SPECTROSCOPYOF 15 BE By JesseDanielSnyder ADISSERTATION Submittedto MichiganStateUniversity inpartialentoftherequirements forthedegreeof Physics{DoctorofPhilosophy 2014 ABSTRACT SPECTROSCOPYOF 15 BE By JesseDanielSnyder Theneutron-unboundnucleus 15 Bewasobservedforthetime.Itwaspopulated usingneutrontransferfromadeuteratedpolyethylenetargetwitha59MeV/u 14 Bebeam. Neutronsweremeasuredincoincidencewithoutgoing 14 Beparticlesandthereconstructed decayenergyspectrumexhibitsaresonanceat1.8 0.1MeV.Thiscorrespondsto 15 Be beingunboundby0.45MeVmorethan 16 Bethustlyhinderingthesequentialtwo- neutrondecayof 16 Beto 14 Bethroughthisstate.Thecrosssectionforneutronpickupwas calculatedtobe1.1 0.6mb,and0.7 0.5mbfromcarbon,anddeuterium,respectively. TABLEOFCONTENTS LISTOFTABLES .................................... v LISTOFFIGURES ................................... vi Chapter1Introduction ................................ 1 1.1Theory.......................................3 1.2PreviousWork..................................5 1.3PopulatingandObserving 15 Be.........................6 Chapter2ExperimentalTechniqueandSetup ................. 7 2.1InvariantMassSpectroscopy...........................7 2.2BeamProduction.................................8 2.3ExperimentalSetup................................9 2.3.1ChargedParticleDetection........................11 2.3.2NeutronDetection............................13 2.4ElectronicsandDataAcquisition........................14 Chapter3DataAnalysis ............................... 17 3.1CalibrationandCorrectionsoftheCharged ParticleDetectors................................17 3.1.1ScintillatingDetectors..........................17 3.1.2CRDCs..................................20 3.2MoNACalibrations................................25 3.2.1EnergyCalibration............................25 3.2.2TimingCalibration............................25 3.2.3PositionCalibration...........................27 3.3EventSelection..................................28 3.3.1IncomingBeamIden......................29 3.3.2CRDCsChargeCollectionGate.....................29 3.3.3ElementIden..........................30 3.3.4IsotopeIden...........................30 3.3.5NeutronIdent..........................34 3.4InvariantMassReconstruction..........................37 3.4.1TheInverseMap.............................38 3.4.2DecayEnergy...............................40 3.4.3oftheCarbonintheDeuteratedPolyethylene..........41 iii Chapter4Simulations ................................ 43 4.1STMoNA.....................................43 4.1.1InitialParameters.............................44 4.1.2CentralTrackLengthIssues.......................46 4.1.3FinalChecks...............................48 4.1.4Geometric...........................50 4.1.5ResonanceModeling...........................51 4.2Geant4.......................................53 4.2.1Comparison................................57 Chapter5Results ................................... 60 5.1ResonanceEnergy.................................60 5.2CrossSection...................................64 5.2.1SystematicUncertainty..........................65 5.2.2CarbonTarget..............................66 5.2.3DeuteratedPolyethyleneTarget.....................67 Chapter6SummaryandOutlook ......................... 71 6.1Summary.....................................71 6.2Outlook......................................72 APPENDIX ....................................... 74 BIBLIOGRAPHY ................................... 77 iv LISTOFTABLES Table1.1Thetwoneutronwiththelargestcontributions....5 Table1.2SpectroscopicFactor(SF)fordecayingtothegroundandexcited state...................................5 Table3.1Thinandthickpositioncorrectionfactors...............20 Table3.2CRDCsslopesand........................24 Table4.1Thecentroidandwidthofthegaussiandistributionusedtomatch thebeam.............................44 Table5.1Thesourcesofthesystematicuncertainty................66 Table5.2Thenumberofreactioneventsfromttargetnucleiforthe CD2target................................70 TableA.1Opticalmodelpotentialsparametersused...............75 TableA.2Opticalmodelpotentialsparametersused...............75 TableA.3Opticalmodelpotentialsparametersusedtomodeltheinteraction.76 v LISTOFFIGURES Figure1.1Tableofisotopesfromhydrogen(Z=1)tooxygen(Z=8).The boundisotopesareshownforeachelement;thetcolorscorre- spondtostable(black),neutronrich(blue),andprotonrich(orange) isotope. 15 Beand 16 Bearebothneutronunboundandareindicated bythegreenboxes............................2 Figure1.2Levelschemeforneutronrichberylliumisotopes.Thesolidlinesin- dicateexperimentallyknownlevelswiththeuncertaintiesbeingrep- resentedbythegraysquares,whereasthedashedlinescomefrom Nushellx calculationsusingtheWBPHamiltonian.Thearrows showthedecaypathtakenfromthepopulationofthe3/2 + stateas determinedfromRef.[17]........................3 Figure2.1Diagramofthebeamproductionmechanism.Theprimarybeamof 18 OisacceleratedthroughtheK500andK1200untilitreachesan energyof120MeV/uandstrikesa3196mg/cm 2 berylliumtarget. TheA1900fragmentseparatorthenselects 14 Befragmentsfromother reactionproducts.............................9 Figure2.2Diagramoftheexperimentalvault.Itshowstheplacementofthe target,quadrupoletriplet,Sweepermagnet,andthedetectors....10 Figure2.3SchematicofaCathode-ReadoutDriftChamber(CRDC)(adopted fromRef.[47])..............................12 Figure2.4Schematicdiagramofthetimingelectronics,logicmodules,andDAQ. IfthereisavalideventinMoNA,theLevel1logicmodulesendsa signaltotheLevel2logicmodulewhichwaitsforasignalfromthe thinLUtodetermineifthereisavalidcoincidence.Ifthereisavalid coincidence,Level2sendsasignaltotheDAQtoreadoutallofthe electronics.IfthereisnocoincidenceintheLevel2sendsoutasignal tofastcleartheelectronics........................15 vi Figure3.1Scintillatorcharge(energy)spectra.Thetoptwoplotsarefromthe thindetector,whilethebottomtwoarefromthethickscintillator. Theeventsweregatedsothatonlyoneisotopewaspresentalong withthebeambeingcenteredinbothdetectors.Theleftplotsshow therawenergycollectedwhiletherightplotsshowthefourPMTs aftergainmatching.ThethinandthickLU,RU,LD,andRDare representedbythecolorred,black,blueandgreen,respectively...18 Figure3.2Uncorrectedthickleft-upenergy(leftpanel)andafterthetimecor- rectionfactorhasbeenapplied(rightpanel)plottedagainstevent number.ThecorrectionfactorsweredeterminedforeachofthePMT forthethinandthickscintillators....................19 Figure3.3 E fromthethinscintillator(leftpanel)andcorrected E (right panel)isplottedagainstthehorizontalpositionofthedetector.The correctionisZdependent,thusitonlystraightenstheberylliumband.20 Figure3.4CRDC2rawchargecollectedvaluesforeachpadfromasweeprun thatilluminatedtheentirefaceofthedetector.............21 Figure3.5CRDC2calibratedchargecollectedforeachpadfromasweeprun thatilluminatedtheentirefaceofCRDC2.Thepedestalshavebeen subtracted,andeachpadhasbeengainmatched............22 Figure3.6CRDC1calibratedchargecollectedforeachpadfromasweeprun thatilluminatedtheentirefaceofCRDC2.Thepedestalshavebeen subtracted,andeachpadhasbeengainmatched.Thecolorrepre- sentsthenumberofcountsperbin...................23 Figure3.7ExamplemaskrunforCRDC2.Thebest(padnumber)isplot- tedvsTAC.Theholesareeasilyidenandgateswereapplied aroundeachoneandthecentroidagaussianwasusedtothe centroidinTACandbest(padnumber)...............23 Figure3.8ExamplemaskrunforCRDC2aftercalibration,CRDC2x(mm)is plottedvsCRDC2y(mm)........................24 Figure3.9ExamplerawQDCspectraforasingleMoNAPMT.Thecosmic muonpeakcanbeseenatapproximatelychannel900,room -rays arelocatedatchannel250andthepedestalisnotpresentsinceithas beenalreadysuppressed.Forthelinearcalibrationthepedestalwas settozeroandthecentroidofthecosmicmuonpeakwassetto20.5 MeVee...................................26 vii Figure3.10Exampletimebetweentherightandleftsidesofabarfrom acosmicmuonrun.Theedgesofthebarareeasilyidenwhich allowsforalinearcalibrationtodeterminetheslopeandThis allowsforthedeterminationofwheretheeventtookplace......28 Figure3.11FlighttimefortheincomingbeamfromtheA1900timingscintillator tothetargetscintillator.The 14 Beiscenteredaround173ns,with thebiggestcontaminantcomingfromlithiumwhichiscenteredat 161.5ns..................................29 Figure3.12CRDC1padsumplottedagainstCRDC2padsum.Nogateswere appliedtothisplot.Theblacklinecorrespondstothegateusedto selectforgoodpadsuminCRDC1andCRDC2............30 Figure3.13Elementidenisdeterminedusingthetimeoftbetween thetargetandthinplasticscintillatorvsenergylossinthethinplastic scintillator.Theelementspresentareidenintheplot......31 Figure3.14Threedimensionalplotofthetimeoftfromthereactiontarget tothethinscintillatorvs.dispersiveangleatthefocalplanevs.dis- persivepositionatthefocalplane.Theplotonlycontainsberyllium isotopes.Thebandscorrespondtotisotopeswiththemost intensebeing 14 Be............................32 Figure3.15ProjectionofFigure3.14wherethecolorcorrespondstotimeoft betweenthereactiontargetandthethinscintillator.Abandofequal timeoftistoconstructaparameterdescribingthecorre- lationsbetweenthedispersiveangleandposition...........33 Figure3.16Theparameterxtxversustimeoftbetweenthereactiontarget andthethinscintillator.Isotopesareidenontheplot,along withwheretheunreactedbeamandreactionproductsarelocated for 14 Be.Theblacklinecorrespondstothegateusedtoremove contaminationofunreacted 14 Be.Inordertoreducetheintensityof theunreactedbeam,agateonbeamvelocityneutronsinMoNAwas applied...................................33 Figure3.17EnergydepositedinMoNAversusthetimeoft.Theplotonly containseventswhereanyberylliumisotopewasidenafterthe Sweepermagnet..............................35 Figure3.18Neutrontimeoftspectrum.Theblackdatapointsrepresentthe timeoftforallberylliumisotopeswhereasthereddatapoints areincoincidencewith 14 Befragments.................35 viii Figure3.19Neutrontimeoftspectrum.Theblackdatapointsrepresentthe timeoftfor 14 Befragmentsthatwereselectedusingthegate showninFig.3.16.Thereddatapointshaveanadditionalgateon depositedenergiesofmorethan3MeVee................36 Figure3.20ThehorizontaldistributionofneutroneventsinMoNAfromthefor- mationof 15 Bebyneutronpick{upfromthetarget..........37 Figure3.21Reconstructedkineticenergyspectrumwhichisusedtotestthein- versemap.Thedatacomesfromanotargetrunthatwasbentinto thecenterofthefocalplanebox.Thereconstructedenergyisin completeagreementwiththevaluepredictedbyLISE++of59MeV/u39 Figure3.22Reconstructedanglespectrumthatisusedtotesttheinversemap. Thedatacomesfromanotargetrunthatwasbentintothecenterof thefocalplanebox.Thereconstructedangleiscentered,g thattheinversemapisworkingproperly................40 Figure3.23Decayenergyspectrumforcoincidence 14 Beandaneutronisshown bytheblackdatapointswiththeirstatisticaluncertainty.Thespec- trumwascalculatedusingEq.2.6.Aresonancecanclearlybeseen atapproximately2MeV.........................41 Figure3.24Decayenergyspectrumfordeuteratedpolyethyleneandacarbon target.A300mg/cm 2 carbontargetwasusedfor16hours,the decayenergyforthecarbontarget(reddatapoints)iscomparedto thedeuteratedpolyethylenetarget(blackdatapoints).Thegates andconditionsusedtoselectandcalibrateforbothtargetswerethe sameandtheresultsarestatisticallyidentical.............42 Figure4.1CRDCpositionandanglespectrum.Eachcomparesdata(dot) toSTMoNAsimulation(line).Thetopleft,topright,bottomleft, andbottomrightpanelshowsthecomparisonfortheCRDC1hori- zontalposition,horizontalangle,verticalposition,andverticalangle, respectively................................45 Figure4.2Atechnicaldrawingofthebeam{linefromthetargettothefocal planebox.ThecentraltracklengthfromthetargettoCRDC1can bedeterminedusingthisdiagram....................46 ix Figure4.3ExperimentalandsimulationdataobtainedwiththeSweepermag- net'scurrentat366A.ThebluelinerepresentsanSTMoNAsimula- tion,whileblackpointsrepresentsexperimentaldata.Theleftpanel asimulatedtotalcentraltracklengthof165.4cmandthe rightpaneluses172.3cm.........................47 Figure4.4AngulardistributionofthereactionusedinSTMoNA,calculated withFRESCOusingtheglobalopticalpotentialsfromRefs.[38,35].48 Figure4.5Comparisonofsimulation(blueline)todata(blackpoints)for 14 Be reactionproductslocatedinthefocalplane.Theparametersare comparedareCRDC1X, X ,Y,and Y whicharelocatedinthe upper{left,upper{right,lower{left,andlower{rightpanel,respectively.49 Figure4.6Comparisonofsimulation(blueline)todata(blackpoints)for 14 Be reactionproductslocatedinthefocalplane.Theparametersare comparedaretargetE, X ,Y,and Y whicharelocatedinthe upper{left,upper{right,lower{left,andlower{rightpanel,respectively.50 Figure4.7GeometricyoftheMoNAandSweepersystem.Itwascalcu- latedforenergiesbetween0and5MeVforaneutronpick{upreaction fromdeuterium..............................51 Figure4.8Theleftpanelshowsthetotalcarbon{neutroninelasticreactioncross sectionusedinthestockG4Physicsclass(JENDL{HE).Theother sixcolorsshowthediscreteinelasticreactioncrosssectionsusedin theMenate Rcode.Therightpanelshowsthehydrogenelasticcross sectionforG4PhysicsClass(Green)andMenate R(Black).Also shownisthecarbonelasticcrosssectionfortheG4Physics(Red)and Menate R(Blue).(adoptedfromRef.[79])..............55 Figure4.9Visualrepresentationoftheelasticcrosssectionsforironaterent energiesfromRef[78].Thecrosssectionsat30,50,and70MeV wereaddedtoMenate R,andthenextrapolatedtotheenergyofthe neutron..................................56 Figure4.10Experimentaldata(Black)fromRef.[77]iscomparedtotheG4Physics (Red)andMenate R(Blue)model.Theleftpanelshowsthemulti- plicityandrightpanelshowstheenergydeposited.Intheleftpanel themultiplicitydistributionswerenormalizedsothatmultiplicity= 1eventsmatched.Therightpanelwasnormalizedfortotalnumber ofevents.(adoptedfromRef.[79])...................58 x Figure4.11ComparisonbetweenthestockG4Physics(Red)andMenate R(Blue) modelsofmultiplicitydistributionforinteractionswithinMoNAwhere raysareproducedfrominelasticreactionswithcarbon.(adopted fromRef.[79])..............................58 Figure5.1 15 Bedecayenergyspectrum.Thedataareshownbytheblackdata pointswithstatisticalerrorbars.Thebesttothedata(solidblack line)isasumofan l =2resonance(greenshort-dashedline)and backgroundcontributionsapproximatedby l =0(redlong-dashed line)and l> 0(bluedottedline)components.............61 Figure5.2Partialexperimentallevelschemeforneutronrichberylliumisotopes. Theheightofthegrayboxesrepresentstheuncertaintiesofthestates. Thedatafortheexcitedstatein 14 Beisfrom[26],thelowerlimitfor the3/2 + isfrom[17],the 15 Be5/2 + stateisfromthepresentwork andthetwo-neutronseparationenergyfor 16 Beisfrom[13].....63 Figure5.3RBSsimulationsusing3.4MeVprotonsimpinginguponacarbon (redline)andaCH 2 (blackline)targetarecomparedtodatafrom RBSanalysis,alsousing3.4MeVprotons.Thecarbondata(red points)anddeuteratedpolyethylenedata(blackpoints)werenor- malizedtothesimulatedcarbontarget.Thereisgoodagreement betweenthesimulateddeuteratedpolyethylenetargetandthedata, whichindicatesthattheratioofcarbontohydrogenis1:2......68 Figure5.4RBSdataforetlocationsonthedeuteratedpolyethylene target,impingedwith3.4MeVprotons.Eachdatasetwasnormalized sothetotalnumberofincomingprotonswerethesame.Thestrength ofthepeakbetweenchannel30and70isindicativeofthepercentage ofhydrogeninthetargetisdeuterium.................69 xi Chapter1 Introduction Oneofthefundamentalquestionsofmodernnuclearphysicshasbeenaimedatbetterun- derstandingthestrongnuclearforce.Thishasbeensupportedbythedevelopmentofthe liquiddropmodel[1,2],andthenuclearshellmodel[3,4,5].Thenuclearshellmodel,in particular,wasdevelopedin1949andusedtoexplainmagicnumbers.Whilethenuclear shellmodelworkswellnearstability,researchhasshownthatasyouapproachthedrip{line themodelstartstobreakdown.Thedevelopmentoftradioactiveionbeamsinthe 1980s[6]hasallowedexplorationuptoandbeyondthelow{Zneutrondrip{line.Implemen- tationofthisisotopeformationtechniquehasallowedobservationsofnovelsuchas neutronhalonuclei[7],neutronradioactivity[8],andnewmagicnumbersobservedaway fromstability[9,10]. Probingtheofthestrongnuclearforcerequiresprotonsandneutronstobecom- binedintcombinationstodeterminetheirresultingproperties.One-andtwo-proton removalreactionsaswellaslight-particletransferreactionshavebeenusedtopopulateun- boundnucleifromneutronunboundhydrogen(upto 7 H[11])to( 28 F[12])isotopes. Ofrecentinterestarenucleiwhichdecaybytheemissionoftwoneutrons;aparticularcase isthegroundstateof 16 Be,whichwasobservedtodecaybytheemissionoftwostrongly correlatedneutrons.Thisdecayat1.35 0.10MeVhasbeeninterpretedasadineutronemis- sion[13,14,15].Theanalysisoftwo-protonradioactivityhasshownthatdiprotonemission 1 Figure1.1:Tableofisotopesfromhydrogen(Z=1)tooxygen(Z=8).Theboundisotopes areshownforeachelement;thetcolorscorrespondtostable(black),neutronrich (blue),andprotonrich(orange)isotope. 15 Beand 16 Bearebothneutronunboundandare indicatedbythegreenboxes. isfavorableonlywhenthedecayviathesequentialemissionoftwoprotonsisenergetically notallowed[16]. Inordertothat 16 Bedecaysdirectlyto 14 Beorifitsdecayproceedssequentially viaintermediatestatesin 15 Beitisnecessarytomeasurethespectroscopyof 15 Bewhich hasnotyetbeenobserved.Figure1.1showsthenucleiforelementsbetweenhydrogenand oxygenwiththeisotopesofinterestforthepresentstudyhighlightedingreen. 16 Bewas previouslypopulatedwithaone{protonremovalreactionfrom 17 B[13]whileasearchfor 15 Bewithatwo{protonremovalreactionfrom 17 Cwasunsuccessful[17].Inthepresent work 15 Bewillbepopulatedwiththe(d,p)transferreactionininversekinematicsusinga secondarybeamof 14 Beonadeuteratedpolyethylenetarget. 2 Figure1.2:Levelschemeforneutronrichberylliumisotopes.Thesolidlinesindicateexperi- mentallyknownlevelswiththeuncertaintiesbeingrepresentedbythegraysquares,whereas thedashedlinescomefrom Nushellx calculationsusingtheWBPHamiltonian.Thear- rowsshowthedecaypathtakenfromthepopulationofthe3/2 + stateasdeterminedfrom Ref.[17]. 1.1Theory Thelevelstructureof 15 BeisunknownandtheoreticalpredictionsWhileearlyshell modelcalculationspredicteda5/2 + groundstatewithanexcited3/2 + stateat70keV [18]morerecentcalculationswith Nushellx [19]inthe s-p-sd-pf modelspaceandthe WBPHamiltonian[20]resultedina3/2 + groundstateand5/2 + excitedstateat300keV. Nushellx calculatesthatthe3/2+groundstateof 15 Bewillbeunboundby2.5MeV.The predictedlevelstructureof 15 BeisshowninFig1.2bythedottedlines. Thepreviousattempt[17]topopulatestatesof 15 Bewiththetwo-protonremovalreaction from 17 Csetalowerlimitforthe3/2 + stateof1.54MeVasindicatedintheFromthe 3 non{observationofneutronsincoincidencewith 14 Beitwassuggestedthatthe3/2 + state probablydecaystothe(unbound)excitedstatein 14 Be.Kondoetal.[21]recently showedthatthis2 + statein 14 Bedecaysdirectlytothegroundstateof 12 Bewiththe emissionoftwoneutronsasthesequentialdecayviathegroundstateof 13 Beisenergetically notallowed.TheblackarrowsinFigure1.2showthisdecaypathofthe3/2 + statein 15 Be. The 17 C(-2p) 15 Bereactionwasnotexpectedtopopulatethe5/2 + statein 15 Bewhich stillcouldpossiblybethegroundstatelocatedatanenergywhereitcouldserveasan intermediatestateforthesequentialdecayof 16 Be.Analternativewaytopopulatethe 5/2 + statein 15 Beisthe(d,p)transferreactionininversekinematicswithasecondary 14 Be beam.Thistypeoftransferreactionhasbeenpreviouslyusedtostudyneutronunbound statesin 9 He[22,23,24]and 27 Ne[25]atGANILbutthiswasthetimeitwasattempted atNSCLwiththeMoNAsetup. The0 + groundstateof 14 Beisdominatedbythe(0s) 2 (0p) 6 (0d 5 = 2 ) 2 and(0s) 2 (0p) 6 (0s 1 = 2 ) 2 asshowninTable1.1.Thetablealsoliststhetwodominantneutroncon- ofthe3/2 + and5/2 + statesin 15 Be.Itisapparentthataneutrontransferred to 14 Beintothed 5 = 2 orbitalhasalargeoverlapwiththe5/2 + state.Incontrast,inthis pictureitisnotpossibletotransferaneutrontothed 5 = 2 orthes 1 = 2 orbitaland coupleittothe0 + statetoforma3/2 + state. Thepossibledecaypathsofthesetwostatesbackto 14 Bearedeterminedbythespectro- scopicfactorswhicharelistedinTable1.2.Thespectroscopicfactorsconsiderallneutron ineachstateandnotjustthedominantshowninTable1.1. The3/2 + stateispredictedtohaveamuchweakeroverlapwiththegroundstatein 14 Be, butamuchstrongeroverlapwiththeexcitedstatein 14 Be.Thisindicatesthatifthe 3/2 + stateof 15 Beispopulatedandifitisunboundbymorethantheenergyforthe 4 Table1.1:Thetwoneutronwiththelargestcontributions tothegroundstatein 14 Beandthetwoloweststatesin 15 Be IsotopeJ ˇ 0s 1 = 2 0p 3 = 2 0p 1 = 2 0d 5 = 2 1s 1 = 2 0d 3 = 2 Contribution 14 Be0 + 24220046% 14 Be0 + 24202033% 15 Be3/2 + 24230042% 15 Be3/2 + 24221037% 15 Be5/2 + 24230047% 15 Be5/2 + 24212025% excitedstate,1.54MeV[26],itwillpredominantlydecaythroughtheexcitedstateof 14 Bewhichwillsubsequentlydecayto 12 Be.Thepredicteddecaypathisshowninthelevel schemeofneutronrichberylliumisotopesinFig.1.2.The5/2 + stateispredictedtohave astrongoverlapwiththegroundstateof 14 Beandwillbestudiedinthisthesis. Table1.2:SpectroscopicFactor(SF)fordecayingtothegroundandexcitedstate of 14 Be, ` correspondstotheangularmomentumofthedecayedneutron. Statein 15 Be ` 0 + SF2 + SF 3/2 + 000.084 3/2 + 20.0431.28 5/2 + 000.15 5/2 + 20.660.096 1.2PreviousWork Previously,littlewasknownexperimentallyabout 15 Be.Ithasneverexplicitlybeenfoundto beunbound.Theheavierisotone 16 Bisunbound[27,28];itcanthusbededucedthat 15 Be alsoisunboundwithrespecttoneutronemission.Thepreviouslymentionedtwo-proton removalreactionwasexpectedtopopulatepredominantlythe3/2+statebecauseithad 5 beenshownthatthespinandparityofthegroundstateof 17 Cis3/2 + [30,31,32].This suggeststhatwhentwo-protonsareremovedfrom 17 Ctheremainingneutronsshouldhave thesameThus 17 Cwillhaveastrongoverlapwiththe3/2 + stateandnotthe 5/2 + stateof 15 Be.Fromthenon-observationofany 14 Befragments,itwasconcludedthat anypopulatedstatesof 15 Bemustbelocatedabovetheunboundexcitedstateof 14 Be, 1.55MeV[26],andthusdecaybytheemissionofthreesequentialneutronsinto 12 Be.The non{observationalsothetheoreticalpredictionsthatthe3/2 + statehasastrong spectroscopicoverlapwiththeexcitedstatein 14 Be. 1.3PopulatingandObserving 15 Be Asmentionedearlier,atmethodforpopulatingthe 15 Bestatesotherthanthetwo- protonremovalfrom 17 Chadtobefound.Thereactionselectedinthepresentworkwas neutronpick{upfromthetargetbythesecondarybeamof 14 Beforming 15 Be.Theneutron willtransfertothe 14 Becoreandisexpectedtostronglypopulatesingleparticlestatessuch asthe5/2 + stateof 15 Be. Topredicttheratethatthe5/2 + statewouldbepopulatedinthisreaction,thecoupled channelreactioncode fresco [33]wasemployed.Theexampleinputforatransfer reactiononpage446fromRef.[34]wasmotoaccountforthetinitialand isotopes,alongwithchangingtheopticalpotentials.FRESCOrequiresopticalmodel potentialsbetween 14 Beand 2 H, 14 Beand 1 H,and 15 Beand 1 H.Theparametersusedare listedinAppendix.Thecalculationwasdoneusingasingleprotonglobalopticalpotential [35]andseveraltdeuteriumglobalopticalpotentials[36,37,38];whichresultedin acrosssectionof1{2mbforthe5/2 + state. 6 Chapter2 ExperimentalTechniqueandSetup 2.1InvariantMassSpectroscopy Theneutron-unboundstatein 15 Bedecaysthroughneutronemission,aprocesswhichhap- pensonanincrediblyshorttimescale( ˘ 10 21 s).Thedecayproductsaretheresidual chargedfragmentandtheneutron.Thedecayenergyofthestatein 15 Beismeasuredusing atechniquecalledinvariantmassspectroscopywhichisderivedfromtheconservationofthe relativisticfour-momentum, P : P =( E;~p ) : (2.1) E isthetotalenergy,and ~p thethree-vectormomentum.Conservationof P isexpressedas: P i = P f + P n (2.2) wherethesubscripts i , f ,and n refertotheinitialnucleus,residualnucleus,andtheemitted neutron,respectively.SquaringbothsidesofEq.2.2yields: P i 2 =( P f + P n ) 2 M 2 (2.3) where M isastheinvariantmassofthesystem.Equation2.3canbeexpressedas: 7 M 2 =( E f + E n ) 2 k ~p f + ~p n k 2 (2.4) ByexpandingandtakingthesquarerootofEq.2.4,theexpressionfor M becomes: M = q m 2 f + m 2 n +2( E f E n p f p n ) : (2.5) where istheanglebetweenthefragmentandneutron.Bysubtractingthemassesofthe decayproductsfromEq.2.5,anexpressionforthedecayenergycanbefound: E decay = q m 2 f + m 2 n +2( E f E n p f p n ) m f m n : (2.6) Inordertomakeameasurementofthedecayenergy,asexpressedinEq.2.6,itis necessarytomeasuretheenergyandangleoftheresidualfragmentandtheneutronasthey leavethetarget.ThemethodforcalculatingthesevariablesisexplainedinSection3.4. 2.2BeamProduction Statesin 15 Bewerepopulatedutilizingasecondary 14 Bebeamwhereaneutronwaspickedup fromeitherthecarbonordeuteriuminthedeuteratedpolyethylenetarget. 14 Beisradioac- tivewithahalflifeof ˘ 4ms[39],andwasproducedwiththemethodoffastfragmentation [40]. AdiagramofthebeamproductionmechanismisshowninFig.2.1.Astablebeamof 18 Oisacceleratedto120MeV/uintheNSCLcoupledK500andK1200cyclotrons [41].Itthenimpingesonaberylliumtargetwithathicknessof3196mg/cm 2 .Thebeam undergoesreactionswithinthetarget,producingalargevarietyofisotopes.Thesereaction 8 Figure2.1:Diagramofthebeamproductionmechanism.Theprimarybeamof 18 Ois acceleratedthroughtheK500andK1200untilitreachesanenergyof120MeV/uand strikesa3196mg/cm 2 berylliumtarget.TheA1900fragmentseparatorthenselects 14 Be fragmentsfromotherreactionproducts. productspassthroughtheA1900fragmentseparator[42]whichselects 14 Bebasedonthe magneticrigidity, Bˆ = p=q .A1050mg/cm 2 achromaticaluminumwedgeislocatedafter theseconddipoletodispersereactionproductsandimproveseparation.Slitsarelocatedat theintermediatefocalplane,whichallowsforselectingtmomentumacceptancesfor theA1900.Themomentumacceptancewasinitiallysetto0.5%.Toincreasethebeamrate, themomentumacceptancewaschangedto2%forthe80%ofproduction.The 14 Be secondarybeamwasfocusedbeyondthetarget,inordertoincreasetheacceptance,withan energyof59MeV/u. 2.3ExperimentalSetup AdiagramoftheexperimentalsetupisshowninFig.2.2.AttheendoftheA1900fragment separator,thebeampassesthroughthe(notshown)oftwoplasticscintillatorswhich 9 Figure2.2:Diagramoftheexperimentalvault.Itshowstheplacementofthetarget, quadrupoletriplet,Sweepermagnet,andthedetectors. provideameasurementofthetimeofht.Beforethesecondtimingscintillatorthebeam passesthroughaquadrupoletriplet,whichfocusesthebeamontothereactiontarget.The primarytargetwasmadeofdeuteratedpolyethylenewithathicknessof435mg/cm 2 which wasusedfor85%oftheexperiment.Thesecondarytargetwhichwasusedfor15%ofthe experimentwasa308mg/cm 2 carbontarget. Afterthebeamunderwentreactionsinthedeuteratedpolyethylenetarget,itisnecessary tomeasureboththeresidualchargedfragmentsandtheneutrons.Theneutronscontinue travelingatnearlybeamvelocityandarerecordedusingtheModularNeutronArray(MoNA) 10 [43,44]whichwassplitintotwosections,centeredat-6 and23 .Chargedfragmentsalso continueatnearlybeamvelocity,butareawayfromzerodegreesbyadipolecalled theSweepermagnet[45]withabendingangleof43 ,aradiusofonemeter,andamaximum rigidityof4Tm.Ithasalargeverticalgapof14cm,whichallowstheneutronstotravel toMoNAuninhibited.Themagnetwassetto3.55Tmtooptimizetransmissionfor 14 Be reactionproducts.Afterthemagnetthechargedparticlespassthroughtwopositionsensitive CathodeReadoutDriftChambers(CRDC)andathinplasticscintillatorbeforestoppingin athickplasticscintillator. 2.3.1ChargedParticleDetection Aspreviousmentioned,theincomingtimeoftismeasuredbytwoscintillatorswhich allowsforremovalofcontaminantswithanalysis.Thedetectorislocatedat thefocalplaneoftheA1900fragmentseparatortheseconddetectorislocated104cm upstreamfromthereactiontarget,resultinginatotaltpathof10.44m.Whena chargedparticlepassesthroughaplasticscintillator,itcreateselectron{holepairs,which recombinecreatingphotons.Thephotonsarethencollectedinaphoto-multipliertube (PMT)thatisopticallycoupledtotheplastic.ThePMTconvertsthephotonsintoan electricalsignalandthenitsothatitcanberecorded.Thedetectionprocess happensonafasttimescale,allowingforadetectionresolutionofunderonenanosecond. TheA1900scintillatoris1008 mthick,whereasthetargetscintillatoris254 mthick. EachscintillatorismadeofBC{404(H 10 C 9 )[46]andiscoupledtoasinglePMTwhichthen feedsthesignalintoaconstantfractiondiscriminator(CFD). Todeterminethevectorofthechargedparticleafterthesweepertwopositionsensitive Cathode{ReadoutDriftChamber(CRDC)areused.AschematicofaCRDCisshownin 11 Figure2.3:SchematicofaCathode-ReadoutDriftChamber(CRDC)(adoptedfromRef. [47]). 12 Fig.2.3.TheCRDCshaveanareaof30X30cm 2 andarewith80%CF 4 and20% iso{butaneatapressureof50Torr.Whenchargedparticlespassthroughthegasitionizes someofthemolecules,releasingelectrons.Theelectronsaresubjecttoa-850Vdriftvoltage, causingthemtodriftupwardstoananodewirewhichcollectsthecharge.Theanodewire isheldat+950V.Locatedneartheanodewireare128aluminumpads,spaced2.54mm apartfromeachother.Thechargecollectedontheanodewireinducesachargeonthese pads. Thedispersivepositionisdeterminedusingthedistributionofthechargecollectedon thealuminumpads.Thechargecollectedoneachpadisplottedasafunctionofpadnumber andwithagaussiantodeterminethecentroid.Thecentroidisthenconvertedfrom padspaceintophysicaldimensionsusingalineartransformation.Theverticalpositionis determinedbythetimebetweentheanodesignalandthemastertrigger. DownstreamofthetwoCRDCsaretwoadditionalplasticscintillators,alsomadeof BC-404,coveringa40X40cmarea.Duetotheirlargearea,theybothusefourPMTs couplednearthecornerslabeledasthin LU ,thin LD ,thin RU ,andthin RD ,respectively.The upstreamscintillatoris0.5cmthickandthedownstreamscintillatoris15cmthick.The thinscintillatorisusedforenergylossandtiming,whereasthethickscintillatorstopsthe chargedfragmentandgivesanindicationofthetotalenergy. 2.3.2NeutronDetection MoNAconsistsof144barsofplasticscintillator,eachmeasuring200cmX10cmX10cm. EachbarismadeofBC-408,whichhasahydrogentocarbonratioof1.104[46].Bothendsof abararecoupledthroughalightguidetoaPMT.ThemodularnatureofMoNAallowsfor multipleInthisexperimentMoNAwassplitwithninewallslocated650cm 13 fromthetargetat-6 with8barsineachwall.Therestofthebarslocated470cmfrom thetargetat23 weresplitintotwogroups,withthefourwallsseparatedby60cm fromthelastewalls.Likewiseeachwallconsistsofeightbars.Thesplit waschosentoachievethelargestpossibleacceptancefortheexpectedlargedecayenergyof 15 Be. Neutrons,duetotheirlackofelectricalcharge,cannotdirectlyexcitetheelectronsof thescintillatingmaterialofMoNA.WhenneutronspassingthroughMoNAhitaproton, thatprotonisthendislodgedfromthelatticeinthebarproducingscintillationlight.Then, thelighttravelsalongthebaruntilitiscollectedbybothPMTs.Thelightiscollected andbyeachPMTandthenconvertedintoanelectricalsignal.Theanodesignal isfedintoaCFD,whichthensendsapulseintoatime{to{digitalconverter(TDC).The timebetweenthetargetscintillatorandtheTDCsignalisusedtodeterminethe neutron'stimeoftfromthetargettoMONA. 2.4ElectronicsandDataAcquisition Theelectronicsanddataacquisition(DAQ)ofthesetuphavebeendescribedextensively inRef.[47,48].Inthissection,thetimingcomponentsalongwiththeinterplaybetween theSweeperandMoNAsetupwillbediscussed.AdiagramoftheelectronicsandDAQfor runningMoNAandtheSweepersetupisshowninFig.2.4. ThetriggerlogicishandledbyprogrammableXilinxLogicModules(XLMs),whichare separatedinto\Level1"and\Level2".Level1determinesifagoodeventhasoccurredin MoNAandthenpassesthatinformationontoLevel2.Agoodeventoccurswhenthereis atleastonebarthathasavalidtimesignalinbothCFDs.TheLevel2thenwaitsfora 14 Figure2.4:Schematicdiagramofthetimingelectronics,logicmodules,andDAQ.Ifthereis avalideventinMoNA,theLevel1logicmodulesendsasignaltotheLevel2logicmodule whichwaitsforasignalfromthethinLUtodetermineifthereisavalidcoincidence.Ifthere isavalidcoincidence,Level2sendsasignaltotheDAQtoreadoutalloftheelectronics. IfthereisnocoincidenceintheLevel2sendsoutasignaltofastcleartheelectronics. 15 triggersignalfromtheSweeperside,withthetriggerfortheSweepersidecomingfromthe thin LU .OncetheLevel2hasacoincidencefrombothMoNAandtheSweeperitsendsthe signalfortheDAQtoreadoutthedataintheelectronics. Thesignalfromthin LU issplitintotwosignals.ThesignalistheSweepertrigger thatgoestotheLevel2.ThesecondsignalgoestotheSweeperTDCandprovidesthe stopsignalforalltheTDCs.ThestartsignalfortheTDCscomesfromalltheothertiming scintillatorsintheSweepersetup.Thescintillatoratthetargetisalsosplit.Thesignal goestotheSweeperTDCaspreviouslydiscussed.ThesecondsignalissenttoMoNAand isusedasthestopsignalforMoNA'sTDCs. 16 Chapter3 DataAnalysis 3.1CalibrationandCorrectionsoftheCharged ParticleDetectors 3.1.1ScintillatingDetectors TherelativetimebetweenthebeampassingthroughtheA1900,target,andthinscintillators isusedtoselectfortheincoming 14 Be,andisotopeseparationafterthesweepermagnet. Elementselectionisperformedusingthethinandthickscintillatorwhichrecordthe E and E total ,respectively.Eachofthetimingdetectorsalongthebeam-lineandinthefocal planeboxrecordthetimeofinteractionrelativetothemastertrigger(thin LU ).Thetime ofinteractionforeachPMTiscalculatedby: t cal =( t raw t raw thin LU ) 0 : 1 ns ch + t (3.1) where t raw isthetimingsignalfromtheA1900,thetarget,orthefourPMTsinthethin scintillator. ThethinscintillatorusesfourPMTs,unliketheA1900andtargetscintillatorswhich onlyuseasinglePMTeach.ThetimefromeachPMTisaveragedtodeterminetheproper time.AbeamdowncenterrunisusedtotheofeachPMTwithrespecttothe 17 Figure3.1:Scintillatorcharge(energy)spectra.Thetoptwoplotsarefromthethindetector, whilethebottomtwoarefromthethickscintillator.Theeventsweregatedsothatonlyone isotopewaspresentalongwiththebeambeingcenteredinbothdetectors.Theleftplots showtherawenergycollectedwhiletherightplotsshowthefourPMTsaftergainmatching. ThethinandthickLU,RU,LD,andRDarerepresentedbythecolorred,black,blueand green,respectively. referencePMT(thin LU ). Thecalibrationoftheenergyforthethinandthickplasticscintillatorsrequiresgain matchingandpositioncorrection.DuetoinstabilityinthePMTsitwasnecessarytoalso correctfordriftsintime.Thestepistogainmatchwhichrequiresthatthelight attenuationbethesameforeachofthePMTs.Tomeetthisrequirementitwasnecessary toselecteventswheretheinteractionwasinthecenterofthescintillators.Thesignalof eachPMTwaswithagaussian,andacorrectionfactordeterminedtomovethecentroids tochannel800and1000forthethinandthickscintillator,respectively.Theleftsideof 18 Figure3.2:Uncorrectedthickleft-upenergy(leftpanel)andafterthetimecorrectionfactor hasbeenapplied(rightpanel)plottedagainsteventnumber.Thecorrectionfactorswere determinedforeachofthePMTforthethinandthickscintillators. Fig.3.1showstherawenergyforthefourPMTsinthethin(top)andthethick(bottom) scintillator,whiletherightsideshowsthegainmatchedenergy. TocorrectforthedriftsintimeforeachPMT,thedatawasbrokeninto10,000blocks. Thecentroidofeachblockwasfoundbywithagaussianandacorrectionfactor determined.ThecorrectionfactorwasthenappliedtotheenergycollectedbyeachPMT onaneventbyeventbasis.Figure3.2showstheuncorrectedthickright-up(leftpanel)and onceithasbeencorrectedfordriftsintime(rightpanel).Thecorrectionfactorsvariedby 3{10%and8{20%forthethinandthickscintillators,respectively. AftereachPMThasbeengainmatchedandcorrectedfordriftsintime,thedeposited energyiscalculatedusing: E dep = q e 2 top + e 2 bottom 2 (3.2) where e 2 top and e 2 bottom aretheaveragedenergyfromthetopandbottomtwoPMTsforthe thickandthinscintillators.Thescintillatorenergyisleftinarbitraryunits,sincetheyare onlyusedtoselectfortreactionproducts. Thestepistoremoveanycorrelationsbetweenhorizontalandverticalpositionofthe 19 Figure3.3: E fromthethinscintillator(leftpanel)andcorrected E (rightpanel)is plottedagainstthehorizontalpositionofthedetector.ThecorrectionisZdependent,thus itonlystraightenstheberylliumband. interactionandthecalculatedenergy.Athirdorderpolynomialwasusedandthecorrection factorsarelocatedinTable3.1. Table3.1:Thinandthickpositioncorrectionfactors 1storder2ndorder3rdorder ThinHorizontal1.420.0377-3.68 10 5 ThinVertical1.005-0.01997.52 10 5 ThickHorizontal-2.53-7.63 10 4 -3.24 10 5 ThickVertical-1.1730.00.0 Figure3.3showstheuncorrected(leftpanel)andthecorrected(rightpanel)thinenergy plottedagainstthehorizontalposition.Thecorrectionsusedwere Z dependentandwere onlyoptimizedforberyllium. 3.1.2CRDCs AsexplainedinSection2.3.1theCRDC'shorizontalandverticalpositionaredetermined fromthechargedistributiononthepadsandthetimencefromthestart(master trigger)andthestop(CRDCanodewire)signals,respectively.EachpadoftheCRDCs issampledeighttimesandtheresultingchargeissummedtodeterminethetotalcharge 20 Figure3.4:CRDC2rawchargecollectedvaluesforeachpadfromasweeprunthatillumi- natedtheentirefaceofthedetector. collectedduringeachevent.Tocalibratethehorizontalpositionitisnecessarytodetermine thepedestals.Forthispurposedatawasrecordedwherenosignalswerepresentinthe CRDCs;thepedestalswerethencalculatedbythetotalchargewithagaussian. Oncethepedestalsaresubtractedeachpadneedstobegainmatched.Thestrengthof themagneticoftheSweepermagnetwasvaried,illuminatingtheentireCRDC2.The chargecollectedforeachpad,whenitcollectedthemostcharge,waswithagaussian andacorrectionfactorwasdeterminedtomovethepeaktotheaveragevalueforallpads. Thecorrectionfactorsneededwerewithin20%oftheaveragevalue.Fig3.4isaplotofthe rawchargecollectedforeachpadofCRDC2,whereasFig3.5showsthecalibratedcharged collectedforeachpad. Certainpadsdisplaychargecollectioncharacteristicsthatarenotindicativeofactual events.Thesepadsaretypicallynoisypadsandneedtoberemovedfromanalysis.The chargecollectedforeachpadwasexaminedandthenoisypadswereremovedfromfuture 21 Figure3.5:CRDC2calibratedchargecollectedforeachpadfromasweeprunthatillumi- natedtheentirefaceofCRDC2.Thepedestalshavebeensubtracted,andeachpadhas beengainmatched. analysis.CRDC1pads96-110hadtoberemovedfromanalysis.Fortunatelythesepads werenottypicallyilluminated.CRDC2hadtwobadpads,24and89. Todeterminewhichpadtheinteractionwasclosestto,aoftheplotofchargecollected bypadnumberwastwithagaussian.Thegaussiancanstillaccuratelythecentroidof theinteractionevenifittookplacenearabadpad.Theverticalinteractionisdetermined byusingaTACwhichrecordsthetimebetweenthestart(thinleft-up)andthe stop(CRDCanodewire).Fig3.7showsaplotofTACvsbestpadtforamaskrunof CRDC2. Nowthatthepedestalshavebeensuppressedandeachpadhasbeengainmatched,itis necessarytodeterminetheslopeandrequiredtoconvertthepadspaceandtacdata andintophysicalunitsofposition.Atungstenmaskwithholesdrilledintoknownlocations wasinsertedinfrontofeachCRDC,shadowingthedetector.Theincomingbeamwasthen defocusedandsweptacrossthefocalplanetoilluminateasmanyholesaspossible.The 22 Figure3.6:CRDC1calibratedchargecollectedforeachpadfromasweeprunthatillumi- natedtheentirefaceofCRDC2.Thepedestalshavebeensubtracted,andeachpadhas beengainmatched.Thecolorrepresentsthenumberofcountsperbin. Figure3.7:ExamplemaskrunforCRDC2.Thebest(padnumber)isplottedvsTAC. Theholesareeasilyidenandgateswereappliedaroundeachoneandthecentroida gaussianwasusedtothecentroidinTACandbestt(padnumber). 23 Figure3.8:ExamplemaskrunforCRDC2aftercalibration,CRDC2x(mm)isplottedvs CRDC2y(mm). conversionfrompadspacetophysicalunitsisasimplelineartransformationusingthepad spacingof2.54mm/pad.Todeterminetheslopeandfortheverticalaxis,alongwith thehorizontalaxisthecentroidfortheholesinpadspacevstacwereconvertedinto physicalunits.AsamplemaskrunisshowninFig.3.7. DuringtheexperimentthemasksweredriveninforeachCRDCatthreeseparateocca- sions.Theresultsforbothdetectorswereconsistentwiththeaveragevaluesfromthethree runs,andwerethenusedfortheentireexperimentalrun.Thevaluesdeterminedforthe verticalslopeandalongwiththehorizontalareshowninTable3.2.Fig3.8is anexampleplotdemonstratingthatthelineartransformationfromtacandpadspaceinto physicalspacehasbeenaccomplished. Table3.2:CRDCsslopesand DeviceYslope(mm/ch)Y(mm)X(mm) CRDC1-0.135137.74-175.21 CRDC2-0.135125.78185.14 24 3.2MoNACalibrations 3.2.1EnergyCalibration Duetoinlighttransmissionthroughtheplasticbarsandofthe PMTs,eachPMTmustbeindividuallygainmatched.Thisisdonewithcosmicmuons whichdepositonaverage20.5MeVeeofenergyintoeachMoNAbar.Onlinegainmatching isusedtomovethecosmicmuonpeaktoapproximatelythesamechannel.Figure3.9shows anexamplehistogramwherethecosmicmuonpeakisatapproximatelychannel900. OncethebiasvoltageforeachPMThasbeenadjustedtolineupthemuonpeaks,a softwareroutineisappliedtothesignalfromeachPMTtoacquiretheslopesand necessarytoconvertfromchannelstounitsofMeVee.Theautomatedroutinethe pedestalvalueandthemuonpeakiswithagaussian.Thecentroidisusedtodetermine theexactchannelofthemuonpeak.Alinearslopeandisthenderivedtoplacethe pedestalatzeroandthemuonpeakat20.5MeVee[49]. 3.2.2TimingCalibration TodeterminetheslopesfortheTDCsinMoNA,atimecalibratorthatsendsasignalevery 40nswaspluggedintothemodules.TheaverageofbothPMTswastakentoderivethe timeofinteraction.FromthispointitisnecessarytodeterminetwoTheisthe individualforeachbarrelativetoareferencebar.Thiswillmakethewholearray's timingself-consistent.Thesecondisaglobalthattiesthearraytogetherwith thereactiontarget. CosmicmuonsareusedtodeterminetheindividualThemuonsareproduced intheupperatmospherefromcosmicraysandaretravelingatnearlythespeedoflight, 25 Figure3.9:ExamplerawQDCspectraforasingleMoNAPMT.Thecosmicmuonpeak canbeseenatapproximatelychannel900,room -raysarelocatedatchannel250andthe pedestalisnotpresentsinceithasbeenalreadysuppressed.Forthelinearcalibrationthe pedestalwassettozeroandthecentroidofthecosmicmuonpeakwassetto20.5MeVee. 29.9cm/ns[50].Theindividualisdeterminedinatwostepprocess.First,eachwallis tiedtogetherusingmuonsthataretravelingmostlyvertical.Toaccomplishthisagatethat requiresall8barsinawallhaveeventsisused.Todeterminetheexpectedtime, t ,between thetopbarandthebarinquestionEq.3.3isused,where n isthenumberofbarsbetween thetwobars,10.3cmistheaveragedistancebetweenthecenteroftwoadjacentbarsand 29.9cm/nsistheaveragevelocityofamuonatthesurfaceoftheearth.Appropriate arethendeterminedbycomparingtheexpectedtimefromEq.3.3andthemeasuredtime t = n 10 : 3 cm 29 : 9 cm=ns (3.3) Todeterminetheforeachwall,itisnecessarytolookatdiagonalmuontracks. Eachwallwastiedtothetopbarinthefrontwallbydiagonalmuontracks.Thisallowed 26 forforeachwalltobedetermined.MoNAwassplitintotwoseparatearrays,with eacharraybeingseparatedbyalargeenoughdistancethatitwasimpracticaltomuons thathitbotharrays.Thusitwasnecessarytogiveeacharrayatglobal Todeterminetheforeacharray,prompt -raysmadeinthetargetwereselected. Theexpectedtimeoftwasthendeterminedusing: ToF = d 29 : 98 cm=ns (3.4) where d isthedistancefromthetargettowheretheinteractiontookplaceincm. Theglobalforbotharraysweredeterminedbycomparingtheexpectedtimeof tofthe -rayswiththemeasuredtimeoft.Forlowenergy -raysthereisawalk despiteusingconstantfractiondiscriminators(CFD).ThewalkwascharacterizedinRef. [51];above2.5MeVeethewalkwasalmostnon-existent.Tocompensateforthewalka gateof3MeVeewasappliedwhendeterminingtheglobalforbotharrays.Toremove contaminationofunreactedbeamarrivingincoincidencewithroom -rays,agateof3MeVee wasappliedtothedataset.Thisremovedthenecessityofcorrectingforthelowenergywalk oftheCFDs. 3.2.3PositionCalibration Todeterminetheenergyandmomentumoftheneutronitisnecessarytoknowwherethe neutroninteractedwithinMoNA.Alasersightingsystemwasusedtodeterminewherethe frontfaceofbotharrayswerelocatedrelativetothetarget.Thenextstepwastodetermine wherealongthebartheinteractiontookplace.Thetimebetweentherightandleft PMTisdirectlyrelatedtothelocationinthebarwheretheinteractiontookplace.InFig. 27 Figure3.10:Exampletimebetweentherightandleftsidesofabarfromacosmic muonrun.Theedgesofthebarareeasilyidenwhichallowsforalinearcalibrationto determinetheslopeandThisallowsforthedeterminationofwheretheeventtook place. 3.10,thetimeerencebetweentherightandleftsignalisplotted.Fromthishistogram, alinearcalibrationisusedtodeterminetheslopeandnecessarytodeterminewhere alongthebartheinteractiontookplace. 3.3EventSelection Duringtheexperiment,foreveryeventofinterest,itwasnecessarytorecordapproximately 10,000events.Theeventsofinterestarewhenthe 14 Bebeampicksupaneutronfromthe deuteratedpolyethylenetargetforming 15 Be,whichthendecaysbackdowntotheground stateof 14 Be.Ifinsteadofdecayingtothegroundstateitdecaysintotheexcitedstate of 14 Beat1.54MeV[26],itwillcascadedowninto 12 Beandisofnointerestinthisanalysis. Thissectionwilldetailtheeventselectiongatesusedtoselectforthereactionprocessof interest. 28 Figure3.11:FlighttimefortheincomingbeamfromtheA1900timingscintillatortothe targetscintillator.The 14 Beiscenteredaround173ns,withthebiggestcontaminantcoming fromlithiumwhichiscenteredat161.5ns. 3.3.1IncomingBeamIden Figure3.11showsthettimebetweenthescintillatorinthefocalplaneoftheA1900 fragmentseparatorandthetargetscintillator.Thisparameterwasusedtoselectforincoming 14 Be.Theprimarycontaminantwaslithiumwhicharrivedat ˘ 10nsbefore 14 Be.These twocomponentsareeasilyseparatedbytheintheirtimeoftbetweenthe a1900scintillatorandthetargetscintillator. 3.3.2CRDCsChargeCollectionGate Toseparatetheisotopesalongwithreconstructingthefragment'senergyandmomentumat thetarget,itisnecessarytohaveaccuratehorizontalpositioninformationinbothCRDCs. ToaccomplishthisitisnecessaryforbothCRDCstohavetchargecollected;which allowsforanaccuratemeasurementofthepositionoftheinteraction. 29 Figure3.12:CRDC1padsumplottedagainstCRDC2padsum.Nogateswereappliedto thisplot.TheblacklinecorrespondstothegateusedtoselectforgoodpadsuminCRDC1 andCRDC2. Figure3.12showsaplotofCRDC2padsumvs.CRDC1padsum.Theblacklineshows thegateappliedtoselectforgoodchargecollectioninbothCRDCs.TheCRDCscharge collectionisdependentonthechargeoftheincomingbeamandinthisexperimentthey werealsousedasapoorelementgatealongwithprimarilybeingusedtorequireagood horizontalinteractionpoint. 3.3.3ElementIden Elementseparationwasachievedbyplottingthecorrected dE fromthethindetectoragainst thetimeoftfromthetargettothethindetectorasshowninFigure3.13.Beryllium, lithium,andheliumarecleanlyiden 3.3.4IsotopeIden TheSweepermagnet,withitslargetotalmomentumacceptanceof12.6%alongwithits inabilitytofocusthefragmentsinposition,makesittoachieveisotopeseparation. 30 Figure3.13:Elementidenisdeterminedusingthetimeoftbetweenthetarget andthinplasticscintillatorvsenergylossinthethinplasticscintillator.Theelements presentareidenintheplot. Toachieveisotopeseparationitisnecessarytounderstandthecorrelationsbetweenthe dispersiveposition,dispersiveangle,andthetimeoftbetweenthereactiontargetand thethinscintillator. Thestepistomakeaplotofthetimeoftbetweenthereactiontargetandthe thinscintillatorvs.dispersiveanglevs.dispersiveposition,atthefocalplaneoftheSweeper magnet.Thefocalplaneislocated0.657mbeforeCRDC1.ThisisshowninFigure3.14; theplotrequiresthatbothCRDCshavegoodpositioninformationalongwiththatonly berylliumispresent.Theisotopebandscanbeidenbutitisimpracticaltomakea threedimensionalgate. Onceisotopebandscanbeseeninthethreedimensionalplotitisnecessarytoproject itontothedispersiveangleandpositionplane,asshowninFig.3.15,wherethecolor correspondstothetimeoftbetweenthereactiontargetandthinscintillator.Inorder tounderstandthecorrelationsbetweenthedispersiveangleandpositionaalongaband 31 Figure3.14:Threedimensionalplotofthetimeoftfromthereactiontargettothethin scintillatorvs.dispersiveangleatthefocalplanevs.dispersivepositionatthefocalplane. Theplotonlycontainsberylliumisotopes.Thebandscorrespondtotisotopeswith themostintensebeing 14 Be. ofequaltimeoft,asshowninFigure3.15,isnecessary.Thegivesthecorrelation betweenfocuspositionandangletobe: xtx = x;focus 0 : 911 x focus 0 : 00585 x 2 focus 6 : 27 10 5 x 3 focus (3.5) Theparameterxtxwhenplottedagainstoftimeoftbetweenthereactiontargetand thethinscintillatorallowsforisotopeseparationasshowninFigure3.16.Eachisotopeis cleanlyidenalongwiththegapwhere 13 Beshouldbeifitwasnotneutronunbound. TheunreactedbeamisideninFig.3.16;itwasnecessarytoapplyacuteliminating theunreactedbeamtoreducethecontaminationfromunreacted 14 Be.Thiscutisshown bytheblackline. 32 Figure3.15:ProjectionofFigure3.14wherethecolorcorrespondstotimeoftbetween thereactiontargetandthethinscintillator.Abandofequaltimeoftisto constructaparameterdescribingthecorrelationsbetweenthedispersiveangleandposition. Figure3.16:Theparameterxtxversustimeoftbetweenthereactiontargetandthe thinscintillator.Isotopesareidenontheplot,alongwithwheretheunreactedbeam andreactionproductsarelocatedfor 14 Be.Theblacklinecorrespondstothegateusedto removecontaminationofunreacted 14 Be.Inordertoreducetheintensityoftheunreacted beam,agateonbeamvelocityneutronsinMoNAwasapplied. 33 3.3.5NeutronIden MoNAdeterminesthetime,location,andenergydepositedforeachinteractionwithinone ofitsbars.InpreviousMoNAexperimentswhichpredominantlyutilizedone-ortwo-proton removalreactions,thetspectrawerecleanandcontainedonlybeamvelocity neutronsfromthedecayofpopulatedstates.However,inthepresentcaseofaneutron pick{upreactionwherethedecayproductisthesameastheincidentbeam,at backgroundfromrandomcoincidencesisobserved. Figure3.17showsthetimeoftversustheenergydepositedinMoNA.This wasgatedonidenberylliumisotopes.Thelargetriangularareabetween50and80ns andreachingupto80MeVeecorrespondstobeamvelocityneutronsfromthedecayof neutron{unboundberylliumfragments.No {raysoriginatingfromthetarget,whichwould appearat21ns,arevisible.Instead,astrongpeakat60nsdepositinglessthan5MeVee wasidenas {raysoriginatingfrominsidethefocalplanebox.Inadditiontwotime- independentbroadbackgrounddistributionscanbeobserved.Thebandthatdepositsless then3MeVeecomesfromroombackground {rays,whereasthebandthatdeposits20to 30MeVeeisduetocosmicmuons. TheprojectionofFig.3.17ontothetaxisisshowninFig.3.18asthe blackdatapoints.Itisdominatedbybeamvelocityneutronsaround70ns.Theshoulder atshortertimesisduetothe -raysfrominsidethefocalplanebox.Whenanadditional gateon 14 Befragmentsonlyisapplied(reddatapoints),themajorityofthebeamvelocity neutronsdisappearindicatingthattheyoriginatepredominantlyfrom 12 Be.Nowthe -rays fromthefocalplaneboxarethelargestpeakwithanadditionalenhancementatlongertimes ( ˘ 90ns)becomevisible.Theseeventscouldbeduetoneutronsemittedfromthetargetor 34 Figure3.17:EnergydepositedinMoNAversusthetimeoft.Theplotonlycontains eventswhereanyberylliumisotopewasidenaftertheSweepermagnet. fromthebeamhittinginsidethefocalplanebox. Figure3.18:Neutrontimeoftspectrum.Theblackdatapointsrepresentthetimeof tforallberylliumisotopeswhereasthereddatapointsareincoincidencewith 14 Be fragments. Thebackgroundcanbefurtherreducedbyapplyingthegateon 14 Bereactionproducts fromFigure3.16.ThisgatehasbeenappliedfortheblackdatapointsinFigure3.19and eliminatesthefocalplane {rays.Remainingcontributionsfromroombackground {rays areremovedbyapplyinganothergateondepositedenergiesinMoNAofmorethan3MeVee. TheresultingtimetspectrumisshownbythereddatapointsinFigure3.19.The 35 Figure3.19:Neutrontimeoftspectrum.Theblackdatapointsrepresentthetimeof tfor 14 BefragmentsthatwereselectedusingthegateshowninFig.3.16.Thereddata pointshaveanadditionalgateondepositedenergiesofmorethan3MeVee. spectrumhasthreedistinctfeatures:promptneutronsfromthed( 14 Be, 15 Be)preaction, slowerneutronsmostlikelyproducedinthetargetorfocalplanebox,andanegligible constantbackgroundofeventsfromcosmicmuonsspreadoutevenlythroughoutthetimeof t.Forthecalculationofthedecayenergyspectrumonlyeventsbetween45and75ns wereselected.Thesamecutisalsoappliedinallsimulations. ThedistributionofthebeamvelocityneutroninthehorizontaldirectionsacrossMoNA isshowninFig.3.20.Thedistributionpeaksaround0 andindicatesneutronsemitted frombeamvelocityfragments.Inaddition,theacceptanceatlargerdistancesislimitedby theverticalgapoftheSweepermagnet.Thegapbetween50and100cmcorrespondstothe gapbetweenthetwopartsofMoNAcenteredat-6 and23 . 36 Figure3.20:ThehorizontaldistributionofneutroneventsinMoNAfromtheformationof 15 Bebyneutronpick{upfromthetarget. 3.4InvariantMassReconstruction Thestrategyofthisexperimentwastouseinvariantmassreconstructiontodeterminethe decayenergyoftheneutronunboundstatein 15 Be.Invariantmassspectroscopywasdis- cussedinSection2.1ingreaterdetail.Theequationusedtodeterminethedecayenergy is: E decay = q m 2 f + m 2 n +2( E f E n p f p n ) m f m n (3.6) wherem f ,E f ,andp f arethemass,energyandmomentumofthefragment,respec- tively.Similarly,m n ,E n ,andp n arethevaluesfortheneutron.Theanglebetweenthe velocityvectorfortheneutronandfragmentis .Fortheneutroncalculatingtheenergy andmomentumistrivial.Theanglecomesfromcalculatingthevectorfromthetargetto theinteractionpoint,andtheenergyandmomentumarecalculatedwith: 37 = 1 1 v c 2 E = mc 2 ~p = m~v (3.7) Determiningtheenergyandmomentumofthefragmentinthetargetismore andrequiresreconstructionofitstrackthroughtheSweeper,asdescribedbelow. 3.4.1TheInverseMap Determiningthefragment'senergyandmomentumatthetargetinvolvestakingparameters fromaftertheSweepermagnetandthentransformingthemintoparametersatthetarget. ThecentralplaneofthemagneticoftheSweepermagnetwasmappedusingsevenHall probes,mountedvertically,onamovablecart.Thecartwasmovedthroughouttheentire areaofthemagnetmappingthemagneticDetailsofthemappingareavailablefrom Ref.[47]. OnceareferenceHallprobemeasurementisrecordedduringtheexperiment,amagnetic mapforthisexperimentisgeneratedusingIGORPRO[52]withthearchivedmea- surements.Theiscalculatedforthemid{planeofthe14cmgapandthenimportedinto COSYINFINITY[53]alongwiththefragment'schargeandmasstoyieldatransformation matrixfromthetargetpositiontothepositionofCRDC1. Thematrix, M 4 ,relatestheparticle'spositionandanglesatCRDC1totheanglesand energyatthetarget.Equation3.8showstherelationsbetweentheparametersattheCRDC1 andthetarget. 38 Figure3.21:Reconstructedkineticenergyspectrumwhichisusedtotesttheinversemap. Thedatacomesfromanotargetrunthatwasbentintothecenterofthefocalplanebox. ThereconstructedenergyisincompleteagreementwiththevaluepredictedbyLISE++of 59MeV/u 0 B B B B B B B B B @ x crdc 1 crdc 1 x y crdc 1 crdc 1 y 1 C C C C C C C C C A = M 4 0 B B B B B B B B B @ target x y target target y E target 1 C C C C C C C C C A (3.8) Toaccomplishthe4-parameterinversionCOSYINFINITYassumesthatthefragment passesthroughthetargetatzero.Thisassumptiondoesincreasetheuncertaintyaboutthe fragment'senergyandangleatthetarget.Toaccountfortheincreaseduncertaintyforthe experimentaldata,thesame4-parametertransformationwasalsousedinthesimulation. COSYINFINITYcreatesthetransformationmatrix, M 4 ,whichconvertsthequantitiesat CRDC1into y target , target x , target y ,and E target . Tochecktheinversemap,datafromwhentheunreactedbeamwasbentintothecenterof 39 Figure3.22:Reconstructedanglespectrumthatisusedtotesttheinversemap.Thedata comesfromanotargetrunthatwasbentintothecenterofthefocalplanebox.The reconstructedangleiscentered,thattheinversemapisworkingproperly. thefocalplaneboxwasused.Thetestoftheinversemapistocomparethereconstructed energytotheexpectedvalue.LISE++calculatestheaverageenergyshouldbe59MeV/u, whichisingreatagreementwiththevaluefromFig3.21. Thesecondtest,whichismoresensitive,istocheckthereconstructedanglewhichshould becenteredatzero.Fig3.22showsthereconstructedangleiscenteredatapproximately zero,forano{targetrunthatwasbentintothecenterofthefocalplanebox. 3.4.2DecayEnergy Thefullreconstructionofboththefragmentandtheneutronsgivesalltheparameters necessarytoperformaninvariantmassreconstructionusingEq.2.6.InFig3.23theblack datapointsgivethereconstructeddecayenergyfor 14 Beandcoincidenceneutrons.The decayenergyspectraisdominatedbyaresonanceatapproximately2MeVandthehistogram containsapproximately700totalevents. 40 Figure3.23:Decayenergyspectrumforcoincidence 14 Beandaneutronisshownbythe blackdatapointswiththeirstatisticaluncertainty.ThespectrumwascalculatedusingEq. 2.6.Aresonancecanclearlybeseenatapproximately2MeV. 3.4.3oftheCarbonintheDeuteratedPolyethylene Adeuteratedpolyethylenetargetwasselectedtomaximizethenumberofnucleithatthe 14 Becouldinteractwith,whileminimizingenergylossinthetarget.Withthedeuterated polyethylenetarget, 14 Becaninteractwitheitheradeuteriumoracarbonatomtoform 15 Be.Toinvestigateanybetweenreactionscausedbyeitherofthesenucleia 300mg/cm 2 carbontargetwasusedforapproximately10%oftheexperiment.Asshownin Fig3.24thedecayspectraforreactionscomingfromcarbon(reddatapoints)anddeuterated polyethylene(blackdatapoints)arestatisticallyidentical.Thisindicatesthatinvariantmass reconstructionisindependentofwhichatomtheneutroncamefrom. 41 Figure3.24:Decayenergyspectrumfordeuteratedpolyethyleneandacarbontarget.A 300mg/cm 2 carbontargetwasusedfor16hours,thedecayenergyforthecarbontarget (reddatapoints)iscomparedtothedeuteratedpolyethylenetarget(blackdatapoints). Thegatesandconditionsusedtoselectandcalibrateforbothtargetswerethesameand theresultsarestatisticallyidentical. 42 Chapter4 Simulations ThedecayenergydepictedinFig.3.23hasthedetectorresolutions,acceptances,andgate conditionsfoldedintotheobservedshape.Toextractresults,twoMonteCarlomethod simulationprogramsareemployed.TheisSTMoNA,whichsimulatesthesecondary beamenergylossinthetarget,thereaction,propagatingtheresidualchargedfrag- mentthroughtheSweepermagnet,andintothechargedparticledetectorsuite.Thesecond isGeant4,whichtakestheneutron'senergyandanglefromSTMoNAatthetargetand propagatesitthroughtheSweeperandintoMoNA.ThisMonteCarlosimulationisusedto understandhowtheneutroninteractswithinMoNA. 4.1STMoNA STMoNAisaMonteCarlosimulationprogram[55].Theinitialparameterssuchasen- ergyanddirectionoftheparticleareinputsintoSTMoNA.Theparticletheninteractsat arandompointwithinthetarget.Forthepresentexperimentaneutronpick-upreaction fromthedeuteriuminthetargetwassimulatedtoastatein 15 Be.Thestateimmediately decaysthroughneutronemissionwiththedecayenergycomingfromanenergydependent Breit-Wignerdistribution,whichwillbedescribedinfurtherdetailinSection4.1.5.The neutron'senergyanddirectionarethenfedintotheGeant4simulation.Thechargedparticle ispropagatedthroughtheSweepermagnetusingaforwardtransformationmatrix(seeSec- 43 tion3.4.1).ThechargedparticlepassesthroughbothCRDCsandintothethinscintillator. Particlesthatfalloutsidethegeometricacceptanceofthedetectorsareeliminatedfromthe analysis.Theoutputdataofthesimulationarerecordedinthesameformasexperimental data,allowingdirectcomparisonbetweensimulationandexperimentaldata. 4.1.1InitialParameters ThebeamparametersusedasinputintothesimulationarelistedinTable4.1;these arethebeamenergy,location(x,y),andincidentangle x ; y ). Table4.1:Thecentroidandwidthofthegaussiandistributionusedtomatchthebeam ParameterCentroid ˙ Energy59.050.0215Mev/u x03mm 04.5mrad y06mm 03.25mrad Thebeamwasdeterminedbyremovingthetargetandmeasuringthebeam's positionandanglesintheCRDCs.InFig.4.1,thedata(blackpoints)arecomparedto theSTMoNAsimulation(blueline)fortheCRDC1horizontalposition,horizontalangle, verticalposition,andverticalangleareshowninthetopleft,topright,bottomleft,and bottomrightpanel,respectively. Oncethebeamwasknownthedeuteratedpolyethylenetargetwasinsertedandthe target'sthicknesswasvarieduntilthelocationinSTMoNAmatchedtheexperimentaldata. ThetargetthicknessnecessarytorecreatetheenergylossinSTMoNAwas435mg/cm 2 whichcomparesfavorablywiththeexpectedthicknessof440mg/cm 2 . 44 Figure4.1:CRDCpositionandanglespectrum.Eachcomparesdata(dot)toST MoNAsimulation(line).Thetopleft,topright,bottomleft,andbottomrightpanelshows thecomparisonfortheCRDC1horizontalposition,horizontalangle,verticalposition,and verticalangle,respectively. 45 Figure4.2:Atechnicaldrawingofthebeam{linefromthetargettothefocalplanebox. ThecentraltracklengthfromthetargettoCRDC1canbedeterminedusingthisdiagram. 4.1.2CentralTrackLengthIssues Afterthebeamewasmatchedwiththebeamsentintothecenterofthefocalplane box,itwascheckedagainststepsweeperswherethemagneticwaschangedtoilluminate theentirefocalplanebox.Nearthecenterthesimulatedstepsweepsmatchedreasonably well;butasthedistancefromthecenterincreasedthediscrepancybetweensimulatedand experimentaldatabecameapparent.Themapsusedinpropagatingthechargedparticlesin STMoNAfromthetargettoCRDC1andtoreconstruct y target , target x , target y ,and E target havethecentraltracklengthasaninput.Figure4.2isatechnicaldrawingthatincludes lengthsforthecentraltrackfromthetargettoCRDC1.Whenthoselengthsaresummed thetotalcentraltrackshouldbe172.3cm.However,themapcreationscripthasadrift distanceof7.5cmfromthetargettowherethemaptakesandthemaphasacentral tracklengthof157.9cm.Addingtheseyieldsatotalcentraltracklengthof165.4cm.This constitutesanceindistanceof6.9cm. Tocheckwhichcentraltrackdistanceisaccurate,mapsweremadewiththetotalcentral trackbeing165.4and172.3cmfortmagnetsettingsusedduringtheexperiment. 46 Figure4.3:ExperimentalandsimulationdataobtainedwiththeSweepermagnet'scurrent at366A.ThebluelinerepresentsanSTMoNAsimulation,whileblackpointsrepresents experimentaldata.Theleftpanelasimulatedtotalcentraltracklengthof165.4cm andtherightpaneluses172.3cm. Themapswithatotalcentraltracklengthof172.3cmweremadewitha7.5cminitialdrift distancefromthetargettowherethemagnetictakesacentraltracklengthin themagneticldof157.9cm,andanadditionaldriftdistanceof6.9cmtoCRDC1.Figure 4.3showstheSweepermagnetsetto366Awiththedatarepresentedasblackpoints.The lefthandpanelshowstheblueSTMONAsimulationwherethemapusedtopropagatethe unreactedbeamtothetargethasatotalcentraltracklengthof165.4cm.Therighthand panelbluelineisaSTMoNAsimulationwherethetotalcentraltracklengthis172.3cm.The magnet'scurrentwassetto306,316,326,336,356,366,and371A,whichilluminatedthe entiresweeperfocalplanebox'sacceptancewhenthe440mg/cm 2 deuteratedpolyethylene targetwasinplace.Foreverycurrentsetting,thetotalcentraltracklengthneededtobe increasedtolineupthecentroidofsimulationdatawiththestepsweepdata.Thedistance necessaryvariedrandomlyfrom5to15cmwithameanof9(3)cm.Atotalcentraltrack lengthof172.3cm,whichcorrespondstothecentraltracklengthfromFig4.2,wasusedfor allanalysispresentedinthisthesis. 47 Figure4.4:AngulardistributionofthereactionusedinSTMoNA,calculatedwithFRESCO usingtheglobalopticalpotentialsfromRefs.[38,35]. 4.1.3FinalChecks InSection4.1.1itwasshownthattheincomingbeamusedinSTMoNAwasin goodagreementwithdatafromunreacted 14 Becenteredinthefocalplanebox.The checkistoimplementthereactionmechanisminSTMoNAandcomparetheresultstothe experimentaldata.Thisprovidesacheckoftheneutronpickupmodeltosimulationthe reaction. Thereactionwasmodeledas 14 Bepickingupaneutronfromthedeuteriumandforming 15 Be,whichimmediatelydecaysbackinto 14 Beandaneutron.Figure4.4showstheangular distributionascalculatedbyFRESCO[33]usingtheglobalopticalpotentialfromRefs. [38,35].ThedecayenergydistributioniscalculatedwithEq.4.1. Figure4.5providesacomparisonofsimulation(blueline)todata(blackpoints)at CRDC1for 14 Bereactionproducts.Figure4.6providesthesamecomparisonsforparameters 48 Figure4.5:Comparisonofsimulation(blueline)todata(blackpoints)for 14 Bereaction productslocatedinthefocalplane.TheparametersarecomparedareCRDC1X, X ,Y, and Y whicharelocatedintheupper{left,upper{right,lower{left,andlower{rightpanel, respectively. 49 Figure4.6:Comparisonofsimulation(blueline)todata(blackpoints)for 14 Bereaction productslocatedinthefocalplane.TheparametersarecomparedaretargetE, X ,Y, and Y whicharelocatedintheupper{left,upper{right,lower{left,andlower{rightpanel, respectively. atthetargetcreatedwheretheinversemappingprocedure(seeSection3.4.1)wasappliedto thedataandthesimulation.Thereisreasonableagreementbetweensimulationanddata forallmeasuredparameters,thereactionmechanism. 4.1.4Geometric Figure4.7showsthegeometricoftheMoNAandSweepersystem.This doesnotincludetheintrinsicofMoNAandthechargedparticledetectors.Itwas 50 Figure4.7:GeometricoftheMoNAandSweepersystem.Itwascalculatedfor energiesbetween0and5MeVforaneutronpick{upreactionfromdeuterium. calculatedwithSTMoNAfordecayenergiesbetween0{5MeVforaneutronpick{up reactionfromdeuterium. 4.1.5ResonanceModeling Thedecayofaneutronunboundresonantstateisatwobodyproblem,involvinganeutron andtheresidualchargedfragment.Itcanbedescribedbytheinversereactionasaneutron scatteringanucleusattenergies.Thecrosssectionforthisprocess, ˙ ( E ),iswell describedbyR{matrixtheory[56]andhastheformofanenergydependentBreit{Wigner distribution[57].Forthedecayonlytheshapeoftheresonancesisrelevant.Theparticular formusedis: ˙ ˘ ` ( E; f ) ( E 0 + ` ( E; f ) E ) 2 + 1 4 ` ( E; f ) 2 (4.1) Eistheneutronenergy;E 0 isthecentralresonanceenergy; f iscalledtheformalwidth; ` 51 istheorbitalangularmomentum; ` and ` aredescribedbyEq.4.2and4.6. Thefunction ` is: ` = f P ` ( E ) P ` ( E 0 ) (4.2) where P ` ( E )isgivenby: P ` = ˆ F 2 ` + G 2 ` r = a (4.3) whereaistheminimumdistanceofapproach,whichisgivenby: a = r 0 ( A 1 = 3 n + A 1 = 3 f )(4.4) and G ` and F ` arecomposedof: G ` = ˇˆ 2 2 J ` +1 = 2 ( ˆ ) F ` =( 1) ` ˇˆ 2 2 J ` 1 = 2 ( ˆ ) (4.5) J ( ` +1 = 2) areJ-typeBesselfunctionsand ˆ = a p 2 ME= h .Thefunction ` isgivenby: ` = f 2 P ` ( E 0 ) ( S ` ( E ) S ` ( E 0 ))(4.6) where S ` istheshiftfunctionandisgivenby: S ` = ˆ F ` F 0 ` + G ` G 0 ` F 2 ` + G 2 ` r = a (4.7) 52 where G 0 ` and F 0 ` arethederivativesofEq.4.5withrespectto r .Theapproximationtothe shiftfunctionscanbefoundinRef.[58]andfor ` =1and ` =2theyare: S 1 = 1 1 ( ka ) 2 S 2 = 3(6+( ka ) 2 ) 9+3( ka ) 2 +( ka ) 4 (4.8) where ka = a p 2 ME= h .ItshouldbenotedintheoriginalpaperfromLaneandThomas thatTableA.1containsatypographicalerror.Thenumeratorfor S 2 islistedincorrectlyas 3(6+( ka ) 4 )insteadof 3(6+( ka ) 2 ). 4.2Geant4 Geant4isasoftwarepackagethatusesMonteCarlomethodstosimulatethepassageof particlesthroughmatter[59].InthepresentanalysisGeant4isonlyusedtosimulatethe interactionoftheneutrons,whileSTMoNAwasusedtohandletheincomingbeam reactioninthetarget,propagatingthechargedparticlethroughthemagneticofthe Sweepermagnet,anddeterminingtheinteractionwithinthefocalplaneboxdetectors.ST MoNAthensavestheemittedneutron'senergyanddirectionandpassesittoGeant4. TheneutronisinitializedintheGeant4framework[59,60]andthenpropagatedthrough theSweepermagnet.Thesimulatedmagnetwascreatedtomatchthedimensionsofthe largegapandneutronwindowintheSweepermagnet.TheSweeperismadeoft materials,butinGeant4itisapproximatedasbeingsolidiron. OncetheneutronisbeyondtheSweepermagnetitispropagatedtoMoNA,whereit caninteractwithinabarofMoNA.Eachsimulatedbarconsistsofplasticwithacarbonto 53 hydrogenratioof1.104andadensityof1.032g/cm 3 whichmatchesBC-408[46].Inaddition, thesimulatedbarsarewrappedwithvinyltapeandhavelightguidesatbothends.Ifthe neutroninteractswithinthebar,theenergydepositedisconvertedtolightoutputusing Birk'sLaw[61],andthelightisattenuatedasitpropagatestobothendsofthebar.Acut isthenappliedtomimicthedetectorthresholdof380keVee.Ifthethresholdwasmet,the timeoftandenergyofeacheventwererecorded. Experimentaldataisabundantforcrosssectionsandangulardistributionforneutrons interactingwithnucleifrom0{20MeV,butfrom20to300MeVthereislimiteddata available.Previousstudieshaveshownthatttechniquesdonotproviderealistic interactionsforneutronsintheintermediateenergyrange(20{300MeV)[62,63,64,65, 66,67].Thelackofanextensivecollectionofexperimentaldatainthisenergyrangelowers theabilityofsimulationstoaccuratelydescribethewaythatneutronsinteractinmaterials. Below20MeV,Geant4usesG4NeutronHPElasticandG4NeutronHPInelastic[70],which arebasedontheEvaluatedNuclearDataFiles(ENDF/B{VI)[68,69].Theycontainhigh precisioncrosssectionsandangulardistributiondataforelasticandtheinelasticreactions. Theinelasticreactiondataincludedetailedinformationaboutthetreactionchannels. Thisprovidesagooddescriptionofneutronsbelowthe20MeV,however,theyarenot appropriateforthepresentexperimentwhereneutronenergiesareintherangeof40{60MeV. Above20MeV,thestockGeant4physicsclassesG4HadronElasticProcessandG4LElastic areusedwhichdescribetheelasticscatteringoftheneutron.Theinelasticreactionsaredeter- minedwithintheG4LENeutronInelasticandG4CascadeInterfaceclasses.Theyarebasedon thepre{equilibriumBertiniintranuclearcascademodel[71],followedbyevaporation.Neu- troninteractioncrosssectionforboththeelasticandinelasticreactionsaretakenfromthe JapaneseEvaluatedDataLibrary(JENDL{HE)[72,73].Thedisadvantageofthisapproach 54 Figure4.8:Theleftpanelshowsthetotalcarbon{neutroninelasticreactioncrosssectionused inthestockG4Physicsclass(JENDL{HE).Theothersixcolorsshowthediscreteinelastic reactioncrosssectionsusedintheMenate Rcode.Therightpanelshowsthehydrogen elasticcrosssectionforG4PhysicsClass(Green)andMenate R(Black).Alsoshownisthe carbonelasticcrosssectionfortheG4Physics(Red)andMenate R(Blue).