CHARACTERIZINGTHEEFFECTOFNEUTRON-RICHNESSONTHEREACTIONDYNAMICSINCHROMIUMANDTUNGSTENSYSTEMS.ByKaleeMichelleHammertonADISSERTATIONSubmittedtoMichiganStateUniversityinpartialentoftherequirementsforthedegreeofChemistry|DoctorofPhilosophy2017ABSTRACTCHARACTERIZINGTHEEFFECTOFNEUTRON-RICHNESSONTHEREACTIONDYNAMICSINCHROMIUMANDTUNGSTENSYSTEMS.ByKaleeMichelleHammertonSuperheavyelementsareprimarilyformedthroughheavy-ionfusionreactions[1,2,3].For-mationofafullyequilibratedcompoundnucleusisacriticalstepintheheavy-ionfusionreactionmechanismbutcanbehinderedbyordersofmagnitudebyqaprocessinwhichthedinuclearsystembreaksapartpriortofullequilibration[1,4,5,6,7,8].Toprovideacompletedescriptionofheavy-ionfusionitisimportanttocharacterizethequasi-process.TheinterplaybetweentheandreactionchannelswasexploredbymeasuringmassdistributionsineighttcombinationsofCr+Wre-actions,withvaryingneutron-richness,attheAustralianNationalUniversity.Thereactionsweremeasuredintwoenergyregimes:oneatcenter-of-massenergies(Ec:m:)13%abovetheBassinteractionbarrier[9]andoneat52.0MeVofexcitationenergyinthecompoundnucleus(ECN).ForthesystemsmeasuredatthehigherenergiesatEc:m:/VBass=1.13thedependenceontheneutron-richnessisclearandanincreaseintheneutron-richnessoftheentrancechanneldecreasesthelikelihoodof[10].However,forthereactionsatECN=52.0MeV,thedependenceislessclearandadditionalfactorsareshowntoplayavitalrole,especiallytheofdeformationontheefusionbarrier.Thepresentworkdemonstratesthatisanimportantprocessincompetitionwithfusioninreactionswithintermediatemassprojectiles,particularlywithmoreneutron-richsystems.formyfamilyiiiACKNOWLEDGMENTSThisworkwasaccomplishedbecauseofthesupportIreceivedfrommanypeople.ItisimpossibletothankeveryonesohereIwillhighlightafewkeycontributors.Firstandforemost,IwouldliketothankmyadvisorDaveMorrissey.WordscannotdescribehowmuchIappreciateyoutakingonthisprojectwithmemidwaythroughandhelpingmecompleteitallin3.5years.Thanksforremindingmetokeepthecartbehindthehorseandforhelpingmeimprovemywritingskills.Iwouldliketothankmycommitteemembers,PaulMantica,WMittig,andSeanLiddickfortheirsupportandsuggestions.Additionally,IwouldliketothankBradSherrillforbeingagreatmentorandencouragingmetoexplorepolicyandstartthenuclearpolicyworkinggroupchapteratMSU.IwouldalsoliketoacknowledgeMichiganStateUniversity,theDepartmentofChemistry,theNSCL,theNationalScienceFoundation,theNSSC,andIGCCfortheirsupportofthiswork.ThisworkwouldnothavebeenpossiblewithoutthesupportofmyresearchgroupAdiWakhleandKrystinStiefel.Thanksforbeingtherethroughallofourcraziness,includingexperiments.Krystin,thanksforbeinganamazingfriendandgreatroommatethroughsometoughtimesingradschool.Thanksforallofyourhelpalongtheway.Adi,thanksforbeingtheretoanswerallofmymanyquestionsabouttheANUset-upandexperiment.IwouldalsoliketothankZachKohleyforproposingtheideafortheexperimentandgivingmetheopportunitybeinvolvedsoearlyinmycareer.JohnYurkon,thankssomuchforyourpatienceinteachingmeaboutmakingdetectors.Someofmybestgradschoolmemoriescomefrombuildingdetectors.ThesupportfromtheNSCLfacultyandwasunparalleled.Thankyouallforlookingoutforme.ivGradschoolwouldnothavebeenthesamewiththeawesomeNuclearChemistrygroup:BeckyLewis,NickiLarson,KatieChilders,ChrisProkop,KortneyCooper,BenCrider,andPaigeAble.ThanksforgreatFridaylunchesandsomememorableWineNights.Iwillmissbeingapartofthiscommunity!Becky,thanksforbeinganawesomefriend,listeningtomevent,actingasasoundingboardforallsortsofideas,andalwaysbeingupforatriptoStarbucks!Nicki,thanksforbeingagreatfriend,teachingmetobeabetterswimmer,andhelpingmesortthroughallofthegradschoolrequirements.Chris,thanksforbeingagreatfriendandmateandalwayspushingmetobemybestthroughoutgradschool.ThankstoalloftheNSCLgradstudents,includingWeiJiaOng,AmyLovell,JennaSmith,ChrisMorse,andZachMeiselforbeingamazingfriends.ThankstotheMSUrunninggroup(JillBerryman,RenanFontus,andJonandMichelleKuchera)forhelpingmerunthestressofgradschoolstress.Jillthanksforlisteningandgreatadviceonnavigatinggradschool.MichelleKuchera,thanksforpushingmetobeabetterrunnerandfornotacceptinganyofmymanyexcusesastowhyweshouldnotrunallthroughMichiganwinters!Ourlongrunchats,trackTuesdays,andtrailtherapyaresomeofmyfavoritegradschoolmemories.ThankstotheANUgroup,DavidHindeandNandaDasguptaforallofyoursupportintheexperimentandanalysis.ThisworkwouldnothavebeenpossiblewithouttheamazingattheANUHeavyIonAcceleratorFacility.ThankstoIanCarterandJoeWalsheforbeinggreatfriendsandentertainingmewhileatANU.Gradschoolwouldnothavebeenpossiblewithoutmyamazingfamily.ThankstotheFenkersformanyinterestingnuclearphysicsdiscussionsandhelp.Kelsey,thanksforshowingmegradschoolwasanoptionandgettingmestartedonagoodpath.IwouldnotbewhereIamtodaywithouttheamazingsupportofmyparents!Youvsetmeupforsuccess.ThanksforneverlettingmesellmyselfshortandpushingmetobewhoIamtoday.Icouldnotdoallofthiswithoutyoursupport.Finally,Alex,gradschoolwouldnothavebeenpossiblewithoutyou.Thanksforlisteningtoallofmystress.Thanksforbeingmybiggestcheerleader.Thanksforstayingpositiveandmakingallthedinnersduringmyoralexam.ThanksforbeingtherewhenIneededtoescapeforgradschoollife.viTABLEOFCONTENTSLISTOFTABLES....................................xLISTOFFIGURES...................................xiiChapter1Introduction...............................11.1SuperheavyElements...............................11.2Heavy-IonFusionReactions...........................31.2.1Capture,˙cap...............................51.2.1.1AngularMomentum......................51.2.1.2ImpactParameter.......................71.2.1.3BassBarrier...........................91.2.2SurvivalagainstFission,Wsur......................101.2.2.1LiquidDropModel.......................111.2.3ProbabilityofformingaCompoundNucleus,PCN...........131.2.3.1...........................141.3ExperimentalSignaturesofQuasiion.....................141.3.1MassDistributions............................151.3.1.1ExcitationEnergyandFusion-Fission.............201.3.2AngularDistributions..........................211.3.3Mass-AngleDistributions.........................221.3.3.1TypesofMassAngleDistributions..............241.3.4EntranceChannelEnergyand...............291.4Heavy-IonFusionReactionswithNeutron-richRareIsotopeBeams.....301.5OrganizationofDissertation...........................31Chapter2ExperimentalDetails..........................322.1SystemSelection.................................322.1.1TwoEnergyRegimes...........................332.1.2Cr+WSystems.............................352.2TheANUHeavy-IonAcceleratorFacility....................362.2.1IonSource.................................392.2.214UDPelletron..............................422.2.3SuperconductingLINAC.........................442.3TheCUBEDetectorSystem...........................442.3.1MWPCs..................................462.3.2StructureoftheCUBEMWPCs.....................46Chapter3DataAnalysisTechniques.......................493.1CoordinateSystem..........................493.2PositionInformation...............................53vii3.2.1PositionCalibrations...........................533.2.2TransformationAmongtheCoordinateSystems............603.3TimingInformation................................643.4KinematicCoincidenceMethod.........................693.5VelocityDetermination..............................733.5.1Usingtodemonstratevperpiszero..................743.5.2CalculatingMR..............................753.5.3EnergyCalculation............................783.5.4TotalKineticEnergyGates.......................793.5.5DeterminationofMRandc:m:.....................81Chapter4Results...................................824.1Cr+W:Ec:m:/VB=1.13............................824.1.1Mass-AngleDistributions.........................824.1.1.1Symmetrization.........................874.1.1.2SymmetrizedMADsforCr+Wsystems...........884.1.2MassDistributions............................934.1.2.1DeterminationofMassWidthfromMassDistribution...934.1.2.2StatisticalApproximationofPureFusion-Fission......964.1.3AngularDistributions..........................1004.1.3.1NormalizationoftheAngularDistribution..........1034.1.3.2QuantitiesneededinAngularDistributionDetermination.1064.1.3.3RelativeDetector.................1094.2Cr+W:E=52.0MeV.............................1114.2.1Mass-AngleDistributions.........................1144.2.2MassDistributions............................1144.2.2.1CurvatureAnalysisTechniques................1234.2.2.2VcationwithEc:m:=VB=1:13systems..........1234.2.3AngularDistributions..........................124Chapter5Discussion.................................1285.1BohrIndependenceHypothesis.........................1285.2Cr+W:Ec:m:/VB=1.13............................1305.2.1FissilityandMassAsymmetry......................1325.2.2MassWidthsComparedtoTheoreticalCalculations..........1355.2.3ComparisonwithAnalyticalCalculationsofPCN...........1385.2.3.1Armbruster'sAnalyticalDescriptionofPCN.........1385.2.3.2Zagrebaev'sAnalyticalDescriptionofPCN..........1405.2.3.3Siwek-Wilczynskana'sAnalyticalDescriptionofPCN....1415.2.3.4ComparisonofResultsofAnalyticalCalculations......1425.3Cr+W:E=52.0MeV.............................1425.3.1AngularMomentum...........................1445.3.2RotationalEnergy............................1455.3.3ofNuclearOrientations......................1475.3.3.1ShapeEvolutionandMassAsymmetry............149viii5.4AngularDistributions...............................1525.5PreviouslyStudiedReactionsforming238Cfand240Cf............156Chapter6Conclusions................................164BIBLIOGRAPHY....................................167ixLISTOFTABLESTable2.1:Chromiumandtungstenisotopicinformationincludingpercentabun-dances(half-lives),2values,andanymagicnumbersinthenucleus.34Table2.2:Tungstentargetandcarbonbackingthickness,andreaction[84]..34Table2.3:Cr+Wsystems,compoundnuclei,relativechangeinneutronsfusionQvalue(Qfus),Bassinteractionbarrier(VB)[9],Ec:m:forbothenergyregimes..............................39Table2.4:Cr+Wsystems,compoundnuclei,relativechangeinneutronsEc:m:,ECN,interactioncrosssection(mb)[88],lmax,andlcrit[88]forbothenergyregimes...........................40Table3.1:CoordinatesineachofthethreesystemsinthisworkforthecenterandfourpositionsaroundtheedgeofthetwoMWPCs.Theedgepositionslistedareatthecenteroftheedgesofthetop,bottom,left,andrightsidesoftheactiveareaofthetwoMWPCs.IntheCartesiansystemsandinrinthesphericalsystemthevaluesaregiveinmm.Inthesphericalcoordinatesystemthevaluesandaregivenindegrees..........................53Table3.2:TheexperimentallydeterminedpositionsinchannelnumbersandthepositionsinmmfortheedgesoftheactiveareaoftheFrontandBackMWPCs............................55Table3.3:SlopesandInterceptsdeterminedforthelinearconversionfromchan-nelnumbertomillimetersfortheMWPCs...............60Table3.4:Componentfortheprojectionsvi;labalongtheXandZaxesinthe(X;0;Z)planeandalongtheXaxisinthe(X;Y;0)plane.Thecomponentsinthe(X;0;Z)planearerelativeto,whileXisinthe(X;Y;0)planerelativetoSeetextforfulldescriptionsofplanesandangles....................71Table4.1:CalculatedvaluesusedinthedeterminationofEsci..........98Table4.2:CalculatedvaluesusedinthedeterminationofEscipre.........99Table4.3:CalculatedvaluesusedinthedeterminationoftheEscirot........99xTable4.4:Experimentalmasswidths˙exp,statisticalestimateforthepurefusion-masswidth˙,andtheratioof˙exp=˙(upperlimitofPCN)forall8systemsmeasuredatthesameEc:m:/VB=1:13......100Table4.5:Thenumberofcountsinthetwomonitors(M),thenumberofpulsereventsintheBackMWPC(P),andthescalersvaluesforthemonitors(Mscal)andpulser(Pscal)fromthemeasurementof50Cr+180Wasanexampleandthecalibrationmeasurementof50Cr+184W....111Table4.6:RelativepeakintrinsicoftheBackMWPCandtheSimonitordetectorsforallsystemsmeasuredinthepresentworkrel-ativetothecalibrationrunof50Cr+184W!234CfatElab=186:0MeV....................................114Table4.7:Curvatureparametersanderrorsdeterminedforall8systemsmea-suredatcenter-of-massenergiesresultingincompoundnucleiwithECN=52:0MeV.............................124Table5.1:Compoundnucleary(˜CN)andmassasymmetry()valuesofeachoftheeightCr+Wsystemspresentedinthiswork.Thedeter-minedupperlimitsofPCN,capturecrosssection,andevaporationresiduecrosssectionsarealsoincluded.................135Table5.2:Averageradii,2values[86],semi-majorradii,andsemi-minorradiideterminedforchromiumandtungstenisotopesconsideredinthepresentwork................................152Table5.3:Bassinteractionbarriers[9]fortheaverageandlimitingorientationsdeterminedfortheCr+Wreactionsconsideredinthepresentwork.154Table5.4:Entrancechannelsystem,y(˜CN),massasymmetry(),center-of-massenergy,energyrelativetotheinteractionbarrier[9](Ec:m:/VB),excitationenergy(E),andupperlimitofPCNfortherelevantsystemsmeasuredinthepresentworkandthesystemspreviouslymeasuredatANUwherethecompoundnucleusformedwas238Cfor240Cf....................................158xiLISTOFFIGURESFigure1.1:Illustrationofanexampleheavy-ionfusionreactionshowingvariousreactionchannels.Keypointsinthereactionpathareemphasizedbythedashedlines.Thearrowsindicatetheprogressionofthereactionwithtime.................................4Figure1.2:Illustrationofthreepossiblereactionoutcomesfromaheavy-ionreac-tion.PanelAdepictselasticscattering,PanelBdepictsdeepinelasticscattering,andPanelCdepictscapture................6Figure1.3:Illustrationofthecrosssectionofaheavy-ionreactionasafunctionofangularmomentum.Theblack,dashedlinerepresentstheline˙=ˇ2(2l+1).Thevarioushashedregionsindicatethevariousangularmomentumvalueswheretprocessesareprominent.Themostprominenttypeofreactionineachangularmomentumre-gionisindicated.Fourtangularmomentumvaluesarecalledout(lcrit,lf,lD,andlmax).Seetextfortheitionofeachoftheindicatedangularmomentumvalues.Adaptedfrom[32].......8Figure1.4:Cartoonexampleoftheofimpactparameter.PanelAshowsasideviewofaheavy-ioncollision.PanelBshowsabeamviewofacollision.Aspresentedinthecartoon,thedarkbluesphereisthetargetandthelightbluesphereistheprojectile.........9Figure1.5:Illustrationofamassdistribution.Thevariouscirclesindicatetheexitchannelfragmentsexpectedatvariousmassratios.Seetextforexplanation................................16Figure1.6:Massdistributiondeducedfromthereactionof12C+208PbatElab=66.0MeV[47].............................18Figure1.7:Massdistributiondeducedfromthereactionof48Ti+192OsatElab=259.9MeV[46].............................19Figure1.8:Massdistributionsreportedin[48]fromthereactionofheliumanduranium-233.Reprintedwithpermissionfrom[48]Copyright(1961)bytheAmericanPhysicalSociety.http://dx.doi.org/10.1103/PhysRev.121.1415............................20Figure1.9:Schematicimageofangularmomentumcouplingcoordinatesystemforadeformednucleus.Adaptedfrom[51]..............21xiiFigure1.10:Themassangledistributionpreviouslydeducedfromthereactionof12C+208PbatElab=66.0MeV[47].................24Figure1.11:Themassangledistributiondeducedfromthereactionof48Ti+192OsatElab=259.9MeV[46].Thedashed,greylineisincludedtohigh-lightthecorrelationbetweenmassandangle..............25Figure1.12:Threeexamplereactions.Illustratingtheofimpactparameterofandangleofrotationofthemassandangleoftheemittedfragments..........................26Figure1.13:Plotofthe42MADsreportedin[40].Inthetopleftcorner,theMADdeducedfromthemeasurementof48Ti+170EratElab=225.0MeVisenlargedtohighlighttheaxislabels.Systemsthatfallalongthesamevertical,red,dashed-ordiagonal,blue,dashed-lineswereformedwiththesameprojectileortarget,respectively.Systemsalongthesamehorizontal,black,dashedlinesformedthesamecompoundnucleus.Reprintedwithpermissionfrom[40]Copyright(2013)bytheAmericanPhysicalSociety.http://dx.doi.org/10.1103/PhysRevC.88.054618..................................27Figure1.14:MADsrepresentativeofTypesI,II,IIIasidenbyDuRietzetal.