.OBSERVATIONOFDOPPLERBROADENINGINBETA-DELAYEDPROTON-GAMMADECAYBySarahSchwartzATHESISSubmittedtoMichiganStateUniversityinpartialentoftherequirementsforthedegreeofPhysics-MasterofScience2016ABSTRACTOBSERVATIONOFDOPPLERBROADENINGINBETA-DELAYEDPROTON-GAMMADECAYBySarahSchwartzTheDopplerbroadeningof-raypeaksduetonuclearrecoilfrom-delayednucleonemissioncanbeusedtomeasuretheenergiesofthenucleons.ThepurposeofthisThesisistotestandapplythisDopplerbroadeningmethodusing-raypeaksfromthe26P(p)25Aldecaysequence.Afastbeamof26PwasimplantedintoaplanarGedetector,whichwasusedasa26P-decaytrigger.TheSeGAarrayofhigh-purityGedetectorswasusedtodetectraysfromthe26P(p)25Aldecaysequence.RadiativeDopplerbroadeningin-delayedproton-decaywasobservedforthetime.TheDopplerbroadeninganalysismethodwasvusingthe1613keV-raylineforwhichtheprotonenergieswerepreviouslyknown.The1776keVrayde-excitingthe2720keV25Allevelwasobservedin26P(p)25Aldecayforthetimeandusedtodeterminethatthecenter-of-massenergyoftheprotonemissionfeedingthe2720-keVlevelis5.11.0(stat.)0.6(syst.)MeV,correspondingtoa26Siexcitationenergyof13.31.0(stat.)0.7(syst.)MeVfortheproton-emittinglevel.TheDopplerbroadeningmethodhasbeendemonstratedtoprovidepracticalmeasurementsoftheenergiesfor-delayednucleonemissionspopulatingexcitedstatesofnuclearrecoilsatleastasheavyasA=25.TABLEOFCONTENTSLISTOFTABLES....................................ivLISTOFFIGURES...................................vChapter1Introduction...............................11.1Introductiontothenucleus............................11.2Typesofnucleardecay..............................11.3Beta-DelayedNucleonEmission.........................21.4PreviousworkinDopplerbroadeningofdelayednucleon-decay.....41.5ExampleofDopplerbroadeninganalysis....................4Chapter2Experiment................................62.1LabLayout....................................62.2Detectors.....................................6Chapter3DataAnalysisandDiscussion....................103.1Gamma-rayIntensities..............................103.2pFeeding.....................................123.3StudyofDopplerBroadenedPeaks.......................133.41613keV......................................173.51776keV......................................19Chapter4Conclusionandoutlook........................22BIBLIOGRAPHY....................................23iiiLISTOFTABLESTable3.1:26P(p)25Alraysobservedinthepresentwork.Themeasured-rayenergiesarereportedinthe1stcolumnwiththeirstatisticaluncertaintiesonly;theglobalsystematicuncertaintyis0.5keV.Anasteriskdenotesraysobservedforthetimein26P-decay.The-rayintensityper26Pdecayisreportedinthe2ndcolumn,wheretheintensityofthe1613-keVlinefrom[13]wasusedfornormalization.The3rdcolumnlistsraysobservedincoincidence..........11Table3.2:The26P(p)feedingof25Alstatesfoundinthepresentworkandpreviouswork[13].The452keV-feedingisgivenasanupperlimit.Upperlimitsarecalculatedata95%conel.Anasteriskdenotesevidenceforexcitedstatesobservedforthetimeviathisdecaychannel.Theintensitiesarenormalizedtothefeedingofthe1613-keVlevelfrom[13].........................13Table3.3:Sourcesofuncertaintyinthe5.11.0(stat.)0.6(syst.)MeV26P-delayedprotonC.M.energyfeedingthe2.72MeV25Alstate...21ivLISTOFFIGURESFigure1.1:Anexampleofdelayedprotonemissionis26P()25Al.Aboveisasectionofthechartofnuclides[1]wherethenumberofprotons,Z,isontheY-axisandthenumberofneutrons,N,isontheX-axis.Thebluearrowrepresentsthe+decayfrom26Pto26Siwhichisthenfollowedbythegreenarrowwhichrepresentstheemissionofaprotonfrom26Sito25Al.............................2Figure1.2:-delayedproton-decayisasequenceofdecaysinwhichaparentnucleus-decaystobecomethesystemshownabove.Nexttheprotonisemittedcausingthenucleusabovetorecoil.Lastlyarayisemittedinanarbitrarydirectionwithrespecttothesurrounding-raydetectors,whichresultsinabroadenedpeakinthe-rayspectrumthatiscenteredontheunshiftedenergy.FigurecourtesyofErinO'Donnell................................3Figure1.3:Spectrumfrom11Lidecaywhichincludesbroadenedpeaksfrom11Li()10BefromSarazinetal[6]...................4Figure2.1:ThelayoutoftheCoupledCyclotronFacilityattheNationalSu-perconductingLaboratory.Thebeamstartsasstableionsthatareacceleratedbythecoupledcyclotrons,theK500andK1200.Oncethestablebeamisaccelerateditisimpingeduponaproductiontarget,9Beinourcase,whichcreatestheisotopeofinterest(26P)alongwithmanyotherisotopes.ThisnewbeamisdeliveredtotheA1900whichhelpstopurifyingthebeamusingmagnets.NextthebeamgoestotheRFFSwhichfurtherthebeam.Finallytherareisotopebeamofinterestissenttotheexperimentalsetup...........7Figure2.2:Theplotshowstheenergylossofaparticleversusthetimeoft(TOF).Eachcircledconcentrationofpointsisatisotope.Theredovalencompasses26Pparticleswhilethegreenandyellowencompassthe24Aland22Naparticles,respectively.........7Figure2.3:(A)TheGermaniumDoubleSidedStripDetector(GeDSSD)withthecryostatopen.ThesecondarybeamwasimplantedintotheGeDSSDwhichdetectedenergyreleasedwhenadecayoccurred.Itwassur-roundedbySeGAintheexperiment.(B)Acomputeraideddesign(CAD)oftheSegmentedGermaniumArray,SeGA.Itiscomposedof16HPGecrystalssurroundingtheGeDSSD,wherethebeamwasimplanted.................................8vFigure2.4:ThisconceptualshowstheGeDSSDsurroundedbytheSeGADetec-tors.FigurecourtesyofDavidPerez-Loureiro.............9Figure3.1:26P-delayed-rayspectrum.All-raypeaksattributedtothe26P()25AldecayarelabeledbytheirenergyinkeV(black).Otherpeaksarelabeledbythe-rayemittingnuclide,withescapepeaksde-notedbyanasterisk(gray).SelectedregionsareshowninmoredetailinFig.3.7andFig.3.8..........................11Figure3.2:25Allevelschemefrom26P(p)25Aldecaydeducedfromthepresentwork.The-raytransitionsobservedaredenotedbyarrowswiththicknessesproportionaltotheirintensitiesandlabeledby-rayen-ergyinkeV.Thepfeedingofthetexcitedstatesisdepictedbythearrowsontheright,whicharelabeledbytheintensities.Thesingleasteriskdenotesavalueadoptedfrom[13].Thedoubleaster-isksdenotestheupperlimitofthe-feedingofthe452keVstateatthe95%ncelevel.........................14Figure3.3:ThisplotshowshowtheboxcarfunctionconvolutedEMGsproduceabroadenedpeak.Inthisexample=1613keV,˙=1.54,˝=1.2,=3keVandtheamplitudeofthesmallerpeaksaresettoone...15Figure3.4:Thepreviouslyknowndecayschemeforthe26P-delayedprotonemissiontothe1613keVexcitedstateof25Al[13].Twoproton-unbound26Sistatesfeedthe1613keV25Alexcitedstate,causingtwot25Alrecoilvelocitiesfollowingprotonemission.....16Figure3.5:Thedecayofatheoreticalparticlewithinitially100daughterparticlesandahalf-lifeof10fsisshownabove.Fortheanalysisthedecaycurvewasdividedintoesectionslikeshownabove.ThetimeusedtorepresenttheDopplerbroadeningofthest20%ofdecayingparticleswouldbethetimeatwhichitisexpectedfor10%oftheparticletohavedecayed.Theotherareevaluatedinthesamemanner..17Figure3.6:Thecomponentsoftheshapeofthe1776keV-raypeakareshownabove.Eachpeakhasthesamenumberofcounts,butthespreadsduetoDopplerbroadeningareerentduetoevaluatingthematthetimehere10%(greensolidline),30%(orangedashedline),50%(greydottedline),70%(yellowdot-dashedline)and90%(bluedoubledot-dashedline)oftheparticleshavedecayed.TheresponsefunctionusedforthisisGaussianforsimplicity.........18viFigure3.7:26P-delayed-rayspectrumintheregionofthe25Alpeakat1613keV.Thepeakat1613keVisbroaderthantheneighboring26Alpeakat1622keV.ThesolidbluelineistheoverallincludingDopplerbroadeningandthereddottedlinerepresentstheComptonscatteringbackground.Belowthedataandtheindividualpeakcomponentsareshown.The1611keV25Mg,1613keV25Aland1622keV26Al-raylinesarerepresentedbythegreendot-double-dashed,golddashedandlightbluedot-dashedlines,respectively..............19Figure3.8:26P-delayed-rayspectrum(redcrosses)intheregionofthe1776-and1790-keVpeakswith(bluesolidline).ThedashedgreenlineshowsthecontributionoftheDopplerbroadened1776-keVpeaktotheoverallThedot-dashedpurplelineshowsthecontributionsofallotherpeaks.Thesmallexcessnear1810keVcouldnotbetobefrom25Al........................20Figure3.9:Thebluedotsshowthe˜2valueforeachoftheinitial25Alkineticenergytested.Thebluelineshowsthequadraticlinethatwasusedtodeterminetheenergywiththeminimum˜2.Theminimumwasfoundtobeat195+4150(stat.)18(syst.)keV............21viiChapter1Introduction1.1IntroductiontothenucleusTheatomisabuildingblockofallmatter.Itisneutralandcomposedmostlyofemptyspace.Essentiallyallofitsmassconcentratedinthepositivelychargednucleuswhiletheremainderofitsmassisinthenegativelychargedelectronswhichsurroundthenucleus.Thenucleusiscomposedoftwotparticles,theprotonandtheneutron.Theprotonisafermionconsistingoftwoupquarksandadownquark,givingitonepositiveelementarycharge.Theneutronisafermionconsistingoftwodownquarksandanupquarkwhichresultsinaneutralcharge.Bothofthesenucleonsareaboutthesamemass.Itisbasicknowledgethat,duetotheelectromagneticforce,likechargesrepelwhileoppositechargesattract.Eventhoughanucleusconsistsofonlypositiveandneutralparticlestheyareboundduetothefundamentalforceknownasthestrongnuclearforceallowingthemtobelong-lived.1.2TypesofnucleardecayNucleitendtoseekmoreenergeticallystableurationsbyundergoingseveraltypesofnucleardecays.Afewofthettypesofdecaysinclude,anddecay.Alphadecayreferstothespontaneousemissionofanparticle.Alphadecayismediatedbyacombinationoftheattractivestrongforceandtherepulsiveelectromagneticforce.Therearesimilardecaysinwhichonlyonenucleon(aneutronoraproton)isemitted.Theseareneutronandprotonemission,namedafterthenucleonthatwasemitted,oftenfromexcitedstates.Thenextfundamentaldecayisdecay,whichistheemissionofaparticlemediatedbytheweaknuclearforce.Therearetwotypesofdecays,and+.Indecayaneutrondecaysintoaproton,particle(electron)andelectronanti-neutrino.In+decayaprotondecaysintoaneutron,+particle(positron)andelectronneutrino.Finally,decayisanelectromagnetictransitionofanucleusinanexcitedstatetoalowerlyingstatewiththesamenumberofprotonsandneutrons.Aray,orhighenergyphoton,isemittedduringthistransition.Thesedecayssometimesoccurinasequence,asinthecaseofbeta-delayedproton-gamma1Figure1.1:Anexampleofdelayedprotonemissionis26P()25Al.Aboveisasectionofthechartofnuclides[1]wherethenumberofprotons,Z,isontheY-axisandthenumberofneutrons,N,isontheX-axis.Thebluearrowrepresentsthe+decayfrom26Pto26Siwhichisthenfollowedbythegreenarrowwhichrepresentstheemissionofaprotonfrom26Sito25Al.decay.Firstaparentnucleusbetadecays.Thenanexcitedstateofthedaughternucleusemitsaproton.Finallythegranddaughternucleusde-excitesviagammadecay.ThedecayoccursasfollowsXAZ!YAZ1!WA1Z2!WA1Z2whereAistheatomicnumber,Zistheprotonnumber,W,X,andYarethenucleusnames,andtheasteriskdenotesexcitedstates.1.3Beta-DelayedNucleonEmissionWhenanucleonisemittedfromanucleusthedaughternucleusrecoils.Foragivendecay,iftheCenterofMass(CM)energy,ECM,isknownthenthevelocityoftherecoilingdaughternucleuscanbecalculatedbyemployingconservationofenergyandmomentum.12mnv2n+12mdv2d=ECM(1.1)mnvn=mdvd(1.2)wheremnandmdarethemassofthenucleonanddaughternucleus,respectively,andlikewisevnandvdarethevelocitiesofthenucleonanddaughternucleus,respectively.Sim-plifying,thevelocityofthedaughternucleuscanbewrittenasvd=mnmdvn(1.3)Thedaughternucleuscanbeleftinanexcitedstatebythedecayandcanthende-excite2Figure1.2:-delayedproton-decayisasequenceofdecaysinwhichaparentnucleus-decaystobecomethesystemshownabove.Nexttheprotonisemittedcausingthenucleusabovetorecoil.Lastlyarayisemittedinanarbitrarydirectionwithrespecttothesurrounding-raydetectors,whichresultsinabroadenedpeakinthe-rayspectrumthatiscenteredontheunshiftedenergy.FigurecourtesyofErinO'Donnellviadecay.IftheinitialvelocityishighenoughandthelifetimeoftheexcitedstateisshortenoughthentheraywillbeemittedwhilethenucleusisstillrecoilingresultingintheDopplershiftofthe-ray-energyinthelaboratoryframe.WhenmanyofthesedecaysoccurtheresultinglineintherayspectrumwillbeDopplerbroadenedduetotheisotropicemissionofthenucleonsandoftheraysfromthedaughternucleus.ThisalsoallowsustotheCMenergyfornucleonemissiondecaysthatareunknown.BymodelingthebroadeningofthepeakthevelocityoftherecoilingnucleuscanbecalculatedandultimatelytheCMenergy.Howeverinmanycasesthedaughternucleusisnotinavacuumandthemediumitisinhassomestoppingpowerthatreducesthevelocity.Thevelocityfoundviathebroadeningisthereforelowerthantheinitialvelocityrightafterthedecay.NaivelyassumingthattheinitialandobservedvelocitiesofthedaughternucleusarethesameresultsintheunderestimationoftheCMenergy.ThiscanberemediedbyusingBethe'sstoppingpowerequationwhichisincorporatedinsoftwarelikeStoppingPowerandRangeofIonsinMaterial(SRIM)[2].Thestoppingpowerofamaterialisdependentontheenergyoftheioninthematerial.Sincetheionisconstantlylosingenergyinthematerialthestoppingpowerisalsoconstantlychangingforthenucleustraversingit.3Figure1.3:Spectrumfrom11Lidecaywhichincludesbroadenedpeaksfrom11Li()10BefromSarazinetal[6].1.4PreviousworkinDopplerbroadeningofdelayednucleon-decayDopplerbroadeningofthiskindhasbeenobservedfromonlyonedecaychannel:delayednucleonemissionfromthe11Li()10Bedecaychannel[3,4,5,6,7].Thebroadeningofthesepeakswasrelativelyclearsincetherecoilingnucleus,10Be,isalightnucleusallowingtheCMenergyfromneutronemissiontogive10Bearelativelylargerecoilvelocity.Therewerefourbroadenedpeaksobservedincoincidencewithneutronsfromthisdecayat2590,2895,3368and6263keV.ThesepeakswereclearlybroadenedinrelationtootherpeaksintherayspectrumascanbeseeninFigure1.3.Thesepeakswereobservedtobebroadenedin-coincidencespectraaswell.Furtherdetailoftheanalysisofthe11Li()10BedecayandforDopplerbroadeningfromdelayednucleonemissioningeneralweregiveninapaperbyFynboin2003[4].Thispaperdescribedthereasonfortheappearanceofthelineshapesinrelationtothehalf-lifeoftheexcitedstateandhowinformationcanbeextractedfromthesebroadpeaks.1.5ExampleofDopplerbroadeninganalysisTheidealcaseforstudyingtheDopplerbroadeningofa-raypeakfrom-delayednucleon-decayiswhenasinglestateintheparentnucleusemitsanucleontofeedastateinthedaughternucleus.Ideallytherearealsonohigherlyingstatesinthedaughternucleusfeeding4thestateofinterestviadecay.Furthermore,thedecayoccursinvacuumandthereforeitisnotnecessarytoincorporatethehalf-lifeofthedecayingstate.Thenonecanconvolutethedetectorresponsefunctionwiththeunderlyingphysicalbroadeningbyconstructingafunctionofidenticaldetectorresponsefunctionsspacedevenlyandcenteredatthenon-shiftedenergyinordertomodelthepeakshape.Thismeansthefunctionusedtodescribethebroadenedpeaksisthedetector'sresponsefunctionspreadoutwithaboxcarfunction.Tohowbroadthepeakis,thedistancefromthecenterofthehighest(orlowest)energyresponsefunctiontothecenterofthecentralresponsefunctioncanbedetermined.ThenbothoftheseenergieswouldbeusedinaDopplershiftequationforenergywherethecentralenergyofthecenterpeakwouldbecalledE0,ortheunshiftedenergy,andthecenterenergyofthemaximumpeakisE0,ortheshiftedenergy.E0=E0cc+vn(1.4)wherecisthespeedoflightandvnisthevelocityofthenucleusatthetimeofdecay.Nowthevelocityofthenucleusatthetimeofdecaycanbefound.IftherecoilanddecayofthenucleushadoccurredinfreespaceconservationlawscouldbeappliedatthispointtothekineticenergyofthenucleonatthetimeofitsemissionandaddittothekineticenergyoftherecoilingnucleustotheCMenergyofthedecay.Unfortunatelythesituationisusuallynotsosimple.Whentherecoiloccursinamaterial,boththestoppingpowerofthematerialandthehalflifeoftheexcitedstateofinterestmustbeaccountedfor.Sincestoppingpowerisenergydependentitismoreaccuratetoiterativelydeterminetheamountofenergylostinafractionofthehalf-lifeandthenre-evaluatethestoppingpoweragainatthislowerenergy.Aftercomputinghowmuchenergywaslostbytherecoilingnucleusinthematerial,theoriginalkineticenergyofthenucleuscanbefound.FinallyusingconservationlawsthekineticenergyoftheprotoncanbecalculatedandalsotheCMenergyofthedecay.5Chapter2Experiment2.1LabLayoutThedatausedinthisthesiswasobtainedduringa26P-decayexperiment(e10034)whichwascarriedoutattheNationalSuperconductingCyclotronLaboratory(NSCL)atMichiganStateUniversity.TheCoupledCyclotronFacilityatNSCLisshowninFigure2.1[8].Aprimarybeamofstable36Arwasacceleratedtoabout150MeV/ubythecoupledcyclotrons(K500andK1200).Thentoproducetheisotopeofinterest,26P,theacceleratedbeamwasimpingeduponaproductiontargetof9Beofthickness1.55g/cm2.Theprocessesofnuclearfragmentationcreatednotonly26P,butmanycontaminantsaswell.TotrytopurifythebeamitnextgoesthroughtheA1900,aseriesoftunedmagnetswhichoutcontaminantsbymagneticrigidity[9].Thisworkssinceeachisotopehasantcharge/massratioandthereforewhenmovingperpendiculartoamagneticeachisotopewillstarttocurveinarcsoftradii.Themagnets,andthereforethemagneticcanbetunedsuchthattheisotopeofintereststaysinthebeamlineandothersarestoppedbyphysicalbarriers.Thisisnotperfectsincethereareisotopeswithverysimilarmagneticrigidities.Theseisotopesendupbeingcontaminantsfortheexperiment.Afterthebeampassesthroughthemagnetsitisfurtherbytimeoftusingaradio-frequencyfragmentseparator[10].Thisresultsinabeamthatis74%purewithmajorcomponentsbeing24Aland22Na.TheparticleidenplotinFigure2.2showstheenergylossofbeamparticlesversustimeoft.Eachconcentrationofpointsindicatesatisotope;thepointscircledinredarethe26Pparticlesofinterest.2.2DetectorsAttheendofthebeamline,the26PbeamwasdirectedintotheS2vaulttotheexperi-mentalsetup.Thesetupconsistedoftwodetectors:acentraldetectorwherethebeamwasimplanted,aGermaniumDoubleSidedStripDetector(GeDSSD),andasurroundingarray6Figure2.1:ThelayoutoftheCoupledCyclotronFacilityattheNationalSuperconductingLaboratory.Thebeamstartsasstableionsthatareacceleratedbythecoupledcyclotrons,theK500andK1200.Oncethestablebeamisaccelerateditisimpingeduponaproductiontarget,9Beinourcase,whichcreatestheisotopeofinterest(26P)alongwithmanyotherisotopes.ThisnewbeamisdeliveredtotheA1900whichhelpstopurifyingthebeamusingmagnets.NextthebeamgoestotheRFFSwhichfurtherthebeam.Finallytherareisotopebeamofinterestissenttotheexperimentalsetup.Figure2.2:Theplotshowstheenergylossofaparticleversusthetimeoft(TOF).Eachcircledconcentrationofpointsisatisotope.Theredovalencompasses26Pparticleswhilethegreenandyellowencompassthe24Aland22Naparticles,respectively.7Figure2.3:(A)TheGermaniumDoubleSidedStripDetector(GeDSSD)withthecryostatopen.ThesecondarybeamwasimplantedintotheGeDSSDwhichdetectedenergyreleasedwhenadecayoccurred.ItwassurroundedbySeGAintheexperiment.(B)Acomputeraideddesign(CAD)oftheSegmentedGermaniumArray,SeGA.Itiscomposedof16HPGecrystalssurroundingtheGeDSSD,wherethebeamwasimplanted.of16highpuritygermanium(HPGe)detectors,theSegmentedGermaniumArray(SeGA).TheycanbeseeninFigure2.3(A)and(B)respectively.TheGeDSSD[11]wastheimplantationsystem,whichisa1-cmthickplanargermaniumdetector.Itisdividedbyelectrodesinto16segmentsthatare5mmwideonthefrontand16similarstripsthatareorthogonalontheback,providing256pixels.ThebeamisimplantedintotheGeDSSDabout300mintothegermaniumcrystal.Thisiswhereallthedecaysofinterestwouldoccur.The-rayspectrumfromSeGAwasenergycalibratedusingthewellknown,stronglypopulatedbackgroundpeaksat1460.8keV(40Kdecay)and2614.5keV(208Tldecay).calibrationswereperformedusingthreetsources,154;155Euand60Co.Thesourceswereplacedonthebeamaxisanddatafromthedecayingsourceswascollected.ThenMonteCarlosimulationsofthecalibrationrunsusingGEANT4[12]wereperformedandcomparedtodatacollected.BackgroundintheSeGA-rayspectrawasfurtherreducedbyusingcoincidencegatingonsignalsfrom-decaysintheGeDSSD.Onlywhenhigh-gaineventswererecordedintheGeDSSDwouldeventsbeacceptedbySeGA.Thetiminggateusedwasa1.2sgate.Thisreducesbackgroundsincethesetupisconstantlydetectingbackgroundradiation,forexamplethe1461keVrayfrom40K.Theonlytimethatanyofthe40Kraysareincludedinthedataiswhentheyaredetectedwithinthe1.2swindowsurroundingaor-delayedprotondecayeventintheGeDSSD.8Figure2.4:ThisconceptualshowstheGeDSSDsurroundedbytheSeGADetectors.FigurecourtesyofDavidPerez-Loureiro9Chapter3DataAnalysisandDiscussionAfterthedatawasobtainedandsortedinformationaboutthe26P()25Aldecaychanneltobeextracted.Theintensityofthepopulationofeachoftheexcitedstatesof25Alcouldbedetermined,theirexcitationenergyandalsoinformationaboutthecenterofmass(CM)protonenergycouldbedeterminedforcertainenergylevels.Eachofthesewillbediscussedinmoredetailinthefollowingsections.3.1Gamma-rayIntensitiesThepeaksdeterminedtobefromthe26P()25Aldecaychannelwereobservedat452,493,844,930,944,1338,1613,1776and1790keVandarelabeledinFig.3.1.ThepeakswereidenbysearchingforpeaksatenergiespreviouslyreportedforthisdecayinRef.[13].Peaksat930and1776keVwerenewtothisdecaychannelandidenaspossible25Al-raysbycomparingthemtoenergyforknown25Allevel[14].Theycorrespondtothetransitionsfromexcitedstatesat2720to1790keVand2720to945keV,respectively,asseeinTable3.2.CoincidencegatingwasalsoperformedtosupportthepreviouslyknownlevelschemeandthepeaksobservedincoincidencearereportedinTable3.1.TothepeaksanddeterminethenumberofeventspertainingtoeachenergytheresponsefunctionofSeGAhadtobedetermined.Theresponsefunctionusedtothepeaksinthe-rayspectrumwasanExponentiallymoGaussian(EMG).f(x)=A2˙(1erf(x˝+˝˙)p2)exp(˝22˙2+x˙)(3.1)whereAistheamplitudeorintegralofthepeak,xrepresentsenergy,representsthecenterenergy,˙isthewidthand˝describesthedecayoftheexponentialcomponent.ThereasonwhytheEMGworkswellasaresponsefunctionforthisspectrumisthatitincorporatestheGaussianresolutionoftheGedetectorswithalowenergytail.10Figure3.1:26P-delayed-rayspectrum.All-raypeaksattributedtothe26P()25AldecayarelabeledbytheirenergyinkeV(black).Otherpeaksarelabeledbythe-rayemittingnuclide,withescapepeaksdenotedbyanasterisk(gray).SelectedregionsareshowninmoredetailinFig.3.7andFig.3.8.Table3.1:26P(p)25Alraysobservedinthepresentwork.Themeasured-rayenergiesarereportedinthe1stcolumnwiththeirstatisticaluncertaintiesonly;theglobalsystematicuncertaintyis0.5keV.Anasteriskdenotesraysobservedforthetimein26P-decay.The-rayintensityper26Pdecayisreportedinthe2ndcolumn,wheretheintensityofthe1613-keVlinefrom[13]wasusedfornormalization.The3rdcolumnlistsraysobservedincoincidence.Energy(keV)Intensity(%)-raycoincidences451.9(3)2.6(3)493,844,930,1338,1776493.1(4)2.4(3)452,844,1776843.5(3)0.8(2)452,493,944930.4(5)0.09(5)452,944944.4(2)1.2(1)844,930,17761338.0(2)0.8(1)4521613.1(3)2.2(2)1775.5(3)1.2(1)452,493,9441790.2(3)0.8(3)11Thisresponsefunctionworkedwellformostofthe25Alpeaks.However,theoftheDopplerbroadenedpeaksat1613and1776keVwasmorecomplex.Themodelingofthesepeakswillbediscussedindetailinthefollowingsections.Usingwell-known24Mg-rayenergiesfromdecayofthe24Albeamcontaminant[15]a2nd-degreepolynomialenergy-calibrationfunctionwascreated.Thecalibrationusedwell-knownroombackgroundpeaksinthe-raysinglesspectrumtoverifyitsaccuracyof0.5keV.Thecalibrated-rayenergiesarereportedinTable3.1.The844keVpeakcontainsasmallcontributionfromanunresolved26P()26Silineatnearlythesameenergy.Inthiscase,wereporttheenergyofthecombinedpeak.Theenergiesareallconsistentwithpreviouslyreportedvalueswhenknown[14].SimulationsusingtheGEANT4Monte-Carlopackage[12]werethencomparedtodatatakenusinganabsolutelycalibrated154;155Eusourceandtherelativeintensitiesofthe24MglinesfromonlinedatatoestablishtheasafunctionofenergyoftheSeGAdetectors.Thecurveallowedfortherelativeintensitiesofthe25Al-raystobedetermined.Duetoindeterminingthetotalnumberof26P-decaysthatoccurredintheexperimenttheabsoluteintensitieswerefoundbynormalizingtothe1613keVray,whichisknowntohaveanabsoluteintensityof2.20.2%[13]basedontheprotonfeedingofthe1613keVexcitedstate(Table3.1).Duetothecloseproximityofthe844keVpeakandthe842keV26Sipeak,itsintensityanduncertaintyweredeterminedbycombiningtheacquired26Sidatasetwithsd-shellmodelcalculations[16]topredict,andsubtract,thesmallcontributionof0.330.17%fromthe26P()26Siline.3.2pFeedingThefeedingofeach25Allevelviapdecayof26Pwascalculatedbysubtractingtheintensityof-decaybranchesfeedingitfromtheintensityof-decaybranchesde-excitingit.Forexample,asseeninFigure3.2,the944keVexcitedstateisnotonlyfedbyprotonemission,butalsothede-excitationofhigher-energystatesviatheemissionof844and1776keVrays.The944keVstatede-excitesviatheemissionof493and944keVrays.Thefeedingofthe944keVstatefromprotonemissionisequaltothesumoftheintensitiesoftheemittedraysminusthesumoftheintensitiesoftherayswhichfeedthe944keVstate,allofwhichcanbefoundinTable3.1.Sincethisexperimentwasnotsensitivetothefeedingofthegroundstateof25AlthevalueofthisfeedingreportedinTable3.2andFig.3.2areadoptedfrom[13].ThepfeedingissummarizedinTable3.2andillustratedinFig.3.2.Thereisgoodagreementwithmostoftheproton-feedingvaluesfromThomasetal:[13].Theonlyexceptionisthefeedingoftheexcitedstateat452keV.Someofthecanbeattributedtotheirinsensitivitytothe2720keVstate,whichprovidesat-rayfeedingofthe452keVstate.Thesmallprotonfeedingcanbeexplainedbytheneedforan`2protontopopulatethisJˇ=1=2+statefromtheJˇ=(2,3,4)+26Sistatesfedbyallowed26Pdecaytransitions.12Table3.2:The26P(p)feedingof25Alstatesfoundinthepresentworkandpreviouswork[13].The452keV-feedingisgivenasanupperlimit.Upperlimitsarecalculatedata95%el.Anasteriskdenotesevidenceforexcitedstatesobservedforthetimeviathisdecaychannel.Theintensitiesarenormalizedtothefeedingofthe1613-keVlevelfrom[13].25Alexcitationenergy(keV)ProtonfeedingPresentwork(%)Ref[13](%)Groundstate27.3(4)452<0.342.1(1)9441.6(3)2.1(5)16132.2(2)2.2(2)17902.3(2)2.3(2)2720*1.1(1)3.3StudyofDopplerBroadenedPeaksTwopeaksinthe-rayspectrumclearlyexhibitDopplerbroadeningfromtherecoilduetoprotonemission.Thosepeaksarefoundat1613and1776keVinthespectrumofFig.3.1.Thepeaksat1613keV(Fig.3.7)and1776keV(Fig.3.8)arefromthede-excitationofthe1613and2720keVexcitedstatesof25Alrespectively.Sinceallofthe25AlpeaksinthespectrumarepopulatedduetopdecayonemightexpectthatDopplerbroadeningshouldbeobservedinallofthe25Alpeaksanalyzedinthiswork.However,duetotheproportionalityoftheDopplershifton-rayenergy,wewerenotsensitivetotheDopplerbroadeningofthelinesat1338keVandbelow.Unfortunately,duetothecloseproximityoftheintense1797keV26Sipeaktothe1790keV25Alpeak,itwasnotpossibletostudythebroadeningofthe1790-keVpeakprecisely.Thephysicalprocesscreatingbroadenedpeaksinour-rayspectrumwasdiscussedindetailintheIntroduction.Fittingthesepeaksrequiresseveralsteps.Ifthebroadenedpeakisfromastatefedbyapreviouslyknownprotonenergy,thenthekineticenergyoftherecoilingnucleusthatemitsthe-raycanbecalculated.Forexample,consideronlythe2288keVCMprotonenergywhichfeedsthe1613keVexcitedstatein25Al.Onecantheinitialvelocityoftheexcited25Alnucleusbyconservationofmomentumandenergyasseenbelow.E=12mpv2p+12mAlv2Al=2288keV(3.2)p=mpvp+mAlvAl(3.3)E=12mp(mAlvAlmp)2+12mAlv2Al=2288keV(3.4)13Figure3.2:25Allevelschemefrom26P(p)25Aldecaydeducedfromthepresentwork.The-raytransitionsobservedaredenotedbyarrowswiththicknessesproportionaltotheirintensitiesandlabeledby-rayenergyinkeV.Thepfeedingofthetexcitedstatesisdepictedbythearrowsontheright,whicharelabeledbytheintensities.Thesingleasteriskdenotesavalueadoptedfrom[13].Thedoubleasterisksdenotestheupperlimitofthe-feedingofthe452keVstateatthe95%celevel.vAl=8:2105ms(3.5)Wheremismass,visvelocityandsubscriptspandAlstandforprotonand25Alnucleirespectively.AssumingthatthedecayoccurredinfreespacethiswouldbethevelocityofthenucleusatthetimeofdecayandthevelocitycanbeuseddirectlytocalculatetheDopplerbroadening.E0(max)=(ccval)E=1616keV(3.6)whereE0(max)isthemaximumshiftedenergythatcanbedetectedduetoDopplershiftandEistheoriginalunshiftedenergyoftheray.E0(max)caneitherbethemaximumorminimumpossibleDopplershiftedenergydependingonthesignofval.Wecanthe14Figure3.3:ThisplotshowshowtheboxcarfunctionconvolutedEMGsproduceabroadenedpeak.Inthisexample=1613keV,˙=1.54,˝=1.2,=3keVandtheamplitudeofthesmallerpeaksaresettoone.inthesetwoenergies,3keV,whichwillbeusedastheparameterwhichdetermineshowbroadourpeakofinterestis[4].Forthesebroadenedpeaks,amodelusingaboxcarfunctionconvoluteddiscretelywiththeEMGresponsefunctionisemployed.AversioncanbeseeninEquation3.7.(3.7)f(x)=A2˙(1erf(x+˝+˝˙)p2)exp(˝22˙2+x+˙)A2˙(1erf(x+0:5˝+˝˙)p2)exp(˝22˙2+x+0:5˙)A2˙(1erf(x˝+˝˙)p2)exp(˝22˙2+x˙)A2˙(1erf(x0:5˝+˝˙)p2)exp(˝22˙2+x0:5˙)A2˙(1erf(x˝+˝˙)p2)exp(˝22˙2+x˙)whereAistheamplitude,isthecentralenergy,˝isthedecayconstant,˙isthewidthoftheGaussianandisthe\stretchparameter",whichistheinE0(max)andEcalculatedabove.Usingtheparametersrelevantforthe1613keVpeak,wecanplottheversionofthepeakandallofitscontributions.However,intheactualcaseofthe1613keV-raypeak,itisknownthattwotCMenergyprotonsfeedthe1613keVlevelin25Al[13]asseeninFig.3.4.Therefore,thefunctionusedinmodelingthispeakrequiresalinearcombinationoftwoboxcarEMGfunctions.Theseboxcarfunctionsarecenteredatthesameenergyandhavethesame˝and˙parameters.Theeinthetwoboxcarfunctionsisthatoneofthefunctionshasanamplitudethatistwicetheother[13]andthattheirstretchparameterist.15Figure3.4:Thepreviouslyknowndecayschemeforthe26P-delayedprotonemissiontothe1613keVexcitedstateof25Al[13].Twoproton-unbound26Sistatesfeedthe1613keV25Alexcitedstate,causingtwot25Alrecoilvelocitiesfollowingprotonemission.Anotherwaythatourcaseisnotappropriateforouractualdataisthatthedecaydoesnotoccurinfreespace.ItinsteadoccursintheGeDSSD,whichisgermaniumand,therefore,therecoilingnucleuswillbegintoslowdownassoonasitisemitted.Itisnecessarytoincorporatethehalflifeoftheexcitedstateof25Althatthe-rayisemittedfromanditisusedalongwiththestoppingpowerofthematerialinwhichthenucleusismovingtodeterminethevelocityofthe25Alatthetimeofdecay.Asshownpreviously,oncethevelocityatthetimeof-rayemissionisdeterminedalongwiththeexpectedenergyoftheraythemaximumpossible-rayenergythatcanbedetectedduetoDopplerbroadeningcanbecalculated.Thepieceofinformationmissingfromourcaseisthefactthatnotallofthedecaysoccursexactlyatthehalf-life.Insteadthatisthetimebywhich50%ofdecaysareexpectedtohaveoccurred.Tomoreaccuratelydepictthisinourmodelweexpandedwhatwasoneboxcarfunctionforeachprotoninto5boxcarfunctionseachofwhichrepresentattimeintervalbetweenprotonemissionand-rayemission.Wediscretizedthedecay,N(t)=N012tt12(3.8)whereN(t)isthecurrentnumberofparticlethathavenotyetdecayed,N0arethenumberoforiginalparticlesthatcandecay,t12isthehalf-lifeandtistime.Usingtheknownvalueof˝,thetimesatwhich10,30,50,70and90%ofthedecaysareexpectedtohaveoccurredwerecalculated.Eachofthesediscretetimeswasusedtorepresent20%ofthedecays,providingerelationshipsbetweentheinitialvelocityandthevelocityatthetimeof-rayemissionthroughthestoppingpower.Figure3.5showstheexponentialdecayforaparticlewithatheoreticalhalf-lifeof10fsandinitialcountof100particles.Blacklinesdividethedecaywhere20%,40%,60%and80%oftheparticleshavedecayed.ForeachC.M.protonenergyaboxcarstepfunctionwascreatedcorrespondingtoeachof16theetimessuchthattheyhadequalintegralsandstretchedinunison.ThestoppingpowerwastreatedbyutilizingSRIMtablesgeneratedfor25Alionsingermanium[2].Forthe1776-keVcasethestoppingpowerwastreatediterativelyin25fsstepstoaccountforitsenergydependenceduetoitsrelativelylonghalf-lifeof201(14)fs[15].Figure3.6showshowtheshapeofthepeakchangeswhenevaluatedatttimesalongthedecayforthe1776keV-raycase.ItillustrateswhyitisimportanttoevaluatetheDopplershiftatmorethanjustthehalf-lifeofthedecay.Therearemoreaccuratewaystotreatthehalf-lifeandstoppingpower;however,thisdiscretetreatmentwastlyaccurateconsideringthestatisticaluncertaintiesinthespectrumandtheabsoluteuncertaintyinthestoppingpower,whichwasapproximatedtobe10%basedonthescatterintheexperimentaldataplotsfromSRIMforaluminumionsingermanium.Figure3.5:Thedecayofatheoreticalparticlewithinitially100daughterparticlesandahalf-lifeof10fsisshownabove.Fortheanalysisthedecaycurvewasdividedintoesectionslikeshownabove.ThetimeusedtorepresenttheDopplerbroadeningofthe20%ofdecayingparticleswouldbethetimeatwhichitisexpectedfor10%oftheparticletohavedecayed.Theotherareevaluatedinthesamemanner.3.41613keVTheC.M.energiesandrelativeintensitiesfortheprotonsthatfeedthe1613keVexcitedstatearewellknown[13].WiththispreviouslyreportedinformationwecouldtesttheDopplerbroadeningmethodbyadoptingtheseenergiesalongwiththeknownlifetimetoconstrainthe(Fig.3.7).17Figure3.6:Thecomponentsoftheshapeofthe1776keV-raypeakareshownabove.Eachpeakhasthesamenumberofcounts,butthespreadsduetoDopplerbroadeningaretduetoevaluatingthematthetimehere10%(greensolidline),30%(orangedashedline),50%(greydottedline),70%(yellowdot-dashedline)and90%(bluedoubledot-dashedline)oftheparticleshavedecayed.TheresponsefunctionusedforthiseisGaussianforsimplicity.TheComptonbackgroundinthe1613-keVregionwascontinuousandandwasthere-foremodeledwithastraightline.Theneighboringcontaminant26Alpeakat1622.26(3)keV(from26Sidecay)[17]wasnotbroadenedandcouldbemodeledwithasimpleEMGwiththeamplitudeandthecentroidasfreeparameters.Anotherbackgroundpeakisintheregionat1611.807(11)keV[17]andistheresultofthewell-knowndecayof25Altoexcitedstatesof25Mg.Sincetheabsoluteintensityofthisrayisknownitwaspossibletotheintensityofthecorrespondingpeaktobe0.112timesthatofthe1613keVpeak.Thisthattheoverlapoftheweak25Mg-raylinetothe25Al-raylinedoesnotcontributetlytothebroadeningofthe1613keVpeak.Initiallythe1613keVpeakwastreatedasiftherewasnoDopplerbroadeningbyusingthesameresponsefunctionusedtomodeltheotherpeaksinthespectrum.Thisyieldedahigh˜2perdegreeoffreedomof138/27correspondingtoap-valueof0.0001.Itwas,therefore,clearthattheassumptionthatthe1613keVpeakshouldbemodeledwiththesameEMGresponsefunctionwithoutbroadeningisincorrect.NextDopplerbroadeningduetotheprotonemissionwasincorporatedintothemodel,asdescribedpreviously.Therearetwotexcitedstatesabovetheprotonthresholdin26Sithatemitprotonspopulatingthe1613keVexcitedstateof25Al,whichundergoesa-raytransitiontothegroundstate[13].TheC.M.energiesofthetwoprotonsare2288(3)keVand5893(4)keVandtheyhavearelativeintensityofI2288/I5893=2.0(Fig.3.4)[13].18Figure3.7:26P-delayed-rayspectrumintheregionofthe25Alpeakat1613keV.Thepeakat1613keVisbroaderthantheneighboring26Alpeakat1622keV.ThesolidbluelineistheoverallincludingDopplerbroadeningandthereddottedlinerepresentstheComptonscatteringbackground.Belowthedataandtheindividualpeakcomponentsareshown.The1611keV25Mg,1613keV25Aland1622keV26Al-raylinesarerepresentedbythegreendot-double-dashed,golddashedandlightbluedot-dashedlines,respectively.TherewassubstantialimprovementoftheafterincludingDopplerbroadeningwiththeseknownvalues(Fig.3.7)anditisintheimprovementinthe˜2perdegreeoffreedomto31.5/27correspondingtoap-valueof0.25.ThistheDopplerbroadeningofthislineaswellastheaccuracyoftheDopplerbroadeninganalysistechnique[4].WewerefurtherencouragedtoutilizethismethodtotrytoextracttheCMenergyfromthe1776keVpeakwhichhasnoknownprotonCMenergy.3.51776keVThe1776keV-raytransitionfromthe2720keVexcitedstateof25Alwasobservedforthetimein26Pdecay(Fig.3.8)[18].SinceithasneverbeenobservedviathisdecaymechanismtheC.M.protonenergyfeedingthe2720keVexcitedstatewasunknown.ThisallowedustoextractthisnewinformationusingtheapplicationoftheDopplerbroadeningmethod.Asinthe1613keVregion,thecontinuousComptonscatteringcomponentoftheback-groundwasmodeledtobelinear.Toprovideanaccuraterepresentationofthebackgroundunderneaththe1776-keVpeakitwasnecessarytoincludetheotherpeaksintheregioninthefunction.The1790keV25Alpeakontheshoulderofthestrong1797-keV26SilinewasmodeledtobeDopplerbroadened;itsshapewasconstrainedusingthethreeknownprotonenergies[13]feedingit,theirratiosandtheknownhalflifeofthe1790keVexcitedstate[14].19Figure3.8:26P-delayed-rayspectrum(redcrosses)intheregionofthe1776-and1790-keVpeakswith(bluesolidline).ThedashedgreenlineshowsthecontributionoftheDopplerbroadened1776-keVpeaktotheoverallThedot-dashedpurplelineshowsthecontributionsofallotherpeaks.Thesmallexcessnear1810keVcouldnotbetobefrom25Al.20Figure3.9:Thebluedotsshowthe˜2valueforeachoftheinitial25Alkineticenergytested.Thebluelineshowsthequadraticlinethatwasusedtodeterminetheenergywiththeminimum˜2.Theminimumwasfoundtobeat195+4150(stat.)18(syst.)keVTable3.3:Sourcesofuncertaintyinthe5.11.0(stat.)0.6(syst.)MeV26P-delayedprotonC.M.energyfeedingthe2.72MeV25Alstate.SourceofuncertaintyUncertainty(MeV)statistics1.0responsefunction0.3stoppingpower0.5background0.1TotheCMenergyforthe1776keVpeakwhileincorporatingstoppingpowerandthehalf-lifeweusedhypothesizedinitial25Alrecoilenergiesandvariedtheminthefrom100to325keVin15keVsteps.Thebestand˜2valuewerefoundforeachoftheseenergies.PlottingtheCMenergiesversusthe˜2valueoftheresultedinanoptimal25Alinitialkineticenergyof195+4150(stat.)18(syst.)keVbasedontheminimumvalueof˜2asseeninFig.3.9.UsingconservationofenergyandmomentumthecorrespondingC.M.protonenergywasfoundtobe5.11.0(stat.)0.6(syst.)MeVcorrespondingtoaproton-emitting26Silevelatanexcitationenergyof13.31.0(stat.)0.7(syst.)MeV.Systematicuncertaintiesfortheprotonenergywerederivedfromtheuncertaintiesintheshapeparametersoftheresponsefunction,uncertaintiesinthestoppingpower,anduncertaintiesinthebackground.AsummaryoftheuncertaintiescanbefoundinTable3.3,whichshowsthatthestoppingpowercontributesthedominantsystematicuncertainty.Theonlyprotonunboundstateof26Sithatisconsistentwithourmeasuredprotonenergyistheisobaricanalogstate(IAS)of26Pat13.015(4)MeV(theonlyknownexcitedstateabove10.8MeV),whichisalsoknowntobestronglypopulatedin26Pdecay[13].21Chapter4ConclusionandoutlookWhilethemethoddemonstratedinthepresentworkisnotquiteofsimilaraccuracytodirecttechniqueswhichmeasuretheprotonCMenergiesfrom-delayedproton-decay,itismuchmoretomeasure-delayedneutronCMenergies.Thepresentmethodmayprovetobeveryusefultothemeasurementofneutronenergiessinceitdoesnotrequiretheemittednucleontobecharged.Therehavebeenproposalstofurthertheway-raydataiscollectedwhichwillbeanextpotentialstepforthismethod.ToobtainmorepreciseresultsinthefutureitispossiblethatCrystalspec-trometer(CDS)measurementswillbethekey[19].IthasalreadybeenproposedtouseCDSatISOL@MYRRHA(Isotopeseparatoron-line)inBelgiumtostudy-delayedneutronemission[20].TheadvantagestousingCDSisthattheresolutionofrayenergiesismuchbetterthanthatofHPGecrystaldetectors.ThedownsideitthatthedetectorforCDSnecessarilyhasalowacceptance,givingitamuchsmallersolidangle,andthereforeamuchlower.Onewaytocombatthisistouseveryintensebeams(likethoseproducedatISOL@MYRRHAor,potentially,FRIB)andtohavelongexperimentalruntimestoallowforthetcollectionofstatistics.ThegreatresolutionofCDSwouldallowfortheCMenergiesfromhighermasscasestobedetermined.Itwillalsoyieldmorepreciseenergiesforlowermasscases.Whilethismaynotbeacompetitivemethodtoobtain-delayedprotonCMenergies,itisttothedetectionoftheCMenergiesof-delayedneutrons,duetotheirneutralnature.Toconclude,thiswastheobservationoftheradiativeDopplerbroadeningfrom-delayedproton-decay,anditwasalsothehighestmass(A=25)forwhichDopplerbroad-eninghasbeenobservedinany-delayednucleon-decay.SincetherewasnotonebuttwopeakswithobviousDopplerbroadeningthisnotonlyallowedustotestthetechniquepresentedin[4]withacasewithaknownCMprotonenergy,butalsoapplythetechniquetodetermineapreviouslyunknownCMprotonenergy.Absoluteintensitiesof8tenergyraysfrom26P()25Alweredeterminedaswasthefeedingof525Alexcitedstatesfromthesamedecay.ThepresentresultshavebeenpublishedinRef.[18].22REFERENCES23REFERENCES[1]S.Y.F.Chu,L.P.omandR.B.Firestone,Tableofisotopes(1998),1998,availableathttp://nucleardata.nuclear.lu.se/toi/pdf/chart.pdf[2]Ziegler,J.F.,&Biersack,J.P.1985,TreatiseonHeavy-IonScience,byBromley,D.Allan,ISBN978-1-4615-8105-5.Springer-VerlagUS,1985,p.93,93[3]Borge,M.J.,Fynbo,H.,Guillemaud-Mueller,D.,etal.1997,PhysicalRev.C.,55,R8[4]Fynbo,H.O.U.,Borge,M.J.G.,all,J.,etal.2004,NuclearPhysicsA,736,39[5]Fynbo,H.O.U.,Borge,M.J.G.,all,J.,etal.2004,NuclearPhysicsA,736,39[6]Sarazin,F.,Al-Khalili,J.S.,Ball,G.C.,etal.2004,PhysicalRev.C.,70,031302
[7]Mattoon,C.M.,Sarazin,F.,Andreoiu,C.,etal.2009,PhysicalRev.C.,80,034318
[8]Bennett,M.B.,Wrede,C.,Chipps,K.A.,etal.2013,PhysicalReviewLetters,111,232503[9]Morrissey,D.J.,Sherrill,B.M.,Steiner,M.,Stolz,A.,&Wiedenhoever,I.2003,NuclearInstrumentsandMethodsinPhysicsResearchB,204,90[10]Bazin,D.,Andreev,V.,Becerril,A.,etal.2009,NuclearInstrumentsandMethodsinPhysicsResearchA,606,314[11]Larson,N.,Liddick,S.N.,Bennett,M.,etal.2013,NuclearInstrumentsandMethodsinPhysicsResearchA,727,59[12]Geant4CollaborationandAgostinelli,etal.2003,Nucl.Instrum.andMethodsA,506,250[13]Thomas,J.-C.,Achouri,L.,o,J.,etal.2004,EuropeanPhysicalJournalA,21,419[14]Firestone,R.B.2009,NuclearDataSheets,110,169124[15]Firestone,R.B.2007,NuclearDataSheets,108,2319[16]Brown,B.A.,2013,privatecommunication
[17]Endt,P.M.1998,NuclearPhysicsA,633,1
[18]Schwartz,S.B.,Wrede,C.,Bennett,M.B.,etal.2015,PhysicalRev.C.(R),92,031302[19]SCKCEN,2016,availableathttp://myrrha.sckcen.be/en[20]Womble,P.C.,Barzilov,A.,Novikov,I.,andHoward,J.,2016,availableathttp://www-pub.iaea.org/MTCD/publications/PDF/P1433_CD/datasets/abstracts/sm_en-16.html25