(adoptedfrom Ref.[79]) isthattheinelasticprocessdoesnotexplicitlydescribethetinelasticchannels. Thus,acustomneutroninteractionmodel,Menate R[74],wasimplementedinthe Geant4platform.Menate RwasoriginallydesignedtosimulateneutroninteractioninNE213 scintillatorsfortheEURISOLdesignstudy[74].Mentate Rusesdiscreteinelasticreaction channelsfortheneutroninteractingwithcarbonabove20MeV.Theinteractionwasincor- poratedintoaC++classderivedfromG4VDiscreteProcesstoallowimplementationwithin theGeant4framework. TheleftpanelofFig.4.8showsthetotalcarbon{neutroninelasticreactioncrosssection fromtheJENDL{HEdatabase[73]usedinthestockGeant4physicsclass;theothersixcolors representsthecarbon{neutroninelasticreactionchannelsusedbytheMenate Rpackage. Below20MeVthestockG4PhysicsclassusesthesamechannelsastheMenate Rpackage,as opposedtothetotalinelasticcrosssection.TherightpanelofFig.4.8showsacomparisonof 55 Figure4.9:Visualrepresentationoftheelasticcrosssectionsforironattenergies fromRef[78].Thecrosssectionsat30,50,and70MeVwereaddedtoMenate R,andthen extrapolatedtotheenergyoftheneutron. theelastichydrogencrosssectionusedintheG4Physicsclass(Green)andMenate R(Black) andtheelasticcarboncrosssectionusedintheG4Physicsclass(Red)andMenate R(Blue). ThereisnointheelasticcrosssectionsintheenergyrangeatwhichtheMoNA{ Sweepersetupistypicallyrun. Menate Ronlycalculatesinteractionsofneutronswithcarbonandhydrogen,whichworks wellfortheplasticscintillatorsinMoNA.TomodeltheSweepermagnet,thecrosssections forironhadtobeaddedtoMenate R.ThecrosssectionswereaddedfromtheENDF/B{ VIdatabase[69]for30,50,and70MeV.Menate Rtheninterpolatestotheenergyofthe 56 neutron.Figure4.9showstheelasticcrosssectionsforironatditenergies.Menate R assumesthattheneutronisabsorbedifitinteractsinelasticallywithiron.Aluminumcross sectionswerealsoaddedtothecodeforpossibleuseinfuturestudies. 4.2.1Comparison TocheckthetwointeractionmodelsusedinGeant4itisnecessarytocomparethemto anexperimentwheretheresultsareeasilyunderstood.Thisrequiresanexperimentthat populatesaneutronunboundstatethatonlyemitsasingleneutron.Suchanexperiment wasaoneprotonknockoutof 17 Cpopulatingthegroundstateof 16 Bwhichdecayedtothe groundstateof 15 B.CompletedetailsoftheexperimentcanbefoundinRef.[77].Forevery 15 Bpresent,thereshouldbeonlyasingleneutron,thusanymultipleinteractionsmustcome fromthescatteringofthatsingleneutron. ThemajorobservablecanbeseenintheleftpanelofFig.4.10whichshowsthe multiplicityoftheexperimentaldata(Black)comparedwithG4Physics(Red)andMenate R (Blue).Thehasbeennormalizedatmultiplicity=1.G4Physics,acrosstheboard, grosslyoverestimatesthemultiplicitycomparedtotheexperimentaldataandtheMenate R model.TherighthandpanelofFig.4.10showstheenergydepositedfortheexperimental data(Black),G4Physics(Red),andMenate R(Blue).G4Physicsoverrepresentsthehigh andlowenergydeposited,whileMenate Relyreproducesthedata.Figure4.10 demonstratesthatthestockG4PhysicsclassisinferiortotheMenate Rpackageindescribing theintermediateenergyrangeneutroninteractionwithinMoNA. SincethemultiplicityanddepositedenergyareproducedfrominteractionsinMoNA,and theelasticscatteringcrosssectionsusedarenearlyidenticalforbothmodels,itimpliesthat theisduetotheinelasticreactions.ThecascademodelusedintheG4Physics 57 Figure4.10:Experimentaldata(Black)fromRef.[77]iscomparedtotheG4Physics(Red) andMenate R(Blue)model.Theleftpanelshowsthemultiplicityandrightpanelshows theenergydeposited.Intheleftpanelthemultiplicitydistributionswerenormalizedsothat multiplicity=1eventsmatched.Therightpanelwasnormalizedfortotalnumberofevents. (adoptedfromRef.[79]) Figure4.11:ComparisonbetweenthestockG4Physics(Red)andMenate R(Blue)models ofmultiplicitydistributionforinteractionswithinMoNAwhere raysareproducedfrom inelasticreactionswithcarbon.(adoptedfromRef.[79]) 58 dramaticallyoverproduces raysrelativeto 12 C ( n; )inelasticreactionchannelwithin Menate R.Thiscanleadto raysthatareproducedinonebarpropagatingtoanother andinducinganinteraction,whichcandrasticallyincreaseinmultiplicityproducedbythe G4Physicsmodelandtheincreaseoflowenergyeventsthatareobserved.Themultiplicity of raysproducedthroughinelasticscatteringwithcarbonisshowninFig.4.11.Itshould benotedthatthisisnotlikelythesolecauseoftheobserveddiscrepancy,butitaccounts formuchoftheFurthervoftheMenate RmodelcanbeenseeninRef. [79]. 59 Chapter5 Results Thisexperimentrepresentsthetime 15 Bewasobservedexperimentally,allowingforthe measurementoftheresonanceobservedinFig.3.23andcalculationofthecrosssectionsfor neutrontransferfromcarbonanddeuteriumto 14 Be. 5.1ResonanceEnergy Themeasureddecayenergyspectrumfor 14 Be+ncoincidencesresultingfromthedecayof 15 BeunboundstatesispresentedinFig.5.1.Theexperimentaldecayenergyspectrumwas usinganenergydependentBreit-Wignerdistribution(seeEq.4.1)whichassumedan l =2decayalongwithabackgroundcontribution.Thebackgroundismostlikelyduetothe populationofunbound,higher-lyingstates.Otherthanthepeakcloseto2MeV,nodistinct resonancefeatureswereapparent.Thebackgroundwasapproximatedwithacombinationof l =0and l> 0components.Thesecontributionswereselectedtoreproducethebackground below1MeVandabove3MeV,respectively.The l =0lineshape(redlongdashes)inFig. 5.1wascalculatedusingtheanalyticapproximation,whichcomesfromRef.[80]: d˙ ˘ 1 k kcos ( a s k ) sin ( a s k ) 2 + k 2 2 (5.1) where a s isthescatteringlength, = p 2 B , B isthebindingenergyof 14 Be, k = p 2 f , 60 Figure5.1: 15 Bedecayenergyspectrum.Thedataareshownbytheblackdatapoints withstatisticalerrorbars.Thebesttothedata(solidblackline)isasumofan l =2 resonance(greenshort-dashedline)andbackgroundcontributionsapproximatedby l =0 (redlong-dashedline)and l> 0(bluedottedline)components. and f isthedecayenergyoftheneutron.NuShellxpredictsa1/2 + stateat3.5MeVin 15 Be thatwilldecaythroughan l =0neutronemissiontothegroundstatein 14 Be,corresponding toascatteringlengthof 2.5fm.Toreproducethebackgroundabove3MeVaBreit-Wigner lineshapewasusedwithacentroidof3.5MeVwithawidthof0.8MeV(bluedots).The overallwasnotsensitivetothedetailedparameterizationsofthebackgroundcontribution. Thus,theseparametersshouldnotbeinterpretedasdistinctstatesin 15 Be. Forthethe l =2resonanceenergy,width,andnormalization,alongwiththe normalizationofthetwobackgroundcontributionswerefreeparameters.Thebesttothe dataisshownbytheblacksolidlineinFigure5.1;itwasachievedwitharesonanceenergy of1.8 0.1MeVandawidthof575 200keValongwiththetwobackgroundcomponents. Theindividualcontributionsofthe ` =2resonance,andthe l =0and l> 0background 61 contributionsareshownbythegreenshort{dashed,redlong{dashed,andblue{dottedlines, respectively.Theresonanceaccountedfor531ofthe768observedeventsinthedecayspectra. Thisobservationcorrespondstotheidenoftheneutron-unboundnucleus 15 Be. Theobservationofthe5/2 + stateat1.8MeVabovethegroundstateof 14 Be,whichhasa massexcessof39.95 0.13MeV[81],meansthat 15 Behasamassexcessof49.82 0.16MeV. Theexperimentalmassexcessfor 15 Beisconsistentwiththevaluefromthe2012atomic massevaluationof49.76 0.4MeV[81]. Shellmodelcalculationswith Nushellx ,mentionedintheintroduction,predictedthe 3/2 + groundstateandthe5/2 + excitedstatetobeseparatedbyonly300keV.Itiscon- ceivablethattheobservedpeakcorrespondstoasumofbothofthesestates,howeverthis isnotrequiredbythedata.Theextractedwidthofthesingle-component575 200keV, isconsistentwiththecalculatedsingle-particlewidthof405keVwhichwasderivedfrom: sp = h 2 MR 2 ( kR ) 2 ` 1 2 ` +1 T ` ( kR )(5.2) where R =1 : 13 A 1 = 3 fmisthenuclearradius, M isthereducedmass, k = p 2 ME= h ,and thetransmissionprobability, T ` ( kR ),isgivenby: T 2 ( kR )= ( kR ) 4 9+3( kR ) 2 +( kR ) 4 (5.3) TheneutronpresentedinSection1.1indicatethatthe5/2 + stateshould bepopulatedsigntlymorethanthe3/2 + stateandthatthe5/2 + statehassubstantial spectroscopicstrengthfordecayingtothegroundstateof 14 Be,whereasthe3/2 + statewill predominantlydecaytotheexcited2 + stateof 14 Be.Thus,theresonanceobservedin Fig5.1istentativelyassignedtothe5/2 + state. 62 Figure5.2:Partialexperimentallevelschemeforneutronrichberylliumisotopes.Theheight ofthegrayboxesrepresentstheuncertaintiesofthestates.Thedatafortheexcitedstate in 14 Beisfrom[26],thelowerlimitforthe3/2 + isfrom[17],the 15 Be5/2 + stateisfrom thepresentworkandthetwo-neutronseparationenergyfor 16 Beisfrom[13]. Thecurrentexperimentdoesnotresolvethequestionwhichofthetwostatescorresponds tothegroundstate.Figure5.2summarizestheexperimentalstatusoftheneutron-rich berylliumisotopes.Thenon-observationof 14 Beinthetwo-protonknock-outexperiment establishedalowerlimitforthedecayenergyofthe3/2 + stateof1.54MeV[17].Thisstate willdecaytotheunboundexcited2 + stateof 14 Bewhichthensubsequentlywilldecay viatwoneutronemissiontothegroundstateof 12 Be.Itwillbetoobservebecauseit willrequirethekinematicreconstructionofthreeneutrons.Thepresentresultsobservethe 5/2 + stateatadecayenergyof1.8 0.1MeV.AsshowninFigure5.2,thisplacesthe 15 Be stateabovethe 16 Begroundstateby450 140keV,reducingitscontributionasapossible intermediatestepforthesequentialdecayfrom 16 Betly. 63 5.2CrossSection Inadditiontomeasuringthedecayenergy,itispossibletocalculatethecrosssectionsfor the 14 Be(d,p) 15 Beand 14 Be( 12 C, 11 C) 15 Bereactions.Thecrosssection,inmillibarns,is calculatedby: ˙ = n r 10 27 n b n t (5.4) where n r , n b ,and n t representthetotalnumberofreactions,beamparticles,andtarget nucleipercm 2 ,respectively.Thenumberoftargetnucleiwasdeterminedusing: n t = N A t t A (5.5) where N A =6 : 02 10 23 mol 1 isAvogadro'snumber, t t isthethicknessoftargetinunits ofg/cm 2 ,and A ismassinunitsofatomicmass.Thecalculationisstraightforwardforthe carbontargetbutforthedeuteratedpolyethylenetargetitisalsonecessarytocalculatethe fractionofdeuteriumtohydrogeninthetarget(seeSection5.2.3). Thenumberofbeamparticles, n b ,wasnotmeasureddirectly.Instead n b wasdeduced bycalibratingthescalersofthetargetscintillator(tss)witharunwheretheunreacted beam(urb)wascenteredinthefocalplaneboxwithoutatarget.Inthisrunthesamegates wereusedasinthereactiondata(berylliumgateontheincomingbeam,padsumgateon bothCRDCs,andtheberylliumgateafterthesweepermagnet),removingtheofthe incomingbeam'spurityandofthechargedparticledetectors. n b = lt n tss n urb b urb lt n urb tss =0 : 58 lt n tss (5.6) 64 where lt isthelivetimeasdeterminedfromthescalers,and n tss isthenumberofevents recordedinthetargetscintillator'sscaler. Thenumberofreactionspopulatingtheresonancewascalculatedas: n r = n s d a lt (5.7) where n s isthenumberofeventsinthedecayspectrawithinthe1.8MeVresonancedivided bytheeofthesetup.Thelivetime, lt =0 : 99,wasdetermineddirectlyfromthe scalers.Thedetector, d ,wasdeterminedtobe d =0 : 0712withanuncertaintyof 20%andcorrespondstotheacceptancesandtheintrinsic.Thedetectorciency wasdeterminedusingacombinationofMonteCarlosimulationsprovidedbyST MONA andGEANT4.Itshouldbenotedthatthesofthechargedparticledetectorswere takenintoaccountinthetotalincomingbeamparticlecalculations.Theanalysisciency, a ,wasbasedonthegateshowninFig.3.16.Thefromthiscutwasestimatedtobe a =0 : 67withanuncertaintyof20%. 