[40]areshowninPanelsA,B,andC,respectively.Thecorrespond-ingmassdistributionsareshowninPanelsD,E,andF.Reprintedwithpermissionfrom[40]Copyright(2013)bytheAmericanPhysicalSociety.http://dx.doi.org/10.1103/PhysRevC.88.054618..28Figure1.15:ZCNasafunctionofZpZtforthe42reactionsincludedin[40].TheidenboundariesbetweentheTypesofMADsareindicatedbythesolid,blue-andlong-dashed,red-lines.Reprintedwithper-missionfrom[40]Copyright(2013)bytheAmericanPhysicalSociety.http://dx.doi.org/10.1103/PhysRevC.88.054618...........29Figure2.1:SchematicdiagramoftheANUheavy-ionacceleratorfacility.Theionsourceisshownatthetop(moredetailinFigure2.3).The14UDPelletronTandemacceleratorisinthecenter,followedbyanana-lyzingmagnetandtheconnectiontotheCUBEbeamline.OnlytheLINACmagnetisindicatedhereandaschematicdiagramofthecompleteLINACisshowninFigure2.2................37Figure2.2:SchematicdiagramoftheANULINAC.Thecryostatsaredepictedaswellasmanybeamlinecomponentsincludingthetwoachromatsandthepreandpostbunchers......................38xiiiFigure2.3:SchematicdiagramoftheoperationoftheSNICSshowingtheactivevolumeofthesource,theionizers,thecathode,thepathofionizedCsandthepathofsputteredsamplematerial.............41Figure2.4:SchematicscalediagramofthelayoutofthedetectorsinsidetheCUBEdetectorsystemasviewedfromabove.Onemonitordetectorisabovethebeampathandtheotherisbelow,seetext........45Figure2.5:RenderingoftheCUBEdetectorsetupasusedinthepresentwork.TheFrontandBackMWPCs,thebeamdirection,thetargetladdersupport,andthetwoSimonitordetectorsareindicated........47Figure3.1:SchematicscalediagramoftheindividualMWPCcoordinatesystemsusedinthepresentwork.ThegraybordersrepresenttheMWPCsupportstructureandthewhiteinnerregionsrepresenttheactiveareaoftheMWPCs.ThefourpositionquadrantsoftheMWPCscathodesareindicated.Thecoordinatesatthecenterofthedetectorandthecenterofeachedgeoftheactiveareaareindicatedinunitsofmm...................................50Figure3.2:SchematicscalediagramoftheCartesiancoordinatesystemusedinthepresentworkinrelationtotheCUBEdetectorsetup.PanelAshowsadiagramoftheCUBEdetectorssetupfromaboveillustratingthe(X;0;Z)plane.PanelBshowsadiagramoftheCUBEdetec-torsetupfromthebeamaxisupstreamofthetargetillustratingthe(X;Y;0)plane.ThecoordinatesatthecenteroftheCUBEandatthecenterofthetwoMWPCsareindicated..............52Figure3.3:SchematicscalediagramofthesphericalcoordinatesystemusedinthepresentworkinrelationtotheCUBEdetectorsetup.PanelAshowsadiagramoftheCUBEdetectorsetupfromabove.Theofandrareindicated.PanelBshowsaviewfromthebeamaxisupstreamoftheCUBEandtheofisindicated.ThecoordinatesatthecenteroftheCUBEandatthecenterofthetwoMWPCsareindicated........................52Figure3.4:Positiondistributionsinthexandydimensionsinchannelnumberobservedfromthecalibrationmeasurementof50Cr+184WatELab=186.0MeVthatwasusedtodeterminethedetectoredgesinFrontandBackdetectors.PanelsAandBcorrespondtothexandypositiondistributionsfortheBackMWPCandPanelsCandDcorrespondtothexandypositiondistributionsfortheFrontMWPC........56xivFigure3.5:TwodimensionalpositionspectrafortheBackMWPC.PanelAshowstherawpositioninformationandthesolidblackrectanglere-thegateappliedtothedatasets.PanelBshowsthepositionspectraafterthegatewasapplied.Botharefor50Cr+180WatELab=284.0MeVasanexample.......................58Figure3.6:TwodimensionalpositionspectrafortheFrontMWPC.PanelAshowstherawpositioninformationandthesolidblackrectanglere-thegateappliedtothedatasets.PanelBshowsthepositionspectraafterthegatewasapplied.Botharefor50Cr+180WatELab=284.0MeVasanexample.......................59Figure3.7:Twodimensionalpositionspectrafollowingtheconversionfromchan-nelnumbertommfortheBack(A)andFront(B)MWPCsobservedduringthemeasurementof50Cr+180WatELab=284.0MeVasanexample..................................61Figure3.8:AngularcoverageoftheBack(A)andFront(B)MWPCsshownaslabonthex-axisandonthey-axisfor50Cr+180WatELab=284.0MeV.................................63Figure3.9:PanelAshowstherawtimingsignalsobservedforcoincidentfrag-mentsintheFront(x-axis)andBack(y-axis)MWPCsfromthemea-surementof50Cr+180WatELab=284.0MeV.PanelBshowstheobservedtimingsignalsfollowingconversiontons.Seetextfordetailsonthisconversion.............................65Figure3.10:TimespectrainchannelnumbersobservedintheBack(A)andFront(B)MWPCsfromtheTACcalibrationswith10nspulses.......66Figure3.11:Illustrationofanexamplesetoftimingsignalsincluding,RFsignalsinthetoppanel,atimingsignalfromtheBackMWPCinthemiddlepanel,andatimingsignalfromtheFrontMWPCinthebottompanel.t0andtarethetimeparametersusedintheCUBEcalibration.Seetextfordiscussion.............................68xvFigure3.12:Illustrationoftheprimaryvectorsconsideredinthekinematiccoin-cidencemethodfortwoemittedfragments.PanelAshowsthepro-jectionofonepossiblecombinationofvectorsontoaplane(X;0;Z)alongthebeamaxis.TheZ-axisrepresentsthebeamaxis.Thesolid,blackvectorsrepresentapossiblesetofVi;c:m:fortwofragmentsi.Thedashed,purplevectorsrepresentonepossiblesetofvi;lab.Asanexample,thetwocomponentsofthetwoVi;c:m:areshown.Thedot-dashed,redvectorsrepresentui;c:m:andthedotdashed,bluevectorsrepresentwi;c:m:.i;labisshownasanexampleoftheof.PanelBshowsaprojectionofonepossiblecombinationofvelocityvectorsontoaplane(X;Y;0)perpendiculartothebeamaxis.Thedashed,blackvectorsrepresentonepossiblecombinationofVi;c:m:forfragmentsi.Thedotdotdashed,skybluevectorsrepresentpossi-bleVi;dev.TheprojectionofeachVi;devonthez-axisisrepresentedbythedotdotdashed,darkpurplevectors(shownjustthezaxisforclarity).Thesolid,orangevectorsrepresentvperp,whichshouldbezeroinbinarykinematics.˚i;devarealsoindicated........70Figure3.13:Perpendicularvelocitydeterminedfor50Cr+180WatELab=284.0MeVasafunctionofthebetweenvparandvcn.Thesolid,blackcircleinPanelArepresentsthegateappliedtothedatasetandhasa1mm/nsradius.PanelAshowsthedistributionbeforethegatewasapplied.PanelBshowsthedistributionafterthegatewasappliedtothedataset..........................76Figure3.14:Thenumberofcountsobservedfor50Cr+180WatELab=284.0MeVshownasafunctionofthebetweenthedeterminedvaluesoffromtheBackdetectorandtheFrontdetectorforgatedcoincidentevents.Thedataisrepresentedasthesolidbluelineandshowsastrongpeakataof180.AGaussianfunctiontothedataisshownasthedashed,redlineandtheboxintheupperrightcornerprovidesthemeansandRMSfromthe....77Figure3.15:Ratioofthededucedtotalkineticenergyfrombinaryfragmentstothetotalkineticenergycalculatedforssionfragmentsfor50Cr+180WatELab=284.0MeVshownasafunctionthedeterminedmassratios.Thesolid,blackpolygoninPanelArepresentsthegatesusedtoremovescatteringeventswithmassratiosintheeregion.PanelAshowsthedistributionbeforethegatewasapplied.PanelBshowsthedistributionafterthegatewasapplied.......80xviFigure4.1:UnsymmetrizedMADsoftheeightCr+WreactionsintheBackMWPCatEc:m:/VB=1.13.isthechangeinthenumberofneutronsinthecompoundnucleusrelativeto50Cr+180W,whereN=132...................................83Figure4.2:UnsymmetrizedMADsgeneratedfortheCr+WreactionsintheFrontMWPCatEc:m:/VB=1.13.isthechangeinthenumberofneutronsinthecompoundnucleusrelativetothelightestsystem,50Cr+180W,whereN=132......................85Figure4.3:Evolutionofamassangledistributionthroughvariousseparationangles.PanelAshowsthefull360degreecoverage.PanelBshowsasymmetrizedMADwitha0-180degreescalein...........88Figure4.4:Themassangledistribution,wherec:m:isshownasafunctionofmassratio,forcoincidenteventsfromthereactionof50Cr+180WatElab=284:6MeV.Thesolid,blackrectanglehighlightsthemasssymmetricregion(MR=0.35-0.65)acrossthefullangularcoverageofthesymmetrizedMAD.Seetextfordiscussion.isthechangeinthenumberofneutronsinthecompoundnucleusrelativetothelightestsystem,50Cr+180W,whereN=132.............90Figure4.5:ThesymmetrizedMADfromthereactionof54Cr+186WatElab=281:7MeV.AsinFigure4.4,thesolid,blackrectanglewasdrawntohighlighttheregionofmasssymmetriceventsbetweenMR=0.35-0.65acrosstheangularcoverageoftheMWPCs............91Figure4.6:SymmetrizedMADsoftheremainingsixCr+WreactionsatEc:m:/VB=1.13.isthechangeinthenumberofneutronsinthecompoundnucleusrelativeto50Cr+180W,whereN=132.....92Figure4.7:MassdistributionsforalleightCr+WsystemsfromthepresentworkatEc:m:/VB=1.13.ThesolidredlinerepresentaGaussiantothedata.ThedashedbluelinerepresentsaGaussianfunctionwiththewidthscalculatedfromastatisticalapproximationsforpureFThisGaussianfunctionhasbeennormalizedtothepeakoftheexperimentalmassdistribution.isthechangeinthenumberofneutronsinthecompoundnucleusrelativeto50Cr+180W,whereN=132..............................94Figure4.8:Unsymmetrizedmassangledistributionforcalibrationrunof50Cr+184WatElab=186.0MeV.Thedashed,blackboxindicatestheangularregionincludedintheangulardistributioncalculations....102xviiFigure4.9:Unsymmetrizedmassangledistributionfor50Cr+180WatElab=284.6MeVasanexampleoftheeventsincludedinthedeterminationoftheangulardistribution.Thesolid,blackboxrepresentsthegateusedtoexcludealleventsoutsidetheeregion........103Figure4.10:Unsymmetrizedmassangledistributionafterthegateonthelikeregionwasappliedtothedatasetfor50Cr+180WatElab=284.6MeVasanexampleoftheangularregionincludedinthedeterminationoftheangulardistribution.Thedashed,blackboxrepresentstheangularregionincludedintheangulardistributioncalculations................................104Figure4.11:Countsinthetwomonitordetectorsforthereactionof50Cr+180WatElab=284.6MeVshownasafunctionofchannelnumber.....107Figure4.12:c:m:distributionsforthereactionof50Cr+180WatElab=284.6MeV....................................108Figure4.13:Distributionofc:m:foreachdeducedlabforthe50Cr+180WatElab=284.6MeV.Thesolid,redlinerepresentsafourthdegreepolynomialtothedistribution....................109Figure4.14:c:m:distributionsforthecalibrationmeasurementof50Cr+184WatElab=186.0MeV...........................110Figure4.15:Theangulardistribution(d˙(lab;E)=dforalleightCr+Wsys-temsmeasureinthepresentworkatEc:m:/VB=1.13shownasafunctionofc:m:isrepresentedbytheblackdatapoints.Thesolid,redlineisasinefunctiontotheexperimentaldatapointsusinga˜2minimization..............................112Figure4.16:UnsymmetrizedMADsobservedintheBackMWPCforalleightsystemspresentedinthisworkatECN=52.0MeV.isthechangeinthenumberofneutronsinthecompoundnucleusrelativeto50Cr+180W,whereN=132.........................115Figure4.17:UnsymmetrizedMADsobservedintheFrontMWPCforalleightsystemspresentedinthisworkatECN=52.0MeV..........117Figure4.18:SymmetrizedMADsfortheCr+WsystemsmeasuredinthisworkatECN=52.0MeV...........................119xviiiFigure4.19:MassdistributionsforCr+WsystemspresentedinthisworkatECN=52.0MeV.Thesolidgreenlinerepresentstheseconddegreepolynomialtothedata........................121Figure4.20:ComparisonoftheresultsfromthetwomethodsfordeterminingtherelativeshapesexperimentalmassdistributionsappliedtotheCr+WdataatEc:m:/VB=1.13.......................125Figure4.21:Theangulardistribution(d˙(lab;E)=dforCr+Wsystemsmea-sureinthepresentworkatECN=52:0MeVshownasafunctionofc:m:isrepresentedbytheblackdatapoints.Thesolid,redlineisasinefunctiontotheexperimentaldatapointsusinga˜2mini-mization..................................126Figure5.1:UpperlimitofPCNdeterminedfortheCr+Wsystemsforming236Cfmeasuredinthepresentworkasafunctionofthemassoftheprojectile.ThesesystemsweremeasuredatEc:m:=VB=1.13.Thecolorsoftheupperlimitmarkerscorrespondtotheprojectileusedinthereaction................................131Figure5.2:CurvatureparameterdeterminedfortheCr+Wsystemsforming236Cfmeasuredinthepresentworkasafunctionofthemassoftheprojectile.ThesesystemsweremeasuredatECN=52.0MeV.Thecolorsoftheupperlimitmarkerscorrespondtotheprojectileusedinthereaction................................131Figure5.3:UpperlimitofPCNforeachsystemmeasuredatEc:m:=VB=1:13isshownasafunctionof(N/Z)CN.Thecoloroftheupperlimitmarkerscorrespondtotheprojectileusedinthereaction............132Figure5.4:Themassasymmetryofthesystemsmeasuredinthepresentworkshownasafunctionofthesystemsy.Thecolorsofthemarkerscorrespondtotheprojectileusedinthereaction............134Figure5.5:DeducedupperlimitsforPCNshownasafunctionofthecompoundnuclearyforthesystemsmeasuredatEc:m:/VB=1.13.Thecolorsoftheupperlimitmarkerscorrespondtotheprojectileusedinthereaction................................136Figure5.6:DeducedupperlimitsforPCNshownasafunctionofthemassasym-metryforthesystemsmeasuredatEc:m:/VB=1.13.Thecolorsoftheupperlimitmarkerscorrespondtotheprojectileusedinthereaction..................................136xixFigure5.7:TDHFcalculationsformassratioMR,chargeratioZR(a)andcon-tacttime(b)for50Cr+180W!240Cfand54Cr+186W!240Cfshownasafunctionofimpactparameterb[10].Theinsertinpanel(a)showsanexampleofadensityplotwherethedinuclearsystemseparates.Theinsertinpanelbshowsanexampleofadensityplotwherethesystemfuses,seethetext.Reprintedwithpermis-sionfrom[10]Copyright(2015)bytheAmericanPhysicalSociety.http://dx.doi.org/10.1103/PhysRevC.91.041602...........139Figure5.8:PCNcalculatedfromthreeanalyticalfunctions[119,29,120]shownasafunctionof(N/Z)CN.Theupperlimitsdeducedforthesystemsinthepresentworkareincludedasthehorizontallines........143Figure5.9:Curvatureparameterinarbitraryunitsdeducedfromthemassdis-tributionforeachsystemmeasuredatECN=52:0MeVasafunction(N/Z)CN.................................145Figure5.10:CurvatureparameterdeducedfortheCr+WsystemsatECN=52:0MeVinthepresentworkasafunctionofthelmax.Thecolorsofthedatapointsindicatetheprojectileusedinthereaction........146Figure5.11:CurvatureparameterdeducedfortheCr+WsystemsatECN=52:0MeVinthepresentworkasafunctionofthelcrit.Thecolorsofthedatapointsindicatetheprojectileusedinthereaction........146Figure5.12:CurvatureparameterdeterminedfortheCr+WsystemsatECN=52:0MeVmeasuredinthepresentworkasafunctionofthemaximumavailablerotationalenergydeterminedasineq.5.9inMeV.Thecolorsofthedatapointsindicatetheprojectileusedinthereaction.148Figure5.13:Thetwolimitingcaseofcollisionwithadeformedtargetnucleus.PanelAshowsacollisionwherethenuclearsymmetryaxesarealigned.PanelBshowsthecasewheretheaxesareanti-aligned........149Figure5.14:CurvatureparametersdeterminedfortheCr+WreactionsmeasuredinthepresentworkasafunctionofEc:m:=VB(aligned)inPanelA,Ec:m:=VB(average)inPanelB,andEc:m:=VB(anti-aligned)inPanelC......................................153Figure5.15:Angularanisotropy,determinedastheratioofW(142)toW(102)forthesystemsmeasuredatEc:m:=VB=1.13shownasafunctionof(N/Z)CNinthepresentwork.Thecolorsofthedatapointscor-respondtotheprojectileusedinthereaction.Thesolid,greenlineindicatestheratioofW(142)toW(102)fora1/sin()function..155xxFigure5.16:Angularanisotropy,determinedastheratioofW(142)toW(102)forthesystemsmeasuredatECN=52.0MeVshownasafunctionof(N/Z)CNinthepresentwork.Thecolorsofthedatapointscor-respondtotheprojectileusedinthereaction.Thesolid,greenlineindicatestheratioofW(142)toW(102)fora1/sin()function..156Figure5.17:Massdistributionsforpreviouslymeasuredsystemsforming238Cfor240CfatcomparableenergiestotheCr+WsystemsmeasuredatEc:m:/VBˇ1.13(panelsA,C,andE)andECNˇ52.0MeV(panelsB,D,andF)...............................159Figure5.18:TheupperlimitofPCNdeterminedforthesystemsinthepresentworkandpreviouslymeasuredatANUforming238Cfor240Cfasthecompoundnucleusareshownasafunctionoftheyofthecompoundnucleus.Thesystemsaredistinguishedininthelegend..160Figure5.19:TheupperlimitofPCNdeterminedforthesystemsinthepresentworkandpreviouslymeasuredatANUforming238Cfor240Cfasthecompoundnucleusareshownasafunctionoftheentrancechannelmassasymmetry.Thesystemsaredistinguishedininthelegend...161Figure5.20:ThecurvatureparametersdeterminedforthesystemsinthepresentworkandpreviouslymeasuredatANUforming238Cfor240Cfasthecompoundnucleusareshownasafunctionoftheyofthecompoundnucleus.Thesystemsforming238Cfareindicatedbythesolidmarkers,whilethesystemsforming240Cfareindicatedbytheopenmarkers.Thesystemsaredistinguishedininthelegend.Theinsetinthelowerrightcorneristhesameplotzoomedinonthesystemsotherthan32S+208Pb....................162Figure5.21:ThecurvatureparametersdeterminedforthesystemsinthepresentworkandpreviouslymeasuredatANUforming238Cfor240Cfasthecompoundnucleusareshownasafunctionoftheentrancechannelmassasymmetry.Thesystemsforming238Cfareindicatedbythesolidmarkers,whilethesystemsforming240Cfareindicatedbytheopenmarkers.Thesystemsaredistinguishedininthelegend.Theinsetinthelowerrightcorneristhesameplotzoomedinonthesystemsotherthan32S+208Pb.....................163xxiChapter1Introduction1.1SuperheavyElementsIn2016fournewsuperheavyelementswerenamed[11,2,12,13,14,15].Thefournewelementshelpansweroneoftheoverarchingquestionsinnuclearphysics:Howlargecananucleusbecomeandstillbeheldtogetherbythenuclearforce?Insuperheavyelementresearchinthe1970'samethod,called\coldfusion"wasproposed,whereamediummassprojectileisimpingedona208Pbor209Bitargetatenergiessuchthatthecompoundnucleusisformedwithapproximately20MeVofexcitationenergy[16,17].Theterm\cold"isaresultoftherelativelysmallexcitationenergiesofthecompoundnuclei.WhilecoldfusionreactionsweresuccessfulintheproductionofsuperheavyelementswithZbetween104and113theproductioncrosssectionsdecreasebymorethanfourordersofmagnitudeoverthatZrange[1].Hotfusionreactions,wheredoublymagic48Caisimpingedonheavyactinidetargets,havetlylargercrosssectionscomparedtothepreviouslyusedcoldfusionreactions[1].Thesereactionsaretermed\hot"fusionreactionsduetotherelativelyhighexcitationenergyofthecompoundnucleusandwereusedtoproducesuperheavyelementswithZof114to118[15,14,11].BeyondaZof118thesuperheavyelementproductioncrosssectionsforbothhotandcoldfusionreactionscontinuetodecrease[18].Additionally,toreachhigherZwithhotfusionreactions,heavieractinidetargetsareneededandthenextactinides,einsteinium,fermium,andbeyond,donothave1isotopeswithlongenoughhalflivestoeasilyprepareatarget[19].Whilesomeworkisfocusedontryingtoproducetheseheaviertargets[20],alargerresearchisexploringalternativemethodsfortheproductionofsuperheavynuclei[18].Inadditiontothedesiretoincreasethenuclearchargeofnewsuperheavynuclei,thereisastrongmotivationtomovetowardsmoreneutron-richsuperheavynuclei.Thismotivationcomesfromthetheoreticalpredictionmadeinthe1960s[21],thatthereexistsaregionofenhancedstabilityaroundneutronnumber184termedthe\IslandofStability"[1,22,23,24,2,25].Themostneutron-richnucleiproducedtodatearestillseveralneutronsawayfromN=184,butanenhancementinstabilityhasalreadybeenobserved[13,14,15,12].Oneproposedmechanismtoreachthemoreneutron-richsuperheavynucleiistouseneutron-richradioactiveisotopesastheprojectilebeams[26,27,28,29].Lovelandetal.[29]usedanalyticalcalculationstocomparetheproductionratesofsuperheavynucleifromreac-tionsofstableandradioactiveprojectilebeamsbasedonthepredictedproductionintensitiesattheproposedRIAfacility.Thisworkconcludedthatstablebeamsgenerallyhavelargerproductionsratesforagivennucleusthanradioactivebeamsduetobeamintensity.However,therearemanynucleithatsimplycannotbeproducedfromreactionsofstableprojectilesandtargets.Itisparticularlytoreachthemoreneutron-richsuperheavynucleiwithstablebeams,thusneutron-richradioactivebeamsmaybethebestpossiblemechanismtoreachthe\islandofstability".Atthewritingofthisdocumenttheuseofradioactivebeamsinsuperheavyelementproductionislimitedduetoextremelylowbeamintensities.However,futurefacilitiesmaymakesuperheavyproductionreactionswithneutron-rich,radioactivebeamspossible.Toassessthefeasibilityofusingradioactiveisotopebeamsintheproductionofsuperheavyelements,itisimportanttohaveafullunderstandingofhowincreasingtheneutronnumberoftheprojectilewillimpactthemechanismforproducingsuperheavynuclei.2Allsuperheavyelementdiscoverymeasurementtodateusedheavy-ionfusionreactions[18].1.2Heavy-IonFusionReactionsAheavy-ionfusionreactionisageneraltermforanyreactionbetweentwonucleilargerthananalphaparticle.Themechanismforheavy-ionfusionreactionsisillustratedinFigure.1.1wherethearrowsindicatetheprogressionoftheexamplereactionwithtime.Theheavy-ionfusionreactionmechanismcanproceedthroughseveralchannels.Theevaporationresidueproductionchannel(neededforsuperheavyelementproduction)issegmentedintothreeprimarystages.First,theprojectileandtargetmustovercometheinteractionbarrierandmutuallycapturetoformadinuclearsystem.Second,thedinuclearsystemmustfullyequilibrateinalldegreesoffreedomtoformafullyfusedcompoundnucleus.Historically,thiswasreferredtoaspossessingthe\extrapushenergy"[30].Third,thecompoundnucleusmustsurviveagainstanddecaybylightparticleemissiontoformanevaporationresidue.Thereactionchannelleadingtotheproductionofanevaporationresidueisshownasthestraight,horizontalpathinFigure1.1.Twootherpotentialoutcomesfromaheavy-ionfusionreactionaredepictedinFigure1.1.1)Thesystemcanfollowthechannelbyseparatingbeforeafullyfusedcompoundsystemisformed.2)AftercompoundnucleusformationthesystemcouldthroughachannelcalledThecrosssectionfortheformationofanevaporationresiduecanbeformallydescribedasfollows,˙ER=1XJ=0˙cap(E;J)PCNWSur(E;J);(1.1)3Figure1.1:Illustrationofanexampleheavy-ionfusionreactionshowingvariousreactionchannels.Keypointsinthereactionpathareemphasizedbythedashedlines.Thearrowsindicatetheprogressionofthereactionwithtime.where˙capisthecapturecrosssection,PCNistheprobabilityofformingacompoundnucleus,andWSuristhesurvivalprobabilityofthecompoundnucleusagainst[29]Inthefollowingsections,thethreeprimarystagesoftheformationofanevaporationresidue(capture,compoundnucleusformation,andsurvivalagainstarediscussed.Theprobabilityofformingacompoundnucleusistheprimaryfocusofthiswork,socaptureandsurvivalareintroduced,thenamoredetaileddescriptionofcompoundnucleusformationfollows.41.2.1Capture,˙capThecapturecrosssectionforaheavy-ionreactioncanbedescribedreasonablywellbytheclassical,geometriccrosssectionwiththesharplimit[31]˙cap=ˇ2lmaxXl=0(2l+1);(1.2)whereisthedeBrogliewavelengthoftheincidentparticle,listheangularmomentumresultingfromthecollision[29].Thesharplimitassumesthatthereissomeangularmomentum(lmax)abovewhichthecapturecrosssectiongoestozero.Capturecrosssectionsforheavy-ioncollisionsaregenerallyontheorderof10to100mb[29].Threeoftheprimarychannelsavailableatthisstageofaheavy-ionreactionaredepictedinFigure1.2.Ifthesystemsdoesnotpossessenoughenergyorhastoolargeofanimpactparameter(discussedinSection1.2.1.2)thenadinuclearsystemwillnotformandthesystemwillelasticallyscatterasillustratedinPanelAofFigure1.2.PanelBdepictsanexampleofadeepinelasticscatteringreactionwherethenucleiarecloseenoughtoexchangeafewnucleonsbutfullenergydissipationdoesnotoccur.Ifthesystemdoesovercomethecapturebarrier,thenadinuclearsystemisformedasdepictedinPanelC.1.2.1.1AngularMomentumFromthegeometriccrosssectionineq.1.2itisclearthatangularmomentumplaysanimportantroleincapture.Theangularmomentumintroducedintothedinuclearsystemsbythecollisionisanindicationofthetypesofreactionchannelsavailable[32].Aplotofthecrosssection(˙)isshowninFigure1.3asafunctionofangularmomentum,whichiscalculatedas˙=ˇ2(2l+1).Thepossiblereactionsatagivenangularmomentumareindicated5Figure1.2:Illustrationofthreepossiblereactionoutcomesfromaheavy-ionreaction.PanelAdepictselasticscattering,PanelBdepictsdeepinelasticscattering,andPanelCdepictscapture.6inFigure1.3.Itisimportanttonotethatthispicturewillbereactiondependentandtheseareallapproximateandrelativevalues.Also,therewillbetoverlapbetweenthesetypesofreactions.Therearefourimportantangularmomentumvaluesindicatedbelowthexaxis.Theislmax,thisisthemaximumangularmomentumvalueatwhichcontactbetweentheprojectileandtargetcanoccur.AtangularmomentalargerthanlmaxelasticscatteringandCoulombexcitationreactionsoccur.Atangularmomentumvaluesjustbelowlmaxquasielasticreactionsanddirectreactions,likeonenucleontransferreactions,occur.Belowlcritcompoundnucleusformationbecomesavailable.Atangularmomentaslightlyabovelcrit,ereactionstakeplace.Thesecanbemultinucleontransferreactions,ortypereactions.Thisregionnearlcritwillbethefocusofthepresentwork.InFigure1.3,lDindicatesthethresholdwherethedirectreactionchannelopensandlfindicatesthethresholdangularmomentavaluewherefusion-likereactionchannelsopen.Inprinciple,allofthesereactiontypescouldbeseparatedbyvariousthresholdangularmomentavalues.Inpractice,theboundariesoftheseregionsaretodetermine.1.2.1.2ImpactParameterInexperimentalnuclearreactionsitcanbemorestraightforwardtothinkofthereactionintermsoftheimpactparameterratherthantheangularmomentum.Impactparameter,b,isasthedistanceofclosestapproachbetweentwonucleiinacollision.Impactparameterisrelatedtoangularmomentumbyb=l.Notethatlisquantizedwhilebisnot.Thus,eachvalueoflwillcorrespondtoarangeinb.Headoncollisions,wherethetwonucleicollidealongtheirrespectivenuclearsymmetryaxes,areasb=0.TwocartoondepictionsofimpactparameteraredepictedinFigure1.4,inPanelAthecollision7Figure1.3:Illustrationofthecrosssectionofaheavy-ionreactionasafunctionofangularmomentum.Theblack,dashedlinerepresentstheline˙=ˇ2(2l+1).Thevarioushashedregionsindicatethevariousangularmomentumvalueswheretprocessesareprominent.Themostprominenttypeofreactionineachangularmomentumregionisindicated.Fourtangularmomentumvaluesarecalledout(lcrit,lf,lD,andlmax).Seetextfortheofeachoftheindicatedangularmomentumvalues.Adaptedfrom[32]8Figure1.4:Cartoonexampleoftheofimpactparameter.PanelAshowsasideviewofaheavy-ioncollision.PanelBshowsabeamviewofacollision.Aspresentedinthecartoon,thedarkbluesphereisthetargetandthelightbluesphereistheprojectile.isviewedfromtheside.Inthisexamplereactionintheframeofthecartoon,thecenteroftheprojectileisabovethatofthetargetresultinginapositiveimpactparameter.InPanelBthecollisionisshownalongthebeamaxisupstreamofthecollisionandonceagainitisapparentthatthecollisionwouldtakeplaceatanimpactparametergreaterthan0.ThewhiteconcentriccircleinPanelBrepresentthatvariouslrings.1.2.1.3BassBarrierAnotherimportantentrancechannelpropertyistheinteractionbarrierassumedforthesystem.TheinteractionbarrierusedinthepresentworkistheBassBarrier[33],whichisusedthroughouttheliteratureinheavy-ionfusionreactions.TheBassbarrierusesasimple,classicaltwo-bodymodeltodescribefusion[34,35].Thenuclearinteractionparameterswerethencalculatedfromaofthemodeltoexperimentalfusionexcitationfunctions[9]9wherethereactioncrosssectionisdeterminedas˙R=ˇR2int 1V(Rint)Ec:m:!:(1.3)Thecriticalradius,Rint,forfusionusedinthisapproachisthehalf-densityradius,whereR=aA1=3-b2(aA1=3)1[9].Previousworkfoundthebesttothedatawhena=1.16fmandb2/a=1.39fm[9,33].TheBassinteractionusedisasV(Rint)=1:44Z1Z2RintbR1R2R1+R2(1.4)wherebisapproximately1MeV/fm[9].1.2.2SurvivalagainstFission,WsurLikethecaptureprocess,survivalagainsthasbeenthoroughlystudiedandcanbereasonablywellcalculated.ThesurvivalprobabilitycanbecalculatedasWsur=Pxn(ECN)imax=xYi=1nn+fi;E(1.5)whereiisthenumberofneutronsemitted,Pxnistheprobabilityofemittingexactlyxneu-trons,ECNisexcitationenergyofthecompoundnucleus,andnnfi;Eisthelikelihoodofemittinganeutroncomparedtothewidth.Ifthesystemde-excitesbyemittingsmallparticles,likeneutron,protons,andalphas,theremainingnucleusiscalledanevapo-rationresidue.Insuperheavyelementformation,thesurvivalprobabilityagainstissmall,ontheorderofpb[36].Mostreactionsfolloweithertheorchannels.10Foccurswhenthesystemreachesfullequilibrationofalldegreesoffree-domandthentheexcitedcompoundnucleusundergoeswhereitseparatesintotwosymmetricfragments.1.2.2.1LiquidDropModelThenucleiinvolvedinheavy-ionfusionreactionsareconsideredinthecontextoftheLiquidDropModelofthenucleus.Inthismodel,thenucleusisapproximatedasanincompressible,uniformlychargedliquiddrop[37].Thebindingenergy(Btot)ofanucleuscanbedescribedbythesemiempiricalmassequationBtot=avAasA2=3aCZ2A1=3aa(A2Z)2A(1.6)whereAisthemassofthenucleusandZisthecharge.Thecots(ai)correspondtovariouscomponentsofthebindingenergy.Thetermisthevolumeterm.Thesecondtermisthesurfacetermandcorrectsthebindingenergyfortheenergylostduetothereducednumberofinteractionsbetweensurfacenuclei.ThethirdtermistheCoulombtermandaccountsforthechangeinbindingenergyduetotheCoulombrepulsionbetweentheprotonsinthenucleus.ThelasttermistheasymmetrytermandaccountsforthechangeinbindingenergyassociatedwithmovingawayfromN=Z.Finally,theisthepairingcorrection.Thetwotermsassociatedwith(orofanucleusarethesurfaceandCoulombterms.Duringthenucleusdeformswhichresultsinachangeinenergybecausethesurfaceareaofthesystemincreases.Simultaneously,theelongationofthesystemsmeansthatthenucleonsareonaveragefurtherapartwhichreducestheCoulombrepulsionbetweentheprotons.Asimilarchangeinenergyappliestosystemsinvolvedin11ThischangeinenergycanbedescribedbyE=Es+EC,whereEsandECarethechangeinthesurfaceandCoulombenergies,respectively.WhenthedeformationofthesystemissmallthesurfaceandCoulombenergiescanbedeterminedfromEs=E0s1+2522(1.7)EC=E0C11522(1.8)whereE0sandE0CarethesurfaceandCoulombenergiesforasphericalnucleusand22isthequadrupoledistortionparameter.AnucleusbecomesunstableagainstwhenEsandECareequal(EsE0s=E0CEC).Fromtheineqs.1.7and1.8itcanbeshownthatECandEsareequalwhenE0C2E0s=1:(1.9)Theratioineq.1.9istermedthessilityparameterandexpressestheyofanucleusasaratiooftheCoulombenergyofachargedspheretotwotimesthesurfaceenergyofasphere.Now,theCoulombenergyofachargedspherecanbeapproximatedasE0C=35Z2e2R0A1=3= aCZ2A1=3!(1.10)whereR0istheradiusofasphericalnucleus,andaCisthecotfortheCoulombterm12ineq.1.6asaC=3e2=5R0.ThesurfaceenergyofaspherecanbeapproximatedasE0s=4ˇR20SA(2=3)=asA(2=3)(1.11)whereSisthesurfacetensionperunitareaandthecoientforthesurfaceenergy(as)ineq.1.6isasas=4ˇR20S.Bysubstitutingtheseapproximationsintoeq.1.9theyparameter(˜)canbedescribedby˜=aC2asZ2A:(1.12)Theratioof(2as=aC)isas(Z2=A)critical.Previousworkhasconcludedthattheyofasystemhasanimportantonthedominatereactionchannelinheavy-ionfusionreactions.1.2.3ProbabilityofformingaCompoundNucleus,PCNIfthesystemreactsatlowenoughangularmomentumandadinuclearsystemisformedthenthenextstageofaheavy-ionfusionreactioninvolvesequilibrationofalldegreesoffreedomasthedinuclearsystemfusestoformacompoundnucleus.Theleastunderstoodportionoftheheavy-ionfusionreactionmechanismistheprobabilityofformingacompoundnucleusPCN.PredictionsforPCNcanvaryby1to2ordersofmagnitude[29].Ifthesystemsseparatesbeforeequilibratinginalldegreesoffreedomthenitissaidtohaveundergone131.2.3.1whichoccursinheavy-ionfusionreactionsoflargesystems,causesthegreatestuncertaintyinpredictionsofPCN.Previousworkhasshownthatbecomesprominentinsystemswithchargeproducts,ZpZt,greaterthan1600[38],thoughithasbeenseeninsystemswithZpZtaslowas800[7].ThechargeproductisoftenusedtocharacterizethesetypesofreactionsbecauseitgivesanindicationoftheCoulombpotentialbetweentheprojectileandtarget.1.3ExperimentalSignaturesofInmanymediummassheavy-ionfusionreactionstheevaporationresiduecrosssectionissmall.Aftercapturemostsystemsfollowtheorreactionchannels.Therefore,thenumberofeventsfromareactioncanbeassumedtobeequivalenttothenumberofeventsthatformedacompoundnucleus.RecallingFigure1.1,thenumberofeventscomparedtothetotalnumberofandeventsprovidesameansofdeterminingtheprobabilityofformingacompoundnucleus,PCN,forthesystem.AllofthesignaturesofdiscussedinthissectionuseacomparisonwithtodeduceinformationaboutthePCNforthesystem.Previousworkhasconcludedthattherearethreesignaturesofthatareusefulindistinguishingbe-tweenand:abroadeningofthemassdistribution,anenhancementoftheanisotropyintheangulardistribution,andacorrelationbetweenmassandangleinthemassangledistribution[39,40].Eachofthesesignatureswillbediscussedindetailinthefollowingsections.141.3.1MassDistributionsInmanyexperimentsdesignedtostudyandcompetition,thetwoexitchannelfragmentsaredetectedandthentheirrelativeorabsolutemassesaredeter-mined[41,42,43,44,39,45,46].Massdistributionsprovideasummarizedoverviewofthemassinformationobservedinthemeasurement.Throughouttheliteraturethemassinformationinamassdistributionispresentedinoneoftwoforms:theabsolutemassofthefragments(Ai)orthemassratiosofthetwofragments(MR;i)[41,42,43,44,39,45,46].InthepresentworkthemassratiowillbeusedandisasMR;1=A1A1+A2(1.13)whereAiisthemassofoneofthebinaryfragments.Allpossibleexitchannelsfromaheavy-ionreactioncontributetotheobservedmassdistributionandcertainsignaturescanbeusedtoidentifytheexitchannels.Acartoonexampleofamassdistributionforareactionwheretheentrancechannelnucleihadmassratiosof0.25and0.75isdepictedinFigure1.5.Thexaxisshowstheapproximatemassratios.Normally,theyaxisofamassdistributionshowscounts,butisignoredforthisdiscussion.Variousexampleexitchannelpairsareshowninthedistribution.Thelightfragmentsareshownabovetheheavyfragmentsforclarityalone.Inamassdistributiontheexitchannelfragmentsfromelasticscatteringeventswillbeobservedatorneartothemassratiosoftheentrancechannel.IntheexamplemassdistributioninFigure1.5scatteringeventsareindicatedby\S".Theexitchannelfragmentsfromdeepinelasticscatteringandfewnucleontransferreactionswillbeobservedatmassratiosveryneartothoseofelasticscatteringevents,stillatthepositionslabeled\S"inFigure1.5.Theexitchannelfragments15Figure1.5:Illustrationofamassdistribution.Thevariouscirclesindicatetheexitchannelfragmentsexpectedatvariousmassratios.Seetextforexplanation.fromreactions,wherefullmassequilibrationisreached,willbeapproximatelysymmetricinmassattheenergiesconsideredinthiswork[46]andareindicatedby\III"inFigure1.5.Now,thefragmentsatthemassratiosregionsindicatedbyeither\I"or\II"resultprimarilyfromnonmassequilibratedreactions,likeInqureactions,thedinuclearsystemsinteractlongenoughfortmasstransfertooccur,butmaynotreachfullmassequilibration.Thereforefragmentspopulatetheregionofamassdistributionbetweentheentrancechannelmassratiosandthesymmetricmassratios.Additionally,itispossibleforreactionstoresultsinfragmentswithmassratiosof0.5somassdistributionsforandfusionreactionscanoverlapinthatregion.Eventsfromreactionsatmassratioslikethoseindicatedby\I"or\II"provide16anobservablesignatureofinaheavy-ionreactionmeasurements.Inaheavy-ionreactionwherenooccurred,therewouldgenerallybethreepeaksexpectedinthemassdistribution.Twooccuratthemassratiosoftheprojectileandtargetfromscatteringreactions.Thethirdoneisobservedatsymmetricmassratiosfromreactions.Whenispresent,themassdistributionisalsopopulatedinbetweenthesepeaks.Thisisreferredtoasabroadeningofthemassdistributionbecausethenarrowpeakatsymmetricmassratiosisbroadenedbytheinclusionofevents.Itisnecessarytonote,however,thatintheextremecasewhereshorttimescalequdominates,theelasticpeakswillappeartobroadentowardssymmetricmassratiosandresultinaminimuminthemassdistributionatmassratiosof0.5.ThemassdistributionpreviouslymeasuredbyWakhle[47]for12C+208PbatElab=66.0MeVisshowninFigure1.6.Thehighmassasymmetry(0.89)andlowchargeproduct(492)ofthissystemindicatethatwillnotbeaprominentexitchannelinthissystem.PCNshouldbeoneandalloftheproductsobservedintheeregionshouldcomefromApeakobservedinthemassdistributioninFigure1.6hasaFWHMof0.12MRunitsandisconsidered\narrow".Onlyonepeakisobservedbecausetheelasticscatteringeventswereoutsidetheacceptanceofthismeasurement.Forcomparison,themassdistributionfor48Ti+192OsatElab=259.9MeVpreviouslymeasuredbyLinetal.[46]isshowninFigure1.7.The48Ti+192Ossystemhasachargeproductof1672andamassasymmetryof0.6,soisexpectedtobeastrongexitchannelinthissystem.Themassdistributionintheeregion(0.35<MR<0.65)hasaFWHMof0.31MRunitsandisconsideredbroadened.17Figure1.6:Massdistributiondeducedfromthereactionof12C+208PbatElab=66.0MeV[47].18Figure1.7:Massdistributiondeducedfromthereactionof48Ti+192OsatElab=259.9MeV[46].19Figure1.8:Massdistributionsreportedin[48]fromthereactionofheliumanduranium-233.Reprintedwithpermissionfrom[48]Copyright(1961)bytheAmericanPhysicalSociety.http://dx.doi.org/10.1103/PhysRev.121.14151.3.1.1ExcitationEnergyandFusion-FissionItisimportanttonotethatthemassdistributionofassioningsystemishighlydependentofexcitationenergy.Aseriesofmassdistributionsfromthereactionofheliumprojectilesonuranium-233areshowninFigure1.8asreportedin[48].Atthelowestenergies,asymmetricdominates,butastheenergyincreasessymmetricbecomesmoreprominent[49,50,51].AttherelativelyhighexcitationusedinthepresentworkandinthepreviousworkatANU(ECN˘50MeVshellareminimizedandfragmentsfromreactionsarefocusedatsymmetricmassratios.20Figure1.9:Schematicimageofangularmomentumcouplingcoordinatesystemforade-formednucleus.Adaptedfrom[51]1.3.2AngularDistributionsTheangulardistributionsfromaheavy-ionfusionreactioncanbeconsideredinthetermsofthetransitionstatemodelforofacompoundnucleus.TheprobabilityofemittingfragmentsfromaparticularstatewiththequantumnumbersJ,M,andKasafunctionofangleisdescribedby[52],PJM;K()=(2J+1)2ˇR2sin4ˇR2jdJM;K()j2(1.14)whereJisthetotalangularmomentum,MistheprojectionofJalongthebeamaxis,andKistheprojectionofJalongthenuclearsymmetryaxis[52].ThedJM;K()functionsarethewavefunctionsofasymmetrictopforagivenJ,M,andK[52].Theangulardistribution(WJM;K())isobtainedbydividingPJM;K()bysin.AnucleuspriortowithquantumnumbersJ,M,andKisillustratedinFigure1.9andthecoordinatesystem.Inthetransitionstatemodel,thefragmentsare21assumedtobeemittedalongthenuclearsymmetryaxis,intheKdirection.ConsidertheextremecasewhereJisperpendiculartothebeamaxis.Then,thepossibledirectionsalongwhichthefragmentsmaybeemittedaredistributedalongthesurfaceofasphereandtheangulardistributioncanbeapproximatedbythefunction1/sin.Previousworkhasshownthatthisapproximationholdsforallbutthemostextremeanglesforangulardistributions[53,54,55].Muchworkhasbeendonetoextendtheuseofthetransitionstatemodelunderstandingoftheangulardistributiontosystemswherequasiionoccurs[54].Thisisatask,butonecanleveragethefactthatthetransitionstatemodelreliesontheassumptionthatthenucleushasequilibrated,whichisnotthecasein[54].Therefore,adeviationintheangulardistributionfromwhatwouldbeexpectedinthetransitionstatemodelcanbetakenasasignatureof[54].1.3.3Mass-AngleDistributionsIfmassandangleinformationisdeducedforeandfragments,thenatwodimensionmassangledistributioncanbegenerated.Mass-angledistributions(MAD)areausefultoolinstudyingreactiondynamicsofheavy-ionfusionreactions[4,56,40].MADsgenerallyrelatethecenter-of-massanglesasafunctionofthecorrespondingmassratioofanobservedfragment.Asdiscussedabove,fragmentswillbeconcentratedatsymmetricmassratiosandbeisotropicinthecenter-of-massframe.Therefore,aMADwillhaveverydistinctappearance:abandofeventsevenlydistributedinanglewillbeobservedatsymmetricmassratios.Anexampleofafusion-MADpreviouslydeducedfor12C+208Pb[47]isshowninFigure1.10,wheretheeventsfallasdescribedabove.Now,ifispresent,theappearanceoftheMADchanges.AnexampleofthededucedMADfor48Ti+192Os[46]isshown22inFigure1.11.AsdiscussedinSection1.3.1isexpectedinthissystemandchangestheappearanceoftheMAD.ThegroupsofeventsnearMR=0.2andMR=0.8arefromelasticscatteringevents.Theeventsintheeregionarenolongerisotropicorconcentratedatsymmetricmassratios.Infact,acorrelationbetweenmassandangleisobservedinMADswhereispresent.Thiscorrelationishighlightedbythedashed,greylineinFigure1.11.ThiscorrelationisdescribedinFigure1.12.InReactionI,theprojectileandtargethavealargeimpactparameter.Theyformadinuclearsystemthatonlyrotatesthroughafewdegreesbeforeseparating.Asaresult,onefragmentisstillsimilarinmasstotheprojectileandtheotherfragmentisstillsimilarinmasstothetargetnucleus.EventssimilartothiscasewillpopulatethemassdistributionsintheregionsindicatedbyIinFigure1.5.Inthesecondcase,ReactionII,thereactiontakesplaceatasmallerimpactparametercomparedtoReactionI.Thedinuclearsystemrotatesmorethan90butlessthan180beforeseparating.ThelongercontacttimeresultsinmoremassexchangerelativetoReactionI,butthesystemisstillnotfullymassequilibrated.AsshowninFigure1.5,thesesystemsareatmoresymmetricmassratiosatII.Inthethirdcase,thatwiththesmallestimpactparameter,thedinuclearsystemrotatesbeyond180.Thecontacttimeislongenoughfortofmassexchangeanditisnolongerpossibletodistinguishbetweentheprojectile-likeandtarget-likefragments.Theselong-timescaleeventsoverlapwiththeeventsinthemassdistribution,makingthemulttodistinguish.WhilethecharacteristicsoftheMADsaresimilarforlong-timescaleandbothreactionchannelscancontributetothereactionproducts.reactions,likeReactionsIandIIinFigure1.12,causethebroadeningofthe23Figure1.10:Themassangledistributionpreviouslydeducedfromthereactionof12C+208PbatElab=66.0MeV[47].massdistributionrelativetopureAsdepictedinFigure1.12,massexchange,angleofrotation,andcontacttimeareallrelated.Thelongerthesystemisincontact,themoreopportunitythereisformassexchange.1.3.3.1TypesofMassAngleDistributionsPreviousworkbythereactiondynamicsgroupatANUhasshownthatmediummassheavy-ionfusionreactionscanbecategorizedintothreetypesbyfeaturesobservedin42MADs[40].AmapoftheMADsforthe42systemsisshowninFigure1.13.Theprojectileusedisshownonthex-axis,theformedcompoundsystemisshownonthey-axis,andthediagonallinesindicatethetargetusedinthereaction.24Figure1.11:Themassangledistributiondeducedfromthereactionof48Ti+192OsatElab=259.9MeV[46].Thedashed,greylineisincludedtohighlightthecorrelationbetweenmassandangle.25Figure1.12:Threeexamplereactions.Illustratingtheofimpactpa-rameterofandangleofrotationofthemassandangleoftheemittedfragments.DuRietzetal.[40]identhreetypesofMADsamongthesereactions.ExamplesofthethreetypeswerehighlightedbyDuRietzetal.asshowninFigure1.14.Thetypesarecorrelatedwiththe\Reactions"discussedaboveandshowninFigure1.12.ExtremelyshorttimescaleisobservedintheMADsforTypeIsystems.ThistypeischaracterizedbyaminimuminthemassdistributionatMR=0.5.Inthesesystems,separationoccursquicklyandverylittlemasstransferoccurs.TheMADandmassdistributiondeducedfromthereactionof64Ni+170ErareshowninPanelsAandDinFigure1.14asanexampleofaTypeIsystem.MediumlengthtimescaleisobservedintheMADsofTypeIIsystems.ThesesystemsarecharacterizedbyacorrelationbetweenmassandangleintheeregionoftheMADandamaximuminthemassdistributionatMR=0.5.TheMADandmassdistributiondeducedfromthereactionof48Ti+186WareshowninPanelsBandEinFigure1.14asanexampleofaTypeIIsystem.TypeIIIsystemsundergolong26Figure1.13:Plotofthe42MADsreportedin[40].Inthetopleftcorner,theMADdeducedfromthemeasurementof48Ti+170EratElab=225.0MeVisenlargedtohighlighttheaxislabels.Systemsthatfallalongthesamevertical,red,dashed-ordiagonal,blue,dashed-lineswereformedwiththesameprojectileortarget,respectively.Systemsalongthesamehorizontal,black,dashedlinesformedthesamecompoundnucleus.Reprintedwithpermissionfrom[40]Copyright(2013)bytheAmericanPhysicalSociety.http://dx.doi.org/10.1103/PhysRevC.88.05461827Figure1.14:MADsrepresentativeofTypesI,II,IIIasidenbyDuRietzetal.[40]areshowninPanelsA,B,andC,respectively.ThecorrespondingmassdistributionsareshowninPanelsD,E,andF.Reprintedwithpermissionfrom[40]Copyright(2013)bytheAmericanPhysicalSociety.http://dx.doi.org/10.1103/PhysRevC.88.054618timescalession.TheMADsforthesesystemsaretodistinguishfromthoseofpurefTheMADandmassdistributiondeducedfromthereactionof32S+202HgareshowninPanelsCandFinFigure1.14asanexampleofaTypeIIIsystem.Adistinctionbetweenthethreetypeswasobservedwhenthechargeofthecompoundnucleuswasplottedasafunctionofchargeproduct(Z1Z2)[40]asshowninFigure1.15.TheboundarybetweenTypesIandIIoccurredalongalinefrom(ZCN,Z1Z2)of(80,1450)to(120,1150)(indicatedbythesolid,bluelineinFigure1.15).TheboundarybetweenTypesIIandIIIwasobservedalongalinefrom(ZCN,Z1Z2)of(80,2000)to(120,1700)(indicated28Figure1.15:ZCNasafunctionofZpZtforthe42reactionsincludedin[40].TheidenboundariesbetweentheTypesofMADsareindicatedbythesolid,blue-andlong-dashed,red-lines.Reprintedwithpermissionfrom[40]Copyright(2013)bytheAmericanPhysicalSociety.http://dx.doi.org/10.1103/PhysRevC.88.054618bythelong-dashed,redlineinFigure1.15).Systemsofparticularinterestarethosethatfallalongthelinesbetweentwoofthesetypesbecausetheymayprovideinsightintothechangeinthereactiondynamics.1.3.4EntranceChannelEnergyandTheentrancechannelcenter-of-massenergy(Ec:m:)isanimportantfactorinnuclearreac-tions,andinparticularandssioncompetition.First,theEc:m:ofthereactionisdirectlyrelatedtothecompoundnuclearexcitationenergy(ECN),sinceECNissimplythesumofEc:m:andtheQvalueforfusion(Qfus).ShellareknowntoplayalargeroleinreactiondynamicsatECNlessthanˇ20MeV[57,51].Second,entrancechanneldeformationhasbeenshown[58,59,41,39,60,61,62,63,64,65]tohinderfu-sioninheavy-ionreactionsatEc:m:neartheinteractionbarrier(VB)[9],wheretherelativeorientationofdeformednucleicantlychangethepotential.291.4Heavy-IonFusionReactionswithNeutron-richRareIsotopeBeamsHeavy-ionfusionreactionswithneutron-rich,radioactivemediummass(8<z<50)pro-jectilesarethusfarfairlyunexplored.Previously,therehavebeenonlythreepublishedresults[66,67,68].Withthenextgenerationrareisotopefacilities,therewillbeoppor-tunitiestounderstandhowtheheavy-ionfusionreactionmechanismisbytheuseofneutron-rich,radioactivebeams.Ingeneral,anincreaseinneutron-richnessleadstoanincreaseintheexperimentallyobservedevaporationresiduecrosssection[25,69,70].How-ever,theimpactofincreasedneutron-richnessontheprobabilityofformingafully-fusedcompoundnucleusisstilldisputed.Muchpreviousworkhasbeendonetoexploretheinterplaybetweenandneutron-richness[71,72,73,74,75,76,77,30,78,79,80,81].However,theseworksledtoconclusions.Someworksconcludedthattheprobabilityofformingacompoundnucleusincreaseswithincreasingneutron-richness[74,72],whileothersobservedadecreaseinPCNwithincreasingneutron-richness[75,73].OnechallengeinalltheseworkswasthattheresultsrequiredatheoreticalmodelofthereactiondynamicstodeterminePCN[71,30,72,77,78,78].SincemodelpredictionsofPCNcanvarytly,thechoiceofmodelgreatlytstheresultsoftheseworks.Inthepresentwork,thechangeinwithincreasingneutron-richnesswasexploredinasystematic,modelindependentway.301.5OrganizationofDissertationInthischapterthemotivationforthisworkwasdiscussed,includingtheofonsuperheavyelementproductionandtheneedtounderstandtheimpactofincreasingneutron-richnessonforfutureSHEresearch.InChapter2theAustraliaNationalUniversity(ANU)Heavy-IonAcceleratorfacilityandthemeasurementsthatwereperformedaredescribed.Then,thetechniqueusedtodeterminethemassratiosandcenter-of-massanglesofthereactionproductsisdescribedChapter3.InChapter4,themassdistributions,angulardistributions,andmass-angledistributionsdeducedforaseriesofCr+Wreactionsattwotreactionenergiesarepresented.Chapter5providesadiscussionoftheresults.Finally,Chapter6givessomegeneralconclusionsfromtheworkpresentedhere.31Chapter2ExperimentalDetailsTheofneutron-richnessonheavy-ionreactiondynamicscanbestudiedbydeducingmassandangulardistributionsforreactionsbetweentisotopesofagivenpairofelements.Inthisapproach,theofneutron-richnesscanbeisolatedfromtheofothervariablesthatareknowntocompoundnucleary[71,30],massasymmetry[7],magicity[82,83],deformation[60,46,63],andchargeproduct[40].Thedesignoftheexperimentcarriedoutaspartofthiswork,includingaforthesystemsandenergiesthatwereselectedandadescriptionoