineartrendalongthecobaltchain from N =39to N =42,thenewLEBITdatademonstratesasubstantial(287keV)reduction inbindingat N =41,creatingasmallkinkinthe S 2 n chainwhichmightsuggestaminor subshellclosureat N =40.IftheuncertainIMSRGpredictionofalow-spingroundstate islaterproventobeaccurate,suggestingthehigh-spinstatemeasuredinthisworkisthe isomericstate,thiskinkwillbereducedandthetrue S 2 n valueswillreturntowardsthe AME2016values.The S 2 n valuefor 70 Co( N =43)increasesduetothedecreaseat N =41, howeverthemassof 70 Coitselfisstillunmeasured,leavingarelativelylargeuncertaintyon thispoint. 53 Figure4.10:Two-neutronseparationenergies S 2 n plottedasafunctionofneutronnumber N forisotopesofiron,cobalt,nickel,andcopper.Greensquarepointscorrespondtonew cobaltvaluesfromthisworkandblackcirclescorrespondtodatafromAME2016[1].Points plottedwithanxmarkerindicatevaluesderivednotfrompurelyexperimentaldatainthe AME2016. 54 Toexaminethe N =40kinkmorequantitatively,theneutronshellgapparameterhas alsobeencalculated,as N ( N;Z )= S 2 n ( N;Z ) S 2 n ( N +2 ;Z ) : (4.3) N isplottedasafunctionofneutronnumberforiron,cobalt,nickel,andcopperin Fig.4.11intheregionof N =40.Whilethenewmeasurementof 68 Cogreatlyreduces N at N =41inthecobaltchain,italsoincreases N at N =39suchthatnorelativepeakis observedat N =40.However,thehighprecisionoftheLEBITresultsrevealsasmallbut tenhancementof N at N =39,somewhatsmallerthanwhatcanalreadybeseen at N =39inthecopperchainandtlysmallerthanthepeakat N =39seeninthe nickelchain.Whileitdoesnotmakeanysensefromashellmodelperspectivetoconsider thisasignofashellorsubshellclosure,thisdoesseemtosuggestsomeasyetunexplained behaviorresultinginadditionalstabilityat N =39inthisregion. Interestingly,theIMSRGcalculationsdiscussedpreviouslycapturethissurprisinglylarge bindingat N =39inthenickelchain.AcomparisonoftheIMSRGcalculationsand theAME2016dataforthenickelchaininthisregionispresentedinFig.4.12.IMSRG calculationsperformedwithinasingleharmonicoscillatorshell(usingonly pf shellfor N 40and sdg shellfor N> 40)demonstratetunderbindingandresultinanunphysical discontinuitycrossing N =40.Asmentionedabove,thisdiscontinuityiswellunderstood tobeduetothelackofallowedneutronexcitationsnear N =40,whichisanartifactof thisparticularchoiceofvalencespace;indeedthebindingistlyimprovedfor N< 40,andthediscontinuityacross N =40disappearswhena pf 5 = 2 g 9 = 2 neutronspaceisused instead.Bothcasescapturethelargebindingat N =39observedintheAME2016data. 55 Figure4.11:Neutronshellgap N plottedasafunctionofneutronnumber N forisotopes ofiron,cobalt,nickel,andcopper.Thegreencurvecorrespondstonewcobaltvaluesfrom thisworkandtheblackcurvescorrespondtodatafromAME2016[1].Pointsplottedwith anxmarkerindicatevaluesderivednotfrompurelyexperimentaldataintheAME2016. Inset:Neutronshellgapplottedasafunctionofprotonnumber Z forisotopeswith N =40 neutrons. 56 Figure4.12:Two-neutronseparationenergies S 2 n plottedasafunctionofneutronnumber N forthenickelisotopicchain.ThesolidblackdataaretakenfromAME2016,andthe dashedlinescorrespondtoIM-SRGtheoreticalcalculations.Bluetrianglesusea 40 Cacore for N 40( pf neutronvalencespace)anda 60 Cacorefor N> 40( sdg neutronvalence space).Redsquaresusea pf 5 = 2 g 9 = 2 valencespaceforprotonsandneutronsfortheentire chainstartingfroma 56 Nicore. 57 Chapter5 DevelopmentofaSingleIonPenning TrapMassSpectrometerforRare Isotopes 5.1SIPTConceptandRequirements TheSingleIonPenningTrap(SIPT)reliesfundamentallyonthenon-destructivenarrowband FT-ICRtechniquediscussedinSection2.2,inwhichthecyclotronfrequencyofanion inaPenningtrapisdeterminedbyusingatunedresonatorcircuittodetecttheimage chargeinducedonthetrapelectrodes.However,theextensionofthistechniquetoasingle radioactiveionpresentsanumberoftechnicalchallengeswhichmustbemettosuccessfully achieveacompletemassdetermination. First,allofthetechnicalrequirementspreviouslydiscussedforproductionandtrappingof aradioactiveionarestillapplicable.ThismakesLEBITanexcellentlocationtohousesuch aproject,asitisalreadysetuptotakefulladvantageoftheworld-classbeamproduction, isotopeselection,andbeamstoppingfacilitiesattheNSCL.Byredirectingtheionsto SIPTjustbeforethe9.4-TTOF-ICRmagnet,SIPTcanalsoutilizetheexistingLEBIT cooler/buncherandionsources.Still,theadditionofSIPTtotheLEBITfacility 58 requiredtheassemblyofanewstretchofbeamlineandanewsuperconductingmagnet withinthelimitedspaceoftheLEBITroom.Amongotherconsiderations,thesespace requirementsmeanthatthebeammustbedirectedarounda115 ° bendtoreachtheSIPT magnet.AdiscussionofthenewSIPTbeamtransportsystemispresentedinSection5.2. OncetheionsreachthePenningtrap,ahighlysensitivedetectionsystemisrequired toreliablydetecttheimagechargecreatedbyasingle,singly-chargedion.Therelevant whichmustbeoptimizedtoachievethisgoalisthesignal-to-noiseratio S=N ,whichis theratiooftherootmeansquare(RMS)voltagesignalgeneratedinanarrowbandFT-ICR detectioncircuittotheRMSJohnson-Nyquistnoise[113].Thisratioisgivenapproximately by S=N ˘ Nq ˆ ˆ 0 r s Q k B TC ; (5.1) where N isthenumberofions, q istheioncharge, ˆ ˆ 0 istheradiusoftheions'orbitrelative tothetrapradius, istheratiooftheionfrequencyandthespectralwidth, k B isthe Boltzmannconstant,and Q , T ,and C arethequalityfactor,temperature,andcapacitance ofthedetectioncircuit,respectively[2,53].ThegoalofSIPTistoobtainmeasurements withasingle,singly-chargedion,thus N and q .Theionandtrapradiiarechosento maximizetheinducedimagechargewhilekeepingfrequencyshiftsduetoimperfections andspecialrelativitywithinacceptablelimits;adetaileddiscussionoftheseconsiderations ispresentedinSection5.3.1.2. Thekeytoreachingadequate S=N forasingleradioactiveisotopethereforeliesinopti- mizingtheRLCdetectioncircuit.Inparticular,thecircuitqualityfactor Q ,as Q = circ circ (5.2) 59 mustbe ˘ 1000orgreater.Achievingsuchanarrowcircuitresonancerequiresasuper- conductinginductorcoil,soSIPTmustbeoperatedatcryogenictemperaturestokeepthe inductorcoilbelowitscriticaltemperature.Cryogenicoperationprovidestheadditional bofverylowthermalnoise,furtherimproving S=N asdemonstratedbythefactorof 1 p T inEq.(5.1). TotestthefeasibilityofperformingmeaningfulscientifcmeasurementswithSIPT,sim- ulateddatawasgeneratedinthetimedomain,Fouriertransformed,andthenwitha Lorentzianfunctioninthefrequencydomain.Theachievable S=N for 100 Sn( t 1 = 2 ˘ 1s) and 78 Ni( t 1 = 2 ˘ 0 : 1s)wasestimatedusingEq.(5.1)withestimatesforSIPTparameters showninTable5.1andassuminganobservationtimeofonehalf-lifeforeachion.Numer- icalpre-factorsneededforEq.(5.1)forahyperbolictrapweretakenfromRef.[53],which usedtherelaxationmethodtocalculatetheelectricpotentialinthistrapgeometry.The simulateddataconsistedofsinewavesofrandomphasewithrandomnoisegeneratedatthe relativeamplituderequiredtoobtaintheexpected S=N .Thecenterfrequencyuncertainty oftheLorentzianwasthenusedtodeterminetheobtainableprecisionforagiven S=N . TheresultsofthesesimulationsarepresentedinFig.5.1.BasedonEq.(5.1),theestimated S=N isaround1.5inthetimedomain.Whilethisnumbermaysoundlow,thetimedomain S=N maybeverysmallandstillrevealaclearpeakinthefrquencydomainprovidedthe signalissampledforalargenumberofperiods.Usingonehalf-lifeforthesampletime,the simulateddataproducedclear,easilypeaksintheFFTwith S=N wellbelow0.1.Asseen inFig.5.1,theobtainableprecisionisexpectedtobearound10 7 orbetter,whichismore thantfornuclearstructureandnuclearastrophysicsstudies. 60 ˆ=ˆ 0 0.5 Q 2000 T 5K C 30pF Table5.1:Parametersusedtoestimatetheachievable S=N fornarrowbandFT-ICRmea- surementswithasingleion. Figure5.1:Frequencydomainprecisionasafunctionofsignal-to-noiseratioforsimulated singleionsignalsfrom 78 Ni + and 100 Sn + 61 Figure5.2:LayoutofthemajorcomponentsofthenewSIPTbeamline. 5.2TheSIPTBeamline AnewsectionofbeamlinewasbuiltinordertotransportionstotheSIPTPenningtrap. Itisimportanttorecognizethatthisbeamlinewasbuiltinadditionto,notinplaceof,the existingLEBITbeamline.Inthenewsetup,ionswilleitherbetransportedtothe9.4-T magnetforTOF-ICRmeasurementsifratesaretlyhigh,ortothe7-TSIPTmagnet forFT-ICRmeasurementswhensingleionsensitivityisrequired.Thelayoutofthenew SIPTbeamlineispresentedinFig.5.2. TodeliverionstoSIPT,a25 ° sphericalkickerdivertsionsejectedfromtheLEBIT cooler/bunchertotheSIPTbeamline.Ionsthenfollowa115 ° cylindricalbender,which includesanelectrostaticquadrupoledoubletateachendandanadditionalelectrostatic quadrupolesingletinthemiddlefortransversefocusing.Apictureofthebenderwith electrostaticquadrupolesispresentedinFig.5.3.Followingthe115 ° bend,ionsfollowa straightawaypathtothe7-Tmagnet,whichincludesthreeBeamObservationBoxes(BOBs) 62 Figure5.3:115 ° cylindricalbender,withintegratedelectrostaticquadrupoledoubletson eachendandaquadrupolesingletinthemiddlefortransversebeamfocusing. fordiagnosticsandtwoeinzellensesforadditionalfocusing.Beamtrajectoriesfromthe kickertothemagnetweresimulatedinSIMION[114]tooptimizetherelativedistancesof theseionopticalelementsandtoestimatethebestfocusingpotentials.Thesimulatedion trajectoriesarepresentedinFig.5.4. ThethreeBOBsalongthestraightawaysectionoftheSIPTbeamlineareequippedwith Faradaycups,MCPdetectors,andphosphorusscreenswithviewingcamerastocharacterize thebeamateachlocation.SIPTBOB1immediatelyfollowsthe115 ° bender,SIPTBOB2 sitsbetweenthetwoeinzellenses,andSIPTBOB3islocatedjustbeforethe7-Tmagnet.The MCPatSIPTBOB3issituatedinaDalytoallowforTOF-ICRmeasurements withSIPT,asdescribedinSection5.3.1.4. AseriesofdrifttubesarethenusedtoguidetheionsinsidethemagnettothePen- ningtrap.Theseinjection/ejectionopticsweredesignedbothtoinjectionsfromtheSIPT beamlineintothetrapandtoallowforreverseextractiontotheDalyMCPforTOF-ICR measurements.Thedesignforthesedrifttubeswasbasedontheopticsusedforextraction fromthe9.4-TPenningtrap,withmotointheallowedspaceandtoprovidethe focusingnecessaryfortheMCPanddecelerationforinjectiononthesamevoltagesettings. 63 Figure5.4:SimulatediontrajectoriesthroughtheSIPTbeamline,fromthekickertothe 7-TSIPTmagnet. 64 Figure5.5:Designdrawingandphotographofthedrifttubeassemblyusedforioninjec- tion/ejectionto/fromtheSIPTPenningtrap. Thedesigndrawingsandaphotographoftheinjection/ejectionopticsarepresentedside-by- sideinFig.5.5.Thesecond-to-lastdrifttubebeforethePenningtrap(DT7)issubdivided longitudinallyintofourcylindricalarcsegmentscenteredonthe x and y axestocreatea Lorentzsteerer[50]tocontroltheinitialmagnetronradiusoftheionsinthePenningtrap. 5.3TheSIPTPenningTrap 5.3.1SpectrometerDesign 5.3.1.1TheSIPTMagnet SIPTusesa7-TsuperconductingsolenoidmagnetfromOxfordInstruments.Magnetsp cationsasprovidedbythesupplierarepresentedinTable5.2.Themagneticiscreated byrunninganominalcurrentof205amperesthroughniobium-titaniumsuperconducting windingsandoperatesat4.2Kinliquidhelium.Activeshieldingisemployedtoreduce thefringeoutsideofthemagnet.A95mmhorizontalroom-temperatureboreprovides 65 CentralField 7.0Teslaat4.2K MagnetOperatingCurrent 205Amperes(Nominal) FieldDecay(72HrsMeasurement) 50ppb/hr LHeVolume 122 10L LHeHoldTime 90days LN2Volume 84 5L LN2HoldTime(Designed) 14days LN2HoldTime(Guaranteed) 10days BoreDiameter 95mm(+2mm/-0mm) OverallLength 985mm 2mm Table5.2:Oxfordmagnetspasprovidedbythesupplier. experimentalaccesstothecentralmagnetic Toslowliquidheliumevaporationlosses,theheliumdewarisshieldedfromroomtemper- aturebyavapor-cooledshieldandliquidnitrogenvessel.Liquidnitrogenisweekly, andliquidheliumisreplenishedapproximatelyeverytwomonths. Asuperconductingswitchwasusedtoshort-circuitthewindingsoncethemagnetwas energizedsothatthemagnetoperatesintruepersistentmode.Thisresultsinexcellent stabilityovertime,withadecayof 50ppb/hr.ICRfrequencyshiftsduetomagnetic decaycanbeaccountedforbytakingoccasionalmeasurementsofreferenceionswith well-knownmass,asdescribedpreviouslyforthecurrentLEBITsystem. Spatialuniformityofthemagneticwasstudiedtoexaminepotentialsystematic frequencyshiftsduetoaxialtrapvibrationscausedbythecryocoolerormagnetic misalignmentfromtheboretube.ThesestudiesarepresentedindetailinAppendixBand showthatthesefrequencyshiftsshouldbenegligibleforSIPT. 5.3.1.2PenningTrapElectrodeSystem Theelectrostaticquadrupolepotentialrequiredforaxialiontisgeneratedbya setofpreciselymachinedhyperbolictrapelectrodes.OtherPenningtrapelectrodegeome- 66 triesarepossible,howeverthehyperbolicgeometryprovidesthebestapproximationofa truequadrupolepotentialwithelectrodes[38].Thisisaparticularlyimportantcon- siderationforSIPT,becausefrequencyshiftsduetoelectricimperfectionsbecomemore pronouncedasionsgetclosertothetrapelectrodes,andimagecurrentdetectionrequires thattheionsbedrivenasclosetotheelectrodesaspossible. ThedesignultimatelychosenfortheSIPTPenningtrapelectrodesystemisbasedon thePenningtrapcurrentlyusedinthe9.4-TmagnetforTOF-ICRmeasurementsatLEBIT, butscaleddownto50%ofthesize.ThisreductionofthePenningtrapsizeallowsionsto getclosertotheelectrodesforbetterimagecurrentpickupwithoutdrivingtheionstoan excessivelylargeradius,whichwouldintroducefrequencyshiftsduetospecialrelativity.A studyoffrequencyshiftsduetospecialrelativityispresentedinAppendixB,and indicatesthatsuchshouldnotbeaconcernforSIPTwiththissmallertrapsize. TheSIPTPenningtrapdesignispresentedinFig.5.6,andtrapdimensionsarepresented inTable5.3.Fieldimperfectionsduetothesizeoftheendcapandringelectrodes arelargelycompensatedbycorrectionringelectrodes,andadditionalimperfectionsdueto thesmallholeintheendcapneededtoallowionstoenterandexitthetraparelargely compensatedbycorrectiontubeelectrodes[41].TheSIPTringelectrodeissegmentedinto eightidenticalpieces,allowingexibilityintheofringsegmentsfordriving andpickingupthemocyclotronandtruecyclotroncomponentsoftheionmotion. TheSIPTtrapelectrodesaremadeofoxygen-freehighthermalconductivity(OFHC) coppertoensuregoodthermalconductivityatcryogenictemperaturesandplatedwith goldtoreducepotentialelectricirregularitiesduetopatchSapphireinsulators areusedtomaintainexcellentthermalconductivityacrossthetrap.PicturesoftheSIPT electrodesbefore,during,andafterassemblyarepresentedinFig.5.7. 67 Figure5.6:DesigndrawingoftheSIPTPenningtrapcorrectedhyperbolicelectrodesystem. TrapdimensionsgiveninTable5.3. a(HeightEndcap-to-Endcap) 28mm b(RadialWidth) 28mm L CR 3.9mm ˆ 0 6.485mm z 0 5.59mm r a 2mm 54 : 74 ° Table5.3:SIPTPenningtrapdimensions(seeFig.5.6.) Figure5.7:SIPTPenningtrapelectrodesbeforeassembly(left),partwaythroughassembly (middle)andafterassembly(right). 68 5.3.1.3CryogenicSystem AsdiscussedinSection5.1,theSIPTdetectionsystemmustoperateatcryogenictempera- turesinordertoachievesingleionsensitivity.Theniobium-titaniumsuperconductingwire usedfortheSIPTinductorcoilhasacriticaltemperatureofaround10K,howeverthis criticaltemperaturedecreasesinstrongmagneticTheexpectedcriticaltemperature intheSIPTmagnetisaround6K.ToreachthislowtemperaturefortheSIPTdetection system,aseriesofstudieswereperformedtodeterminethecoolingpowerrequirements consideringradiativeheatlossesandconductivelossesthroughwireleadstoroomtempera- ture[115].Allowingforsomeuncertaintyinthesestudiesandpossibleprovisionsforfuture systemchanges,itwasdeterminedthat1.5Wofcoolingpowerat4Kshouldbemorethan t. ThesecoolingrequirementsaremetbythePT415cryorefrigeratorwithCP1110helium compressorfromCryomech,Inc.Vendorspforthismodelaresummarizedin Table5.4.Thisisapulse-tubecryocooler,whichhasthehighlyimportantfeatureofno movingpartsinthelowtemperaturesectionofthedevice,resultinginverylowvibrations, highreliability,andlowcostofoperationandmaintenancecomparedtoothercryocoolers. Thismodelalsohasaremotemotoroption,whichisimportantbecausetheentireLEBIT systemisbiasedto30kVduringonlineexperiments.Theremotemotoroptionallowsthe compressorpackagetoremainatgroundoutsidetheLEBITroom,connectedbytransfer lineswithahigh-voltageinsulatingbreaktothecoldheadwhichismountedtotheSIPT magnetat30kV. TheSIPTcryocoolerincludestwotemperaturestages.Thestagereachestemper- aturesaround45Kandisthermallycoupledtoacoppershieldwhichsurroundsthelower 69 ColdHead CoolingCapacity 1.5W@4.2Kwith40W@45K LowestTemperature 2.8Kwithnoload CoolDownTime 60minutesto4Kwithnoload Weight 55lb(25kg) CompressorPackage Weight 420lb(190.5kg) Dimensions(LxWxH) 24x24x31in(61x61x79cm) PowerConsumption@SteadyState 10.7kW Table5.4:VendorspforPT415cryorefrigeratorwithCP1110heliumcompressor fromCryomech,Inc. temperaturestage,blockingthesightlinetotheroomtemperaturesurroundingstoreduce radiativeheating.Thesecondstageoperatesaround4.2K,thoughitcanreachaslowas 2.8Kwithnoload.ThisstageisthermallycoupledtothekeySIPTcryogeniccompo- nentsincludingthesuperconductingresonatorcircuit,cryogenicandPenningtrap electrodes. AdiagramofthecryogenicstagesofSIPTispresentedinFig.5.8.Thecoldheadsits insidetheSIPTdetectionbox,whichmountsonthebackendoftheSIPTmagnet.Along copperarmconnectstothecoldheadandextendsintothemagnetboretothecryogenic electronics,resonatorcircuit,andPenningtrap.InsidetheSIPTdetectionbox,acopper boxconnectstothe45Kstageandsurroundsthecoldhead,blockingthesightlinefrom the4.2Kstagetotheroomtemperaturesurroundings.The45Kstagealsoconnectstoa longhollowcoppertubewitharemovablelid.Thistubeextendsthroughthemagnetbore andactsasbotha45Kshieldandabenchtoholdalloftheexperimentalcomponentsthat sitinsidethemagnet,includingthecryogenicdetectionelectronics,Penningtrapelectrode system,andtheioninjectionoptics. 70 Figure5.8:OverviewoftheSIPTcryogenicsystemcomponents. 5.3.1.4TOF-ICRDetection SIPTwasdesignedtoallowstandardTOF-ICRdetectioninadditiontoFT-ICRformea- surementsandoptimization.Centraltothismulti-usedesignistheexecutionof reverseionextraction.Asinthe9.4-TPenningtrap,ionsdeliveredtoSIPTpassthrougha setofinjectionopticsincludingaLorentzsteerer[50],whichpreparestheionsinaninitial magnetronmotioninthePenningtrap.AquadrupoleRFdriveisthenappliedtoconvert theslowmagnetronmotionintofastmocyclotronmotion.Unlikethe9.4-Tsystem, however,ionsintheSIPTtrapcannotbeejectedouttheoppositesideofthetrapfrom whichtheywereinjected.Instead,whenTOF-ICRdetectionisdesired,theionsmustbe extractedinthesamedirectionfromwhichtheyenteredthetrapandpassthroughthesame injectionopticsintheoppositedirection,beforetheyaredetectedonanMCPdetectorina DalyjustoutsidethemagnetboreatSIPTBOB3. 71 Figure5.9:ConceptualoverviewofreverseionextractionforTOF-ICRmeasurementswith SIPT. TheconceptofTOF-ICRdetectionwithreverseextractionispresentedinFig.5.9.The keyfromthe9.4-TTOF-ICRsetup,asidefromchangingthedirectionoftheions' motionaftertrapping,isthattheLorentzsteerervoltagesandtheDalycollectorvoltage mustbeswitchedwhentheionsareejectedfromthetrap.OninjectionintothePenning trap,theLorentzsteerershouldsteertheionstertopreparetheinitialmagnetron motion.OnejectionfromthePenningtrap,theLorentzsteerermustbeswitchedtoallow theionstopassbywithoutchangingcourse.Conversely,theDalycollectorshouldbeset toallowionstopassbyunimpededoninjection,butmustbeswitchedtoamorenegative voltageonejectionfromthePenningtrapsothattheionsarecollectedtherefordetection. 5.3.1.5FT-ICRDetectionCircuitDesign Single-ionFT-ICRdetectionrequirescarefulcircuitdesignconsiderationtocreateasstrong ofasignalaspossiblewhileminimizingnoise.Certainstagesofthecircuitmustalsooperate insidethe7-TSIPTmagnetandatcryogenictemperatures,requiringadditionaldesign 72 Figure5.10:SchematiccircuitdiagramoftheSIPTcryogenicanddetectionelec- tronics. considerationstoensureperformancedoesnotdegradeinthisextremeenvironment.The detectionelectronicswerepurchasedfromStahlElectronicsduetotheirexperienceand expertiseinelectronicsdesignandmanufacturingforsimilariontrapprojects. AschematicoftheSIPTcryogenicdetectioncircuitispresentedinFig.5.10.Theimage currentdetectionschemeisdeterminedbythewiringoftheeightringelectrodesegments(see thediscussionofmultipolarFT-ICRdetectionschemesinSection2.4).FortestsofFT- ICRdetectionwithSIPT,thetraphasbeenwiredfordipolepickupof + .Threeadjacent ringsegmentswerejumpedtogethertoprovideampleelectrodesurfaceareaforimagecurrent pickup.Thethreeadjacentsegmentsoppositethepickupsegmentsweregroundedforsignal reference.Inprinciple,astronger + signalcouldbeobtainedbyusingthesesegmentsfor signalpickupaswellandconnectingtheoppositesidesofthetraptoatial asisdoneforroom-temperatureFT-ICRpickupwithMiniTrap.However,StahlElectronics 73 hasfoundfrompastexperiencethatthesingle-inputcryogenictheyprovidedfor SIPTperformsfarbetterthantheirtialsoonlyasinglesectionofthe trapringisusedforsignalpickup.TheremainingtworingsegmentsareusedfortheRF signalsneededtodrivetheions'motion. AtunablesuperconductingRLCresonatorcircuitisthenusedtoimprovethequalityof theimagecurrentsignal.ThegeneralformofOhm'slawinanACcircuitis V = I j Z j ; (5.3) fromwhichitclearlyfollowsthatevenaverysmallcurrentsourcecangenerateasubstantial voltagesignaliftheoverallcircuitimpedanceist.InaparallelRLCcircuit,the absolutevalueoftheimpedanceisgivenby j Z ( ! ) j = Q!L s 1+ Q 2 ! 2 ! 2 circ 1 2 : (5.4) Wecanseefromthisequationthatthemaximum j Z j ,andthereforethemaximumvoltage signal,isachievedwhen ! = ! circ =1 = p LC .Atthisvalue,theimpedancesduetothe circuitcapacitanceandinductancecanceleachotherouttheonlyremainingimpedanceis theparallelresistance,givenby j Z ( ! = ! circ ) j = R p = Q! circ L = Q ! circ C : (5.5) SeveralimportantcircuitdesignconsiderationsfollowfromEq.(5.5).First,whenchoosing L and C tomatch ! circ withtheexpectedICRfrequency,itisdesirabletomake L aslarge 74 aspossibleand C assmallaspossible.Typicallythetotalcapacitance C ,whichincludes thecapacitancefromthetrapelectrodesaswellasstraycapacitancesfromthewiresand input,canbelimitedto ˘ 20pF,requiringaninductanceontheorderofhundreds of Hfortypical + and c valuesofsingly-chargedionsina7Tmagnetic Eq.(5.5)alsodemonstratesthatitisimportanttomakethecircuitqualityfactor Q as largeaspossible.Tothisend,asuperconductingNbTicoilisusedfortheinductor,reducing theseriesresistanceacrossthecoiltozerowhencooledbelowthecriticaltemperature.By alarge Q meansanarrowfrequencyresponse(Eq.5.2),suppressingallnoise outsidethisnarrowbandwheretheFT-ICRsignalisexpected. Thecenterfrequencyoftheresonatorcircuitmustalsobetunabletomatchtheexpected ICRfrequencyoftheiontobemeasured.Thetunablerangeofagivenresonatormustcover severalatomicmassunitstoensurethatastablereferencemassisavailableformagnetic calibrationsandtoallowtuningthroughthebeamlinewithanisotopeclosertostability beforeswitchingtotheisotopeofinterest.Toachievethis,thecryogenicfromStahl Electronicsisequippedwithtwogallium-arsenidehigh-Qvaractordiodesinparallelatthe inputoftheThesevaractordiodeshaveavoltage-dependentcapacitance,witha nominalrangeof2.4pFto14pF.Thisprovidesapproximatelya 8%tuningrange. Thecryogenicutilizesstate-of-the-artGaAsFETtechnologytoprovidelow noiseat4.2K.Thenominallinearvoltagegainforthecryogenicis ˘ 11x.Tominimizenoisepickuponthewires,thisiskeptascloseaspossibletothe Penningtrap.Itwastestedbythemanufacturerattemperaturesof4Kwithnomagnetic andinmagneticupto6Tat10Kanddemonstratednolossofperformancein theseconditions. Theoutputfromthecryogenicisdeliveredbycryogeniccoaxialcabletoaroom 75 temperatureA7-2onmodule,alsoprovidedbyStahlElectronics.The tionofthismodulecanbesetbytheuserinfourdiscretesteps:20x,40x,100x,or200x.The A7-2alsoprovidesstable,low-noiseDCsupplyvoltagestothecryogenicandmoni- torsthebiasingconditions.AninternalPIDloopadjuststhesupplyvoltagesasneeded,and LEDindicatorsprovidefeedbacktotheusertoanalyzepossiblemalfunctionsandcabling problemsinthecryogenicregion. 5.3.2ControlsandDataAcquisition InitialtestsofFT-ICRdetectionwithSIPTusedanSR1audioanalyzerfromStanford ResearchSystemstocompletetheFTTanalysis.Thetime-domainsignalfromtheroom temperaturewassenttoalow-noisefrequencymixer,whichsubtractsagiven localoscillatorfrequencyfromtheentiresignal.Thisfrequencymixingshiftstheionsignal toamuchlowerfrequency,allowinghigh-resolutionsignalsamplingwithlessdata.The time-domainoutputofthefrequencymixerwasthensenttotheSR1forFFTanalysis,and thefrequency-domainoutputfromtheSR1wassavedtoaLEBITcomputer. Foronlinebeamexperiments,itwillnotbedesirabletousetheSR1becausethedata transferratesarelimitedbythehardwareandwouldintroduceseriousdeadtimeinthe measurementprocess.Instead,thetime-domainsignalfromtheroomtemperatuream willbedeliveredtoaPXI-5114oscilloscopefromNationalInstruments,whichcurrentlypro- cessestheionsignalsusedforTOF-ICRdetectionatLEBIT.Anear-termfutureprojectwill betowriteanalysiscodetoprocessthistime-domainsignal.Asmostdatainanextremely low-ratebeamexperimentwillbedevoidofanyionsignal,animportantcomponentofthis analysiscodewillbesettingthresholdstodetermineinrealtimeifanacquiredsignalcon- tainsionsignatures.Potentiallyusefuldatawillbesaved,andblankdatawillbedeletedto 76 Figure5.11:FlowchartsoutliningtheSIPTdataacquisitionprocesscurrentlyusedfor testing(left)andthatenvisionedforfutureonlineexperiments(right). avoidtakingupharddrivespace.UltimatelythisreadbackforFT-ICRdatawillbeincorpo- ratedintotheMassMeasurementsoftwarepackageusedforTOF-ICRlivedataacquisition. Awchartoutliningthedataacquisitionprocesscurrentlyusedfortestingandthat envisionedforfutureonlineexperimentsispresentedinFig.5.11. AdescriptionofthecontrolsanddataacquisitionsystemcurrentlyusedatLEBITcan befoundintheappendicesofRef.[116].SIPTcontrolshavebeenincorporatedintothe LabVIEW-basedserverusedtocommunicatewithLEBIThardware.Thisincludesallof thebeamlinecomponentssuchaspowersupplies,vacuumpumps,andgatevalves,aswell astheAFGsusedtodrivetheions'motionandtheAFGusedasthelocaloscillatorfor thefrequencymixer.ScreenshotsoftheQt-baseduserinterfaceusedforSIPTcontrolsare presentedinFig.5.12. 77 Figure5.12:ScreenshotsoftheQt-baseduserinterfaceusedforcontrolofSIPThardware devicesincludingpowersupplies,AFGs,vacuumpumps,andgatevalves. 5.4CommissioningoftheSingleIonPenning Trap 5.4.1RoomTemperatureCommissioning ThesttestsoftheSingleIonPenningTrapwereperformedatroomtemperature,using stable 39 K + ionsfromtheLEBITthermalionsourcetotestiontransport,trapping,TOF- ICRdetection,andbroadbandFT-ICRdetectionwithalargenumber( ˘ 1000)oftrapped ions. TheSIPTbeamlinecomponentsperformedwellasexpectedfromthebeamopticssimu- lationsdiscussedinSection5.2. ˘ 95%iontransportwasobservedaroundthe115 ° bend(fromBOB4toSIPTBOB2)withminimaladjustmentfromthesimulatedelectrode potentials.ThistransportncywasdeterminedbycomparingFaradaycupioncurrent 78 Figure5.13:10msTOF-ICRresonanceof c for 39 K + usingreverseionextractionfromthe SIPTPenningtraptotheSIPTDalyMCP. measurements. ThetrappedionswithSIPTwereobservedusingthereverseextractionmethod discussedinSection5.3.1.4.IonswereinjectedintothePenningtrap,trappedfor40ms,and thenejectedinthesamedirectiontheyenteredandobservedontherationMCP atSIPTBOB3.TOF-ICRdetectionwasthendemonstratedbyapplyinganRFdrivesignal toasingleringsegmentfor10ms,scanningtheRFfrequencyaround c andmeasuringthe ttotheDalyMCP.TheresultingTOF-ICRresonanceispresentedinFig.5.13. TotestFT-ICRdetectionatroomtemperature,thenarrowbanddetectioncircuitwas bypassedandtheroomtemperaturetialusedforMiniTrapwasconnectedto thetrappickupelectrodes.Theoutputofthewasthensentthroughthefrequency mixerandtheSR1audioanalyzerwasusedforFFTanalysis.Adipoleimagecharge pickupschemewasusedtodetectthemocyclotronmotion.Onceionsweretrapped, 79 Figure5.14:DemonstrationofbroadbandFT-ICRdetectionwithSIPTatroomtempera- ture.Theionpeakseeninthiscomesfrompickinguptheimagecurrentgenerated bythemocyclotronmotionofmany( ˘ 1000) 39 K + ions.Thedatapresentedhereis theaverageofveconsecutiveshots,eachofwhichuseda256msacquisitiontime. anRFexcitationwasappliedat + todrivethemocyclotronmotiontoalarger radius,pushingtheionsclosertothetrapelectrodestoincreasetheimagechargepickup. Inthismanner,astrong + signalwasobservedinthefrequencyspectrumontheSR1.An exampleoftheroomtemperatureFT-ICRresonancesobtainedinthismannerispresented inFig.5.14. 5.4.2CryogenicCommissioning 5.4.2.1Coolingto4K Onceroomtemperaturedetectionwassuccessfullycompleted,thenextstepwastoincorpo- ratethecryogenicsystemrequiredforsingleiondetection.AsdiscussedinSection5.3.1.3, theSIPTcryogenicsystemrequiresgoodthermalconductivityacrossthe4Kstageand 80 Figure5.15:SIPT4KstagewrappedinMylartoreduceradiativeheatingfromthesur- rounding45Kstage.TwolayersofMylarwrappingwerenecessarytoreachtemperatures of ˘ 4K. thermalinsulationfromroomtemperaturetoensurethatthecryogeniccomponentsinside themagnetreachandmaintaintlylowtemperature.Particularlyimportantisthe NbTiresonator,whichmustremainbelowthecriticaltemperature T c (approximately6K ina7Tmagnetictoremaininasuperconductingstate.Totestthis,Cernoxcryogenic temperaturesensorswereattachedatvariouslocationsalongtheSIPTcryogenicstagesto monitorthetemperatureafterthecryocoolerwasturnedon. Onthestcool-downtrial,thetemperatureatthecenterofthemagnet(nearthetrap andresonatorcircuit)onlyreached9.8K,althoughthetemperatureatthecoldheadgotas lowas7.1K.Toimprovethethermalconductivitytothecenterofthemagnet,ApiezonN cryogenichigh-vacuumgreasewasappliedtothejointswhereseparatecopperpiecesjoin. Tominimizeradiativeheatingfromtheouter45Kstage,the4Kstagewaswrappedintwo layersofMylar,withaninsulatingmeshlayerseparatingthetwolayersofMylar.Apicture ofthe4KstagewrappedinMylarisshowninFig.5.15.Incombination,thesechangeswere ttoallowtheregionatthecenterofthemagnettoreach ˘ 4.5K. 81 Figure5.16:600 HNbTiinductorcoil(left)andNbTiinductorcase(right)usedforthe high-QSIPTFT-ICRdetectioncircuit.Theinductorcoilconsistsof194turnsof250 m NbTiwirewithtubularTcoatingwrappedaroundaTcore.Thewindingswere thencoveredbyanadditionallayerofTtape,whichprovidesbothmechanicalsupport andsomeadditionalamountofthermalconductivity. Thecryogenicdetectionelectronicsweretheninstalled.TheNbTiinductorqualityis diminishedbythepresenceofnon-superconductingmetals,sothecoiliswrappedarounda PTFEbobbinandhousedwithinaNbTicase.APTFEscrewisusedtomountthebobbin totheresonatorcase.ApiezonNgreasewasappliedatalljunctionstoimprovethermal conductivity.PicturesoftheNbTiinductorcoilandcasearepresentedinFig.5.16. Thecryogenicandcryogenicboardweremountedtocopperbackingsin theregionbetweenthePenningtrapelectrodesystemandtheNbTiresonatorcase.Allof thewireconnectionsfromthe4KstageforDCvoltageapplicationuseconstantanwireto minimizeheattransferfromroomtemperature.Thesewireswererunalong4Ksurfacesand then45Ksurfacesbeforereachingtheroomtemperaturefeedthroughstokeepthewiresas coldaspossible.RFsignalsrequirebetterelectricalconductivity,socryogeniccoaxialcable (typeCC-SR-10)wasusedfortheconnectionsfromtheoutputofthecryogenicam andfortheRFiondrivesignals.Apictureofthewired4Kcomponentsispresentedin 82 Figure5.17:SIPT4Kchamberwithallcomponentsmountedandwired(bottom).The designdrawingofthisregionisincludedforreference(top). Fig.5.17. Onceallcryogeniccomponentswereinstalled,wireswereruntomonitortheresistance acrosstheinductorcoilasthetemperaturedropped.AsdemonstratedinFig.5.18,afterthe trapregionofthe4Kstagereacheditsminimumtemperature,ittookseveralmorehours fortheNbTicoiltocoolbelowitscriticaltemperature.Afteranother12hours,however, thisthresholdwascrossedandtheresistancedroppedtonearly0Residualresistance ismostlikelyduetoslightinthelengthofconstantanwireleadsconnectedto oppositeendsoftheinductorcoil. 5.4.2.2ResonatorCircuitResponse Theresponseoftheresonatorcircuitwasthentestedatcryogenictemperaturesbyfeeding in20mVppnoiseovera2MHzbandwidthtooneoftheRFdrivesegmentsofthetrap's 83 Figure5.18:ResistanceacrosstheNbTiinductorcoilplottedovertimealongsidethetem- peraturereadingsfromtheCernoxtemperaturesensorsmountedonthecoldheadandthe backoftheSIPTPenningtrap.Roughly12hoursafterthetemperaturesensorsreached theirminimumvalues,theNbTicoilcooledbelowitscriticaltemperatureandentereda superconductingstate,asevidencedbytheresistancedroptonearly0 84 ringelectrode.TheoutputfrequencyspectrumwasobservedusingtheSR1audioanalyzer. Twounexpectedwereobservedwhiletestingtheresonatorinthismanner.First, thecombinationofhighmagneticandlowtemperaturesathequalityfactorof thevaractordiodesusedtotunethecenterfrequencyoftheresonator.Thisgreatlyreduced theoverallqualityfactoroftheresonatorwhenthevaractordiodeswereconnected.Second, whenthevaractordiodesweredisconnectedtoachieveahighqualityfactor,averytalland narrowpeakwasobservedrightatthecenterfrequencyofthecircuit.Thispeakappeared tobesomesortofself-excitationofthedetectionelectronics,asitremainedevenwhenno noiseordrivingsignalwasfedintothetrap. Bothofthesehavebeentemporarilymitigatedtoproceedwithcryogenic testing,andpotentiallong-termsolutionshavebeenexaminedaswell.Forinitialcryogenic testswithSIPT,thevaractordiodeshavebeendisconnectedandreplacedwithalue high-Qpolystyrenecapacitors.Thevaluesofthesecapacitorswerecarefullyselectedtoplace thecenterfrequencyoftheresonatorcircuitascloseaspossibletotheexpected + frequency of 85 Rb + ,whichisreadilyavailablefromtheLEBITthermalionsource.Additional tuningwasaccomplishedbyadjustingthetrappingpotentialtoshift + accordingtoEq.2.5 sothat + isequalto circ . StahlElectronicswascontactedtodiscusslong-termforthevaractordiodeissueas well.Theresponsewasthat,althoughpreviousbatchesofthesevaractordiodesfromthe samemanufacturerhadnotshownthisissue,thecurrentbatchhadshownsimilarlypoor behaviorelsewhere.Theothergroupthatexperiencedtheseissuesfoundthattheissuecould beresolvedbyslightlyelevatingthetemperatureofthediodes.TheStahlteamhastherefore deliveredasmall,thermallyinsulatedprintedcircuitboardwithadditionalvaractordiodes andresistorsforheating.Theideaisthatthisboardwillbemountedonthe4Kstage 85 nearthecryogenicaandslightlyheatedbytheresistorsuntilthevaractordiodes aretlywarmthatthehighQisrestored.Ofcourse,thisreliesontthermal isolationtoensuretheNbTiinductorisnotwarmedtoapointwheresuperconductivityis lost.Thiswillbetestedinthenearfuture.Anotherpotentiallong-termsolutionfortuning theresonatorcircuitistouseavariableplatecapacitorwhichismechanicallytunedby rotationusinga4-Kpiezodrive.ThisoptionwouldallowveryhighQfactors,butwould alsorequiremoretmotothecurrentsystem. Theresonatorself-excitationpeakwasalsofoundtobetemperature-dependent,andit couldbeeliminatedbyslightlyelevatingthetemperatureoftheentire4Kstageusinga heaterresistermountedtothecoldheadwithoutraisingthetemperaturetlyhigh todestroythesuperconductivity.Alternatively,theself-excitationpeakcouldmostlybe eliminatedbyturningtheA7-2PIDcontrolofthecryogenicsupplyvoltagesandmanually adjustingtheauxiliarybiasingvoltagebyasmallamount.Thiscouldbeabitrisky,however, asthereisonlyaverysmallwindowoverwhichthesupplyvoltageeliminatestheself- excitationpeakanddoesnotexceedtheacceptablesupplyvoltagerange.Withoutthe PIDloopon,itispossiblethatslighttemperaturecouldbringbacktheself- excitationpeakorpushthesupplyvoltageintoarangethatdegradesthecryogenicam performance.Additionaltestingandexperiencewilllikelydeterminewhetherelevatingthe temperatureormanuallyadjustingthecryogenicsupplyvoltageisthebetteroptionfor eliminatingtheself-excitationpeak. Forinitialcryogenictesting,thetemperatureofthe4Kstagewaselevatedto ˘ 5.2Kto eliminatetheself-excitationpeak.Theresonatorresponseobservedatthistemperatureon theSR1isshowninFig.5.19.Averyclear,narrowresonancepeakisobservedatacenter frequencyveryneartheexpected + frequencyof 85 Rb + ,andtheresonatorQfactorfound 86 Figure5.19:FrequencydomainresponseoftheSIPTnarrowbandFT-ICRcryogenicde- tectioncircuitoperatingat ˘ 5.2K.Thisverynarrowfrequencyresponsecorrespondstoa circuitQfactorof2785,whichisgreaterthanwhatisrequiredforsingleiondetection. fromthispeakwithaLorentzfunctionisQ=2785,exceedingtheQfactorof ˘ 2000 advertisedbythemanufacturer.Withsucharesponse,singleiondetectionshouldbewell withinreach. 87 Chapter6 SummaryandOutlook ThePenningtrapmassmeasurementsof 68 Coand 69 CowerecompletedatLEBIT,re- ducingtheatomicmassuncertaintiesbymorethananorderofmagnitudefromtheAME2016 data,allowingfordetailedstudiesofnuclearstructureintheareanear Z =28and N =40. Althoughfurtherstudiesareneededtoelyestablishtheorderingofthetwo - decayingstatesin 68 ; 69 Co,noevidenceforasubstantialsubshellclosureacross N =40was observedinthe 27 Coisotopes,consistentwith S 2 n studiesalreadycompletedfor Z 28. InordertogreatlyextendLEBIT'sreachonthenuclearcharttoexoticisotopesfarfrom stability,theSingleIonPenningTraphasbeendeveloped.SIPTusesthenon-destructive narrowbandFT-ICRtechniquetoallowcompletemassmeasurementswithasingleion.No suchdevicehasyetbeenemployedatarareisotopefacility.WhenSIPTcomesonline,it willenableprecisemassmeasurementsofspeciesfarfromstabilitywhereproductionrates areextremelylow.Thiswillprovideapathtoexploretheroleofmagicnumbersfarfrom stabilitybyexploringmasstrendsinthevicinityofmagicanddoubly-magicnucleisuchas 78 Niand 100 Sn. AnewPenningtrapandaccompanyingbeamlineweredesignedandcommissionedfor SIPTattheLEBITfacility.TOF-ICRandbroadbandFT-ICRdetectionweredemonstrated withgreatsuccessatroomtemperature.Ahighlysensitivecryogenicresonatingdetection circuitwasthenaddedandtested.Thedetectioncircuitnowdemonstratesexcellentbehavior 88 compatiblewithprecisionmeasurementsatsingle-ionsensitivity. Single-ionFT-ICRdetectionwithstableionsisexpectedinthecomingweeks.The extensiontoradioactivespeciesisthenrelativelystraightforward,asSIPTisalreadysetup totakefulladvantageofthebeamproduction,stopping,andpreparationfacilitiescurrently usedformassmeasurementswithLEBITattheNSCL. Withthe9.4-TTOF-ICRPenningtrapproducingvaluablescienresultslikethecobalt measurementspresentedinthisthesisandthe7-TSIPTsystemnowbeingcommissioned, LEBITisverywellpositionedtoextenditsalreadywell-establishedprogramofprecise, accuratemassmeasurementsofrareisotopes.AsFRIBreachescompletioninthenext fewyears,LEBITwillbewell-poisedtotakefulladvantageofthemanyopportunitiesfor cutting-edgenewrareisotoperesearch. 89 APPENDICES 90 AppendixA CharacterizationoftheMiniTrap Magnetometer LEBIThaspreviouslydemonstratedtheabilitytoperformsuccessfulnarrowbandFT-ICR measurementswiththedevelopmentoftheMiniTrapmagnetometer[117].MiniTrapisa cylindricalPenningtrapcurrentlyhousedinthe9.4-TLEBITmagnetjustdownstreamfrom theprimaryLEBIThyperbolicPenningtrapandslightlyoofthemainbeamaxis.Rather thanmeasuringrareisotopesdeliveredfromthecyclotronfacilityorstableisotopesfromone oftheLEBITsources,MiniTrapincludesaself-containedelectrongunwhichionizes residualbackgroundgastogenerateionswithinthetrapvolume.FT-ICRresonancesofthese ionscanthenbeusedtotrackchangesinthemagneticatahighlevelofprecision. Theultimateaimofthisprojectistoeliminatetheneedtoperformreferencemea- surementsinthemainhyperbolictrapduringonlineexperiments.Instead,MiniTrapcan beusedtoperformreferencemeasurementsofstablebackgroundgasionssimultaneousto rareisotopemeasurementsinthemainhyperbolictrap.Thiswouldprovidetwoimpor- tantadvantages:trackingnon-linearmagneticandmakingthemostuse ofvaluablebeamtime.Thecurrentsystemofalternatingrareisotopemeasurementswith referencemeasurementstotrackchangesinthemagneticreliesonalinearinterpolation betweenreferencemeasurementstodeterminethemagneticstrengthatthetimeofthe 91 rareisotopemeasurement.Whilenon-linearchangesinthemagneticeldhavebeenshown tocontributetotheoverallsystematicmassuncertaintyonlyonalevelof ˘ 10 10 [63], MiniTrapcouldbeusedtoeliminatethisuncertaintyaltogetherandmonitorforunexpected spikesoranomalousdeviations.Perhapsmoreimportantly,MiniTrapcouldeliminate theneedtopauserareisotopemeasurementstotakeoccasionalreferencemassmeasurements inthemainhyperbolictrap.OnlinebeamtimeattheNSCLishighlycompetitiveandtotal operatingcostsarequitelarge,soeliminatingtheneedtopausethedeliveryofrareisotopes toLEBITduringonlineoperationwouldbeavaluablecontribution. MiniTrapwasoriginallytestedinanisolatedenvironmentandperformedwell,moni- toritoringmagneticationsatarelativeprecisionof ˘ 10 8 .H 3 O + wasiden astheprimaryresidualgascomponentionizedbytheMiniTrapelectrongun.Ascreen- shotofanFFTspectrumfromthesetestsofMiniTrap,reproducedfromRef.[117],is presentedinFig.A.1.Frequencycomponentsfromboththetruecyclotronandmo cyclotronmotionscanbeseeninthisspectrum. TestsofMiniTrapinthe9.4-TLEBITmagnet WhenMiniTrapwasmovedtoitscurrentlocationinthe9.4-TLEBITmagnet,additional testswererequiredtodeterminetheoptimalparametersforproducing,driving,anddetecting ionsinthenewenvironment.Broadbanddetectionwasinitiallyusedtodetecttheions' magnetronmotion,andthemocyclotronfrequencywasthendeterminedwithadipole cleaningscan.TheresultsofthisscanareshowninFig.A.2.Whentheions'mo cyclotronmotionwasexcitedatthecorrectfrequency + ,theionsweredrivenintothewalls ofthetrapandlost,resultinginareductionintheamplitudeofthedetectedmagnetron 92 FigureA.1:ALabVIEWscreenshotofFFTresonancesofbothmocyclotronmotion (left)andtruecyclotronmotion(right)ofH 3 O + ionsmeasuredwiththeMiniTrapmagne- tometerusingabroadbandFT-ICRquadrupoledetection signal. Nextaseriesof\traptuning"scanswereperformed.Keepingthetrapdepth U 0 (the potentialbetweentheendcapandringelectrodes)xed,theratiooftheendcap andringelectrodevoltageswasvariedtodeterminethesettingswhichbestapproximated atruequadrupolarelectrostaticpotential.Foreachvoltageratio,anRFexcitationwas appliednearthemocyclotronfrequency + andthefrequencyofthedetected + signalintheFFTwasrecordedasafunctionoftheappliedRFexcitationamplitude.As theRFamplitudeincreased,theionsweredriventolargerradii.Theresultsofthesescans arepresentedinFig.A.3.Anendcappotentialof9.15Vandaringvoltageof-1.25V werechosenbecause,atthesesettings,themeasuredfrequencyshowedtheleastvarianceas theionsweredriventoincreasinglylargeradii,indicatingagoodapproximationofatrue quadrupolarelectrostaticpotential. TheoptimalfrequencyandamplitudeforRFexcitationofthemoedcyclotronmotion 93 FigureA.2:Resultsofthedipolecleaningscanusedtodeterminethemocyclotron frequency + ofionizedbackgroundgasmoleculesintheMiniTrapmagnetometerafterit wasmovedtoitscurrentlocationinthe9.4-TLEBITmagnet. FigureA.3:MiniTraptuningscansusedtodeterminetheoptimalratiobetweentheendcap andringpotentials.Thetrapdepthwasheldconstantat10.4V.Aratioof9.15to-1.25 betweentheendcapandringpotentialswasfoundtoproducethebestapproximationofa quadrupolarelectrostaticpotentialbecause,atthesesettings,themeasuredionfrequency variedtheleastastheionsweredriventoincreasinglylargeradii. 94 FigureA.4:Amplitude(top)andcenterfrequency(bottom)ofthe + peakintheFFT spectrumasafunctionoftheappliedRFexcitationfrequency.Theplotsontheleftwere obtainedwitha200mVppRFexcitationandtheplotsontherightwereobtainedwitha 150mVppRFexcitation.Theobservedbehaviorisdiscussedinthetext. weredeterminedbymeasuringthefrequencyandamplitudeoftheFT-ICRsignalat + as afunctionoftheRFfrequency,asshowninFig.A.4.WhentheRFamplitudewastoo largeandtheRFfrequencymatched + ,theioncloudwasdriventowardsthewallsof thetrap,shiftingthemeasuredfrequencyandreducingtheFFTamplitude.WhentheRF amplitudewassettoamoreappropriatevalue,theFFTamplitudewasmaximizedwhen theRFfrequencymatched + andthemeasuredfrequencyremainedconstantoverawide rangeofappliedRFfrequenciesinthevicinityof + . AnewresonatorcircuitalsohadtobebuiltfornarrowbandFT-ICRdetectionwith MiniTrapinthe9.4-TLEBITmagnet.Infact,twonewresonatorcircuitswerebuilt,one fordetectionofthemocyclotronmotionandonefordetectionofthetruecyclotron motion.Themocyclotronmotiondetectioncircuitiswiredfordipolepickupandtuned toresonatenear + ,whilethetruecyclotronmotiondetectioncircuitiswiredforquadrupole pickupandtunedtoresonatenear c .Thetworesonatorscaneasilybeexchangedtoswitch betweendetectionofthetwomotions.UnlikeSIPT,theMiniTrapresonatorsarenon- 95 FigureA.5:FrequencydomainresponseoftheMiniTraproomtemperatureresonantcircuit usedfornarrowbandFT-ICRdetectionofthetruecyclotronmotionoftrappedH 3 O + ions. superconductingandoperateatroomtemperature.Thefrequencydomainresponseofthe truecyclotronmotiondetectioncircuitispresentedinFig.A.5.Thisresonatorhasaquality factorQof ˘ 82.ThecenterfrequenciesoftheMiniTrapresonatorscanbeadjustedbyhand witharotaryvariablecapacitor. MiniTrapStatus AftertheinitialdevelopmentandsuccessfultestingofMiniTrapdocumentedinRef.[117], MiniTrapwasinstalledatitsintendedlocationinthe9.4-TLEBITmagnet.FT-ICRsignals havebeenobservedfromH 3 O + ionsat , + ,and c ,andnewresonatorcircuitswerebuilt fornarrowbanddetectionofthemocyclotronandtruecyclotronmotions.Optimal settingsforFT-ICRdetectionhavebeendeterminedfromanextensiveseriesofparameter scans. RecentattemptstobenchmarkMiniTrap'sabilitytomonitormagnetic againstmeasurementswiththemainTOF-ICRtrapprovedlesssuccessfulthantheprevious 96 tests(whichwereconductedinamoreisolatedenvironment),trackingthemagnetic onlyatarelativeprecisionof ˘ 10 6 duetoshot-to-shotfrequencyvariations.Testsare currentlyunderwaytoidentifythecausesofthesevariationsandeliminatethecausesor mitigatetheectstoachievethehigherlevelofprecisionrequiredforscienuse. 97 AppendixB EvaluationofSystematicFrequency ShiftsforSIPT MagneticFieldUniformity Spatialuniformityofthemagneticmustbeconsideredtoensurethatanysystematic frequencyshiftsduetoinhomogeneityarenegligible.Inparticular,weconsidertwo possibleshiftsduetotrapvibrationscausedbythecryocooler,andshiftscausedby misalignmentbetweenthetrapaxisandthemagnetic.Theformercanbeestimatedby c c = d B rel d Z Z (B.1) where c c istherelativefrequencyshift, d B rel d Z isthegradientoftherelativemagnetic strength,and Z isthepeak-to-peakamplitudeofthetrapvibrations.TheOxfordmagnet spindicatethattheon-axishomogeneityoveradistanceof 40mmfrom thecenterofthemagnetis < 3 : 75ppm.Conservativelytakingthisinhomogeneitytobe 4ppmoverjustthecentral10mmofthemagnet,thisgivesaworst-casegradient of4 10 7 = mm.TheSIPTcryocooler,discussedindetailinSection5.3.1.3,doesnot providenumbersfortheexpectedoscillationamplitude.However,similartwo-stagepulse 98 FigureB.1:Illustrationofthemisalignmentangle betweenthemagneticandthe Penningtrapaxis. tubecryocoolersspecifyexpectedpeak-to-peakamplitudeslessthan20 m,leadingtoa frequencyshiftoflessthan8ppb,whichisbelowthelevelofprecisionexpectedforSIPT. Furthermore,theseshiftswillaverageoutformeasurementslongerthan17msbecausethe cryocoolercycleis60Hz. Thepotentialangularmisalignmentoftheboreaxisandthemagneticillustrated inFig.B.1,mustalsobeconsidered.ThePenningtrapaxisisalignedtotheaxisofthe 40-Kcoppercylinderwhichhousesalloftheexperimentalcomponentstobeinsertedinto themagnetbore,andthiscylinderisinturnalignedtobecoaxialwiththemagnetbore. Thusanangularmisalignmentbetweenthemagneticandtheboreaxiswouldalsolead tothesamemisalignmentwiththePenningtrapaxis,whichwillsystematicallyshiftthe cyclotronfrequency c .Thisshift c canbeapproximatedby c ˇ 9 4 2 1 2 2 (B.2) 99 FigureB.2:FrequencyratioshiftsduetomisalignmentbetweenthePenningtrapaxisand themagneticasafunctionofionmass,assuminga6umassbetweentheion ofinterestandthereferenceion. where isthemagneticmisalignmentasshowninFig.B.1, isthetrapellipticity parameter,and istheionmagnetronfrequency[53].Thefrequencyratiobetweenthe ionofinterestandthereferenceionusedforthemassdeterminationwillthenshiftby R = c; 1 c; 2 c; 1 + c c; 2 + c : (B.3) Assuminganytrapellipticityisnegligible, R wascalculatedoverawiderangeofmass valuesandforavarietyofmisalignmentangles .TheresultsarepresentedinFig.B.2. Herewehaveusedanextremecasewherethemasscebetweentheionofinterest andthereferenceionis6u(anylargermostlikelycouldnotbesupportedbya singleresonator).ThespprovidedfortheOxfordmagnetindicateanangular alignmentuncertaintyof0.5 ° .AsweseefromFig.B.2,a0.5 ° misalignmentwouldresultin massshiftsjustslightlybelow10 7 . Tochecktheactualangularalignmentbetweenthemagneticandtheboretube,an 100 NMRprobewasusedtomeasurethemagneticataseriesofpointsalongtheaxialplanes 4cmfromthecenterofthemagnet,ataradiusof2.5cm.Thesedatawerethenusedto constructasetofradarplots,whicharepresentedinFig.B.3.Fromthis,thecenterofgravity wascalculatedandashiftofonly ˘ 0.0002mmwasfound,correspondingtoamisalignment angleof ˘ 0 : 002 ° .AsseenfromFig.B.2,anyshiftsinthemassdeterminationfromthis tinymisalignmentarewellbelowtherelevantlevelofprecisionexpectedforSIPT. Additionalfrequencyshiftscouldbeintroducedfromimperfectmachiningormisalign- mentoftheSIPTPenningtrapaxisandthe40-Kcopperboretubeinsert.Theseshifts willbeevaluatedexperimentallyonceSIPTisoperational.Ifnecessary,theseshiftscanbe compensatedbyintroducingellipticitytothetrapaccordingtoEq.(B.2). SpecialRelativity Relativeshiftsinthemocyclotronfrequencyduetospecialrelativityaregivenby + + = 1 2 qB mc 2 ˆ 2 + (B.4) where c isthespeedoflightand ˆ + istheradiusofthemocyclotronmotion[38]. Usingthisequation,frequencyshiftsfromspecialrelativitywerecalculatedforionsofvarious massesina7-Tmagneticasafunctionof ˆ + .TheresultsareplottedinFig.B.4.The innerradiusoftheSIPTPenningtrapelectrodesystemis6.485mm,andthesimulateddata usedinSection5.1demonstratedthatsingleionmassmeasurementsarepossiblewithSIPT assumingaradiusof0 : 5 ˆ 0 ˇ 3 : 2mm.ItisclearfromFig.B.4that,evenforrelativelylight ions,frequencyshiftsduetospecialrelativityatthisradiusarebelow10 7 andthereforeare 101 FigureB.3:RadarplotsofthemagneticstrengthintheSIPTmagnetdeterminedfrom NMRmeasurementsafterthemagnetwasenergized. 102 FigureB.4:Relativemoedcyclotronfrequencyshiftsduetospecialrelativityplottedas afunctionofmocyclotronradius ˆ + forionsofvariousmassesina7-Tmagnetic unlikelytoberelevantatthelevelofuncertaintyexpectedforSIPT.Moreover,anyspecial relativityshiftswilllargelycanceloutwhenanionofsimilarmassisusedforcalibration. 103 AppendixC LimitingCaseRatioof 68 Co -DecayingStates AsseeninFig.4.8,the 68 Cogammaspectrumshowsclearpeaksat595keVand324keV (associatedwithdecayfromthehigh-spinstate)andnoclearpeakat478keV(associated withdecayfromthelow-spinstate).Thegoalofthefollowingcalculationsistodetermine, basedonthenumberofcountsobservedinthegammaspectrum,alimitingcaseforwhat fractionofthe 68 CoobservedatthePenningtrapduringthemassmeasurementcouldhave beenthelow-spinstate. Theupperlimitofthepeakareafortheunobserved478keVgammawasdetermined usingthemethodpresentedinRef.[118].Theprobabilityofhavingapeakarea a value greaterthan A is = Z 1 A g ( a )d a: (C.1) Forameanbackgroundvalue B 0 withstandarddeviation ˙ B ,thefunction g ( a )canbe approximatedas g ( a )= N e ( a a ) 2 = 2 ˙ 2 p 2 ˇ˙ (C.2) where a = C B 0 , C isthenumberofcountsinthespectrumovertherelevantregion, 104 ˙ 2 = ˙ 2 B + C ,and N isanormalizationconstantsuchthat Z 1 0 g ( a )d a =1 : (C.3) Alinearwasusedtoestimatethebackgroundovertherelevantregionfrom360- 660keV,andthedataintheregionsfrom473-483keV,from500-520keV,andfrom550- 630keVwereexcludedfromthebackgroundsothatthepeaksintheseregionswouldnot thebackgrounddetermination.Theresultingwasintegratedovertheregionfrom 473-483keVtodeterminethebackgroundfortheunseen478keVpeak.Thebackgroundwas foundtobe B 0 =1197,withanuncertainty ˙ B =50.Thetotalnumberofintegratedcounts overthisregionis C =2333.Usingthesenumbers,Eq.(C.1)wasthensolvednumerically with =0 : 32,correspondingto68%(1 ˙ )statisticalandtheupperlimitwas foundtobe A =1169. Thiswasthencomparedwiththe595keVpeak,whichincludes2383totalcountsinthe regionfrom590-600keVandabackgroundof B 0 =788withanuncertainty ˙ B =56.Fora lowerlimitonthenumberofcountsinthispeakwith1 ˙ wassetto0.68,and thelowerlimitwasfoundtobe A =1560. Foranincomingrate r ,theproductionrateof 68 Coisgivenby dN dt = r : (C.4) Solvingthisentialequationgives = r (1 e ) : (C.5) 105 Attime t =0,thereisnoactivity.As t goestoy,theactivityapproaches r ,andan equilibriumisreachedwheretherateofdecayisequaltotheincomingrate.Thegamma spectrumusedforthisworkwascollectedfor2823s,whichisaverylongtimecomparedto thehalf-livesofthehigh-spinandlow-spin -decayingstatesof 68 Co(0.23(3)sand1.6(3)s, respectively[88])sotheequilibriumcasecanbeusedtodeterminethenumberofdecaysfor thelow-spinstate(state1)andthehigh-spinstate(state2)insomeamountoftime t : N 1 = r 1 t (C.6) N 2 = r 2 t (C.7) Todeterminetheexpectednumberofdetectedgammasat478keVandat595keV,the numberofdecaysfromeachstatemustbemultipliedbytheabsoluteintensity I ,thedetector atthatenergy det ( E ),andthegeometric geo .Takingtheratioofthe numberofexpectedgammasateachenergy,thegeometricycancelsout,leaving N 478 N 595 = N 1 N 2 I 478 I 595 det; 478 det; 595 = r 1 r 2 I 478 I 595 det; 478 det; 595 : (C.8) Theonlyreportedintensityforthe595keVgammacomingfromdecayfromthehigh-spin stateis32%[88].Theonlyabsoluteintensityreportedforthe478keVgammais6%[95], whichgivesarelativeintensityof12%comparedtothe2033keVgamma,whichisfairly consistentwiththerelativeintensitiesof11%and16%reportedinRefs.[88,94]. Thedetectorwascalibratedusing 152 Eu, 133 Ba, 60 Co, 137 Cs,and 22 Nasources. Theat444keVwasfoundtobe0.045(5),andtheat662keVwasfound tobe0.044(4).Notethattheseincludesomeunknowngeometricfactor,however 106 asonlytheratioisrelevantforthisdiscussionthegeometricfactorisunimportant.These twodemonstratethatanyindetectorbetween478keVand 595keVshouldbenegligible.Furthermore,thedetectorreachesitsmaximum value < 300keV,soifanythingthedetectorshouldbelowerforthe595keVpeak thanthe478keVpeak,whichwouldindicatethepresenceofmoreofthehigh-spinstate.As thesecalculationsaimtodetermineanupperlimitontheamountlow-spinstatethatcould havebeenpresent,itisthereforesafetotake det; 478 ˇ det; 595 .SolvingEq.(C.8)forthe ratio r 1 =r 2 thengives r 1 r 2 = N 478 N 595 I 595 I 478 (C.9) andtheupperlimitisthen r 1 r 2 < 1169 1560 0 : 32 0 : 06 =4 : (C.10) Thisindicatesthat,althoughthereisnoclearindicationofapeakat478keVfrom decayofthelow-spinstateof 68 Co,itispossiblethatthelow-spinstatecouldhavestillbeen presentatarateashighasfourtimestherateofthehigh-spinstate.Thisratiobecomeseven moreextremewhenconsideringdecaylossesinthePenningtrap,asthehigh-spinstatehasa tlyshorterhalf-lifethanthelowspinstate(0.23(3)sand1.6(3)s,respectively[88]). AsdiscussedinSection4.3.1,theRFexcitationtimewasnotthesameinallmeasurements, howeverthemajorityofthemeasurementsuseda100msRFexcitation.Thisisalsothe longestexcitationtimeused,andthereforeworksforthelimiting-casescenario.Anadditional 20msofdipolecleaningtimewasused,foratotalof120msinthePenningtrap.The limiting-caseratioisthen r 1 r 2 < r 1 r 2 0 e 1 t e 2 t =(4) e ln(2) (0 : 120s = 1 : 6s) e ln(2) (0 : 120s = 0 : 23s) ˇ 5 : (C.11) 107 The 68 CoTOF-ICRresonancesobtainedinthisworkthereforecouldhaveincludedupto etimesasmanylow-spinionsashigh-spinions.Itisstillthereforehighlyuncertainwhich statewasmeasuredinthiswork.GiventhatthegammaspectrumshowninFig.4.8shows clearevidencethatthehigh-spinstatewaspresentatthegermaniumdetectorandthereis nopositiveevidencethatthelow-spinstatewaspresent,themeasuredstateisstillcurrently believedtobethehigh-spinstate,butanyfutureworkbasedontheseresultsshouldbe awareoftheseassumptionsandtheassociateduncertaintyinthestateassignment. 108 BIBLIOGRAPHY 109 BIBLIOGRAPHY [1]M.Wang,G.Audi,F.G.Kondev,W.J.Huang,S.Naimi,andX.Xu.TheAME2016 atomicmassevaluation(II).Tables,graphsandreferences. 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