5.2.1SystematicUncertainty TheindividualcontributionstothesystematicuncertaintyarelistedinTable5.1.The analysisanddetectoruncertaintywerebothdiscussedattheendoftheprevious section.Anotheruncertaintyisduetothereactionmechanismusedinthesimulation.The angulardistributionofthefragmentswasdeducedfromtheerentialcrosssectionscalcu- latedbyFRESCO(seeFig.4.4).TheSweepermagnetacceptanceforangulardistributions calculatedfromthreeditopticalpotentials[36,37,38]dibynomorethan5%. Theuncertaintyofthetargetthicknesswasestimatedtobe2%and15%forthecarbonand 65 Table5.1:Thesourcesofthesystematicuncertainty. SourceCarbonTarget(%)CD2Target(%) Analysis( a )1010 Detector( d )2020 tialCrossSection55 TargetThickness215 Total3750 deuteratedpolyethylene,respectively.ThelatterwillbediscussedinmoredetailinSection 5.2.3.TheerrorslistedinTable5.1correspondtotheaverageerrorandthetotalrelative erroriscalculatedfromthesumoftheserelativeerrors. 5.2.2CarbonTarget Thecrosssectionforneutronpickupfromcarbonwasdeterminedbyusinga t t;carbon = 308mg/cm 2 carbontargetfor16hours.FromFig.3.24itcanbeseenthatthedecay energyspectraforthecarbontargetwasstatisticallyidenticaltothedeuteratedpolyethylene target.Duetothelimitedstatisticsitwasnotpossibletotheresonanceandseparate itfrombackgroundcontributions.Thusthetotalnumberofeventsinthespectrumwas scaledbytheratiooftheresonancecontribution(531 23)tothetotalevents(791 28) forthedeuteratedpolyethylenetargetresultingin n s =18 4.Thetotalnumberof reactionscanthenbecalculatedtobe, n r =380 75.UsingEq.5.5withacarbontarget thicknessof t t =0 : 308g/cm 2 givesthetotalnumberoftargetnuclei n t =1 : 545 10 22 . Thenumberofincomingbeamparticleswas n b =2 : 29 10 7 .Thecrosssectionforneutron transferfromthecarbontargetwasthen ˙ carbon =1 : 1 0 : 6mb.Theuncertaintywas composedofthestatisticaluncertainty, ˘ 20%,andanestimatedsystematicuncertaintyof ˘ 37%(Table5.1).Thecrosssectionisconsistentwiththecrosssectioncalculatedwith 66 fresco (0.7mb)usingopticalpotentialsderivedfromtotheangulardistributionofthe reaction 12 C( 12 C, 11 C) 13 Cat50MeV/nucleon[82]. 5.2.3DeuteratedPolyethyleneTarget Thecrosssectionforneutrontransferfromdeuteriuminthedeuteratedpolyethylenetarget isslightlymorecomplicated.Thestepistodeterminethetotalnumberofincoming beamparticles, n b .Thedeuteratedpolyethylenetargetwasonlya ˘ 2X2cm 2 square whichdidnotcoverthewholebeamsocorrectionshadtobeappliedtoaccountfor beamparticlesthatmissedthetarget.Thepercentageofincomingnucleithatwouldstrike thedeuteratedpolyethylenetargetwasdeterminedtobe90%bySTMoNAsimulations. This,alongwiththedatafromthescalers,providesatotalincomingparticlenumberof n b =2 : 36 10 8 . Thesecondstepistocalculatethenumberofdeuteriumatomsinthe t t;CD 2 =440mg/cm 2 deuteratedpolyethylenetargetwithamoversionofEq.5.5. n t;deuterium = N H =N C F D N A t t;CD 2 M C + N H =N C ( F D M D + F H M H ) (5.8) N H =N C istheratioofhydrogentocarboninthetarget, F D isthefractionofthehydrogen thatisdeuterium,and F H isthefractionofhydrogenthatis 1 H. N H =N C , F D ,and, F H weredeterminedusingRutherfordBackscatteringSpectrometry(RBS)analysis[83],with datatakenattheHopeIonBeamAnalysisLaboratory.Foragivenangletheenergyloss ofthebackscatterediondependsonthemassandchargeofthetargetnuclei.Thisallows foradeterminationofthecompositionofthetargetmaterial.ShowninFig.5.3areRBS simulationsforprotonsimpinginguponacarbon(redline)andaCH 2 (blackline)target. 67 Figure5.3:RBSsimulationsusing3.4MeVprotonsimpinginguponacarbon(redline) andaCH 2 (blackline)targetarecomparedtodatafromRBSanalysis,alsousing3.4MeV protons.Thecarbondata(redpoints)anddeuteratedpolyethylenedata(blackpoints)were normalizedtothesimulatedcarbontarget.Thereisgoodagreementbetweenthesimulated deuteratedpolyethylenetargetandthedata,whichindicatesthattheratioofcarbonto hydrogenis1:2. ItiscomparedtoRBSdataforacarbonanddeuteratedpolyethylenetarget,normalized totheexperimentalcarbontargetdata.ThesimulatedCH 2 targetmatchedthedeuterated polyethylenetargetdata,whichindicatesthattheratioofhydrogentocarbonis N H =N C =2. Thepeakcenteredatchannel60inFig5.3isfromprotonsbackscatteringofdeuterium. Thestrengthofthepeakallowsfordeterminingthedeuteriumtohydrogenratio.Avisual inspectionofthetargetedshowedsomeinhomogeneities,sotheRBSanalysiswasrepeatedat 5tlocationsacrossthetarget,asshowninFig.5.4.Fromtheratioofthelowenergy peaktotheriseitispossibletodeterminethepercentageofhydrogenthatisdeuterium.The purityofdeuteriumwas100%,100%,100%,75%,and50%fortheelocations,respectively. Tomitigatethenon{uniformityofthedeuteratedpolyethylenetarget,theaveragepuritywas 68 Figure5.4:RBSdataforetlocationsonthedeuteratedpolyethylenetarget, impingedwith3.4MeVprotons.Eachdatasetwasnormalizedsothetotalnumberof incomingprotonswerethesame.Thestrengthofthepeakbetweenchannel30and70is indicativeofthepercentageofhydrogeninthetargetisdeuterium. used( F D =0.85 0.15).Thetotalnumberofdeuteriumatomsinthedeuteratedpolyethylene targetwascalculatedtobe: n t;deuterium = 2 0 : 85 N A t t;CD 2 M C +2 (0 : 85 M D +0 : 15 M H ) =(2 : 8 10 22 0 : 4 10 22 ) =cm 2 (5.9) Thevaluenecessarytocalculatethecrosssectionisthetotalnumberofreactions duetoneutrontransferfromdeuterium.Usingthenumberofreactionsintheresonance (531),the( d ; a ;and lt ),andEq.5.7givesthetotalnumberofreactionsas n r;total =8650 300.Theexpectednumberoftransfersfromcarbonwascalculatedas: 69 n r;carbon = n b ˙ carbon n t;carbon 10 27 =4150 800(5.10) where ˙ carbon isthecrosssectionmeasuredinSection5.2.2and n t;carbon isthetotal numberofcarbonatomsinthetargetwhichisgivenby: n t;carbon = N A t t;CD 2 M C +2 (0 : 85 M D +0 : 15 M H ) =1 : 65 10 22 =cm 2 (5.11) Subtractingthenumberofreactionsduetocarbonfromthetotalnumberofreactions givesthenumberoftransfersfromdeuteriumas n r;deuterium =4500 1100. Table5.2:ThenumberofreactioneventsfromttargetnucleifortheCD2target. TotalCarbonDeuterium 8650 3004150 8004500 1100 Finally,withthesenumbersandEq.5.4thecrosssectionforneutrontransferfrom deuteriumcalculatedtobe ˙ deuterium =0 : 7 0 : 5mb.Thesystematicerroris50%for thedeuteriumtransferaslistedinTable5.1.Themeasuredcrosssectionisconsistentwith fresco calculationsforthetransferfromdeuteriumusingseveralrentglobaloptical potentials[36,37,38];whichresultedincalculatedcrosssectionsfrom1{2mb. 70 Chapter6 SummaryandOutlook 6.1Summary Theobservationofaneutron{unboundstatein 15 Behasbeenmeasuredusinginvari- antmassspectroscopy.Theneutron{unboundstatewaspopulatedusingneutronpick{up froma440mg/cm 2 deuteratedpolyethylenetargetwitha59MeV/u 14 Besecondarybeam. Neutronsfromthedecayoftheunboundstatein 15 BeweremeasuredusingMoNAwhereas thechargedfragmentswerewiththeSweepermagnetanddetectedinthefocal planeboxusingasuiteofchargedparticledetectors.MonteCarlosimulationswhichtake intoaccountacceptances,resolutions,andtheinteractionoftheneutronwithinMoNAwere comparedtoaninvariantmassspectrumwhichwasusinganenergy{dependentBreit- Wignerdistribution.Thebesttothedatawasachievedusing ` =2withtheresonance energyof1.8 0.1MeVandawidthof575 200keV.Theresonancewasassignedtothe predicted5/2 + state.Thisremovesthepossibilitythatthe5/2 + statein 15 Becanserve asanintermediatedecayfor 16 Be,gtheresultsfrom[13].Thecrosssectionfor neutronpick{upfromcarbonwasmeasuredtobe ˙ carbon =1 : 1 0 : 6mb,whereasthecross sectionforneutronpick{upfromdeuteriumwasmeasuredtobe ˙ deuterium =0 : 7 0 : 5mb. 71 6.2Outlook Thepresentedworkdoesnotsolvetheproblemofwhetherthe3/2 + orthe5/2 + stateisthe groundstateof 15 Be.Inapreviousworkthelowerlimitofthe3/2 + statewasdetermined tobe1.54MeV[17].Thismeansthatifthe3/2 + stateislocatedbetween1.54and1.8MeV itwillcorrespondtothegroundstateof 15 Be.Todetermineifthe3/2 + orthe5/2 + isthe groundstateof 15 Beitisnecessarytodeterminethelocationofthe3/2 + state. Thebestwaytodothistaskistwoprotonstrippingfrom 17 Cwhichwillprimarily populatethe3/2 + of 15 BeandwhichwasattemptedinRef.[17].Oncethe3/2 + stateis populateditwillprimarilydecaytotheexcitedstatein 14 Beat1.54MeVandthen decaybytwoneutronemissionto 12 Be[21].Thisdecaypathwassuggestedbythedataof Ref.[17],howeverthestatisticswerenotttoreconstructthe4{bodydecayenergy. Threeneutrondecaysrequirehighstatisticsduetothecutsnecessarytodetermineifthe eventsaretruethreeneutroneventsorifoneortwooftheneutronsinteractedmultiple times. Thesecondpossibilityisthatthe3/2 + statewilldecaydowntothegroundstateof 14 Be. ThisdecaypathwasnotobservedinRef.[17]andisexpectedtobesmallandthuswillalso requirehighbeamratestomeasurethatpathway. AtthepresenttimetheintensitiesoftheNSCLarenotttodeterminethelo- cationofthe3/2 + state.However,withtheexpectedbeamintensityattheFacilityfor RareIsotopeBeams(FRIB)whichiscurrentlyunderconstruction,thisquestionwillbe resolved.Currentlytheonlyfacilitythathastheintensitiestoperformthisexperimentis theRadioactiveIsotopeBeamFactory(RIBF)atRIKEN.Anotherfacilitythatwillbeable todeliverthenecessarybeamintensitiesforthisexperimentistheFacilityforAntiproton 72 andIonResearch(FAIR)willhavetheintensitiesnecessaryonceitcomesonlinetoperform thisexperiment. 73 APPENDIX 74 Appendix OpticalModelPotentialsParameters TheopticalmodelpotentialparametersusedinFRESCOtocalculatethecrosssections forneutronpickupfromdeuteriumandcarbonarelistedinTableA.1,A.2,andA.3.The subscripts v , s , so , i denotethevolumeinteraction,surfaceinteraction,spin-orbitinteraction, andtheimaginarypartofthoseinteractions,respectively. Toperformthethecalculationforneutronpick{upfromdeuteriumFRESCOrequires thepotentialbetween 14 Beand 2 H(TableA.1), 14 Beand 1 H,and 15 Beand 1 H(TableA.2). TableA.1:Opticalmodelpotentialsparametersused tomodeltheinteractionbetween 14 Beand 2 H. Ref.V v r v a v V v;i r v;i a v;i V s;i r s;i a s;i V so r so a so MeVfmfmMeVfmfmMeVfmfmMeVfmfm Ref.[36]55.91.180.720.000.000.0029.11.270.826.00.870.87 Ref.[37]42.01.170.8116.71.560.810.000.000.003.71.230.81 Ref.[38]66.91.150.757.901.350.617.501.400.683.60.971.01 TableA.2:Opticalmodelpotentialsparametersused tomodeltheinteractionbetween 14 Beand 15 Bewith 1 H. ReferenceIsotopeV v r v a v V v;i r v;i a v;i V so r so a so MeVfmfmMeVfmfmMeVfmfm Ref.[35] 14 Be43.21.20.75.91.20.44.51.20.7 Ref.[35] 15 Be43.81.20.75.91.20.44.51.20.7 Tocalculationthecrosssectionforneutronpick{upfromcarbon,FRESCOrequiresthe 75 potentialbetween 14 Beand 12 C, 14 Beand 11 C,and 15 Beand 11 C.Thebestpotentialfor eachinteractioncamefroma 12 C( 12 C, 11 C) 13 Creactionandwasusedforallthreeinterac- tions.ThepotentialisgiveninTableA.3. TableA.3:Opticalmodelpotentialsparametersusedtomodeltheinteraction between 14 Beand 12 C, 14 Beand 11 C,and 15 Beand 11 C. ReferenceV v r v a v V v;i r v;i a v;i MeVfmfmMeVfmfm Ref.[82]1500.640.88425.01.0170.73 76 BIBLIOGRAPHY 77 BIBLIOGRAPHY [1]E.Rutherford etal. ,ProceedingsoftheRoyalSocietyA 123 ,(1929). [2]N.BohrandJ.Wheeler,Phy.Rev. 56 ,426(1939) [3]M.Goeppert{Mayer,Phys.Rev. 78 ,16(1950). [4]M.Goeppert{Mayer,Phys.Rev. 78 ,22(1950). [5]O.Haxel,J.H.Jensen,andH.Suess,Phys.Rev. 75 ,1766(1949). 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