SEARCHFORTHEISOVECTORGIANTMONOPOLERESONANCEVIATHE 28 SI( 10 BE, 10 B+ )REACTIONAT100MEV/U By MichaelJ.Scott ADISSERTATION Submittedto MichiganStateUniversity inpartialentoftherequirements forthedegreeof Physics-DoctorofPhilosophy 2015 ABSTRACT SEARCHFORTHEISOVECTORGIANTMONOPOLERESONANCEVIA THE 28 SI( 10 BE, 10 B+ )REACTIONAT100MEV/U By MichaelJ.Scott Theisovectorgiantmonopoleresonance(IVGMR)isafundamentalmodeofcollective oscillationinwhichtheneutronandprotoninanucleusradiallyexpandandcon- tractinanout-of-phasemanner.ObservationoftheIVGMRhasbeenThenon- spin-transferIVGMRresonanceisobscuredbyitsspin-transfercounterpart,theisovector spingiantmonopoleresonance(IVSGMR).Theproblemisthelackofasuitableprobefor measurementofnon-spin-transfer,isovectorevents.Bywayofthe( 10 Be, 10 B+ )charge- exchangereaction,selectivityfortheexcitationoftheIVGMRcanbegained.Isolation of S =0, T =1reactionsisachievedthroughexcitationofthesuperallowedFermi transition 10 Be(0 + ,g.s.) ! 10 B(0 + 1 ,1.74 T =1),whichisdetectedbyobservationof the1022keVgammarayfromthedeexctationoftheisobaricanaloguestatein 10 Btothe 10 B(1 + 1 ,0.718MeV)state.Theapplicabilityofthisprobeinseparationof S =0, T =1 reactionsisobservedwithdatatakenona 12 Ctargetthroughselectivityinobservationofthe 12 C(0 + ,g.s.) ! 12 B(1 + ,g.s.)transition,whichis S =1byIVGMRstrengthin 28 Alisidenusingthethe 28 Si( 10 Be, 10 B+ )reactionatE( 10 Be)=1000MeV.Isovector monopolestrengthisobserveduptoE x ( 28 Al)=30MeV.Theobservednon-energyweighted sumrulestrengthforpeaksat9and21MeVisdeterminedtobe66 36%and59 32%, respectively.ExctractedIVGMRandisovectorgiantdipoleresonancedistributionsarealso comparedwithresultsfromcalculationsinthecharge-exchangerelativistictimeblocking approximation. ToLulu-Reachingyourdreambeginswithasinglestep.Thepathmaybelong,but yourdiligencewillserveyou. iii ACKNOWLEDGMENTS IwouldliketobeginbythankingRemcoZegersforallofhishelpinmygraduatestuddies atMichiganStateUniversity.Withoutyourguidance,Icouldnothavecomethisfar.Thank youforansweringallofmyquestions...morethanonce. Iwouldliketopersonallythankthemembersofthecommittefortheirguidancethrough myacademiccareeratMichiganStateUniversity:AlexBrown,EdBrown,SeanLiddick, andArtemisSyprou. IwouldliketothanktheandoperatorsoftheNationalSuperconductingCyclotron laboratoryfortheirexpertiseinrunningthelab.Withtheirassistancewewereabletorun asuccessfulexperiment. Ihaveenjoyedthecompanyofmyfellowgraduatestudentsandfreindsinthelab.Some- timesoneneedsagoodlaughtotaketheirmindofaproblem. TomydaughterLulu.Thankyouforbeinganinspiration.Iwantedtogotoschoolto bettermyself,sointurnIcouldbebetterforyou.Daddylovesyou. TomywifeKristie.Iappreciateallthatyoudoforourfamily,andthesupportthatyou giveme.WithoutyouIknowIcouldnotputinthehoursthatarenecessarytocomplete mytasks.Infact,asIamwritingthis,itisaftermidnightandIcanhearyougrindingmy formeforthemorning.Yes,Iknowitislate...Yes,IknowIneedtogetupinthe morning...Okay,I'llgotobednow.Iloveyoudearly. iv TABLEOFCONTENTS LISTOFTABLES .................................... vii LISTOFFIGURES ................................... ix Chapter1Introduction ................................ 1 Chapter2ExperimentalConsiderationsfortheIsovectorNon-Spin-Flip MonopoleResonance .......................... 5 2.1ProbingfortheIVGMR.............................6 2.2The( 10 Be, 10 B+ )ProbeforIsovectorNon-Spin-FlipExcitations......10 2.3TargetSelectionandConsiderations.......................12 2.3.1 28 Si....................................12 2.3.2 12 C.....................................14 Chapter3TheoreticalDescriptionofGiantResonances ........... 17 3.1MacroscopicPicture...............................17 3.2MicroscopicPicture................................20 Chapter4TheoreticalCross-SectionCalculationsandApplications .... 29 4.1ThetialCross-Section..........................30 4.2TheDistortedWaveBornApproximation....................31 4.2.1CalculationofOpticalModelPotentials.................39 4.3FormFactors...................................40 4.3.1TheeNucleon-NucleonInteraction...............41 4.3.2One-BodyTransitionDensities.....................44 4.3.2.1IntheShellModel.......................45 4.3.2.2IntheNormalModesFormalism...............45 4.3.3Single-ParticleWavefunctions......................47 4.4ResultsofCalculation..............................48 Chapter5Experiment ................................ 51 5.1BeamPreparationandDelivery.........................51 5.1.1CoupledCyclotrons............................52 5.1.2A1900FragmentSeparator........................52 5.1.3Incomingbeamratemeasurement....................55 5.2TechnicalDescriptionofthe 10 B+ Measurement...............55 5.2.1S800Spectrograph............................57 5.2.1.1IonOpticsThroughaPlaneSymmetricMagneticField...57 5.2.1.2DispersionMatching......................60 v 5.2.1.3FocalPlaneDetectors.....................66 5.2.1.4TrajectoryReconstructionintheS800Spectrograph....68 5.2.1.5AngularResolutionImprovementinNon-DispersiveDirection70 5.2.2GammaRayDetection..........................71 5.2.2.1GRETINAandDetectorPlacement..............75 Chapter6DataAnalysis ............................... 79 6.1Calibrations....................................80 6.1.1S800Calibrations.............................80 6.1.2GRETINACalibrations.........................84 6.1.2.1SourceCalibrations.......................84 6.1.2.2In-FlightCorrections......................87 6.2ParticleIden...............................90 6.3ExcitationEnergyReconstruction........................93 6.4CoincidenceData.................................102 6.5ExperimentalResolutions............................105 6.6Cross-sectionCalculations............................107 Chapter7Results ................................... 112 7.1MultipoleDecompositionAnalysis........................112 7.1.1 12 C(0 + ,g.s.)( 10 Be, 10 B+ (0.718MeV)) 12 B(1 + ,g.s.)MDAResults..115 7.1.2 28 Si( 10 Be, 10 B+ (1.022MeV)) 28 AlMDAResults...........117 7.2Extractedtialcross-sectionsin 28 Al...................120 7.2.1Comparisonwiththeoreticalcalculations................123 Chapter8Conclusion ................................. 128 8.1Summary.....................................128 8.2Outlook......................................129 BIBLIOGRAPHY ................................... 131 vi LISTOFTABLES Table2.1Eventratesandinputstocalculation.Calculationswereperformed forcross-sectionsupto1 and5 scatteringangleinthecenter-of- mass.Seetextforcalculation......................12 Table2.2Estimatedexcitation-energyresolutionin 28 Alviathe 28 Si( 10 Be, 10 B + (1022MeV))reaction.Thereconstructedenergyofthe 10 Bparti- clesintheS800spectrographatNSCL[24,25]includesaconservative estimateforthequalityofdispersionmatching.Thecontributionto theresolutionduetorecoilof 28 Albydecatbygammaemis- sionincludescontributionsfromboththe1.022MeV(0 + ! 1 + )and subsequent0.718MeV(1 + ! 3 + )transitionsasindicatedinFigure 2.4.Thecontributionfromtheenergylossthroughthe targetaccountsforthefactthattheenergylossesof 10 Beand 10 B particlesinthetargetandthereactionpointinthetargetis unknown..................................13 Table4.1Possibleangularmomentumtransfers,separatedbyparity.High- lightedinredarethe S =0usedinthisstudy............48 Table5.1RelevantparametersusedinthesimulationofGRETINAresolution anddetectionofthe1.022MeVtransitionin 10 B[28].The Implementedcolumnrepresentstheurationusedinthisexper- iment.TheAlternativecolumnrepresentsanotherpossible rationformeasurement..........................78 Table6.1MaskcalibrationparametervaluesobtainedfromCRDCmaskmea- surement.............................83 Table6.2Referenceenergiesforvofgammarayenergycalibration and...............................85 Table6.3Referenceenergiesforvofgammarayenergycalibration and...............................90 Table6.4ofellipticalgateon 10 BinPID...............93 vii Table6.5Relevantexperimentalresolutionsand..........105 Table7.1ScalingfactorsobtainedfromtheMDAofthe 12 C(0 + ,g.s.)( 10 Be, 10 B+ (0.718 MeV)) 12 B(1 + ,g.s.)reactionasshowninFigure7.3.Scalingfactors representthescalingofthetheoreticallycalculatedangulardistribu- tionnecessaryforthesumtorepresentthedataasshowninEquation 7.1.....................................115 Table7.2KnownandcalculatedGTstrengthforthe 10 Be(0 + ,g.s.) ! 10 B(1 + , 0.718MeV)transition..........................116 Table7.3Comparisonoftheobservedpeakpositionoftheextracted L = 1(dipole)distributionforthe 28 Si( 10 Be, 10 B+ ) 28 Alreactionwith thepeakpositionoftheIVGDRmeasuredinpreviousexperiments throughthe 28 Si( ,n)[4], 28 Si(n,p)[92], 28 Si( 7 Li, 7 Be)[93],and 28 Si( , abs )[41]reactions.Wherenecessary,energiesrelativetotheground stateof 28 Siwereconvertedtothegroundstateof 28 Al........121 Table7.4TheoreticalDWBAcross-sectioncalculationfor q =0(nomomentum transfer)and0 scatteringangleforeachindividualstateparticipat- ingintheIVGMRin 28 Si.Thenormal-modesstrengthobtainedwhen calculatingtheOBTDfortheDWBAcross-sectionisalsoshown.The ratioofthecross-sectiontothestrengthshowsthatanassumption oflinearitybetweenstrengthandcross-sectiondoesnotholdbetween states...................................123 Table7.5TotalpredictedstrengthfortheIVGMRandIVGDRascalculated inthenormal-modesandRTBAframeworks..............124 viii LISTOFFIGURES Figure1.1Schematicrepresentationofvariouscollectivemodes.Multipoles showncorrespondto L =0(monopole), L =1(dipole),and L =2(quadrupole).Figuretakenfrom[1]..............2 Figure2.1Illustrationsofparticle-holecontributionstotheIVGMRinthe 28 Si ! 28 Alsystem.ThehorizontalgraydashedlinerepresentstheFermi level,uptowhichtheparticlesthegroundstate.TheIVGMR isacoherentsuperpositionoftheexcitationshighlightedwithgreen arrows...................................6 Figure2.2Transitiondensitymultipliedby r 2 forexcitationoftheIVGMRin 28 Alfrom 28 Si.ProbingtheIVGMRispreferablydoneusingaprobe thatisstronglyabsorbedatthesurface(asschematicallyindicatedby theshadedarea),toavoidthecancellationofthetransitionstrengths duetotheexteriorandinteriorcomponentsofthetransitiondensity.7 Figure2.3Previousexperimentfor 40 Causingthepionchargeexchangereaction [10].ThepeakrepresentingtheIVGMRisindicated.Totheright oftheIVGMRisapeakrepresentingtheIVGDR.TheIVGMRis coveredbythebackgroundcomponent,drawnwithdashedlines.The threecurvesweretothedataforextractionoftheIVGMR....8 Figure2.4Thelevelschemeof 10 Bofrelevanceforthe( 10 Be, 10 B+ )reactionto isolate S =0transitions.The 10 Be(0 + ;T =1 ;g:s: ) ! 10 B(0 + ;T = 1 ; 1 : 74MeV)transitionisaccompaniedbya1.022MeVgamma-ray fromdeexcitationtothe0.718MeV1 + state..............10 Figure2.5Gamma-rayspectrumwithDopplercorrectioninthe 90 Zr( 10 C, 10 B) reaction[20]................................11 Figure2.6Thelevelschemeofthe 12 Bofrelevencetothe( 10 Be, 10 B+ )reaction. Highlighedbythered,dashedarrowisthe 12 C(0 + ,g.s.) ! 12 B(1 + ,g.s.) transition.Statesin 10 Bupto2.72MeVarealsolisted........15 ix Figure2.7Excitationenergyspectrumforthe 12 C( t , 3 Hereactionat115MeV/ u . Ofinterestforthisstudyisthestrongpeakat0MeVinthe 12 B spectrumfromthe 12 C(0 + ,g.s.)( t , 3 He) 12 B(1 + ,g.s.).Graphicadapted from[29].................................16 Figure3.1(a)DataobtainedfortheISGMRviainelasticscatteringof parti- clesatsmallanglesfromReference[32].Thesolidlinerepresentsthe locationoftheISGMRasafunctionofmass(A)fromReference[30], andthedashedlinerepresentsanimprovementfromtotheestimate withbetterknowledgeofthenuclearincomressibilitytermfromRef- erences[8,9].(b)DataobtainedfortheIVGMRfrompionscattering fromReferences[10,11].Thesolidlinerepresentsaninitialestimate fromthehydrodynamicalmodel,andthedashedlinerepresentsthe improvementstothemodelwhenincludingsurface[33]....18 Figure3.2Schematicrepresentationofthewidthofthecollective1p-1hstate intoadirectcomponent " andaspreadingcomponent # .The spreadingcomponentcanbefurtherbrokenintotermsdescribing statisticaldecayoftheequilibriumcompoundnucleus ## anddecay oftheintermediate,pre-equilibriumstates "# .Figurereproduced from[40]..................................25 Figure3.3TheoreticalandexperimentalGTstrengthdistributionsin 208 Pb(up- perpanel)andtheircumulativesums(lowerpanel)[42].Thetoppanel illustratesthefragmentationofthestrengthallowedintheRTBA, ratherthancollectingstrengthintoonemajorpeak.Here ! repre- sentstheexcitationenergyofthe 208 Pb................26 Figure3.4ResultsoftheRTBAcalculationfortheIVGMRandtheIVGDRby E.Litvinova[43,42].StrengthshavebeensmearedwithLorentzians of2MeVinwidth............................27 Figure4.1Illustrationofthepropagationofaprojectilebetweenscatteringevents.34 Figure4.2Coordinatefortheformfactorcalculationwherethepro- jectile/ejectilesystemiswitha,brespectivelyandthetar- get/residualsystemiswithA,Brespectively..........40 x Figure4.3Energydependenceofthecentralcomponentsoftheeinter- action.Thesquarevolumeintegrals j J j 2 aresquareamplitudesfor thethet-matrixrepresentingthetransitionbetweenandinitial states,from[65].Shadingschematicallyrepresentingthetransition fromcomplexreactionmechanismstosingle-stepreactionsat100 MeV/ u isdescribedin[18]........................43 Figure4.4Angulardistributionsfor 28 Si( 10 Be, 10 B) 28 Alascalculatedwith,at E X =15 : 0 MeV ..............................49 Figure4.5Angulardistributionsfor 12 C( 10 Be, 10 B) 12 Bascalculatedwith,at 2 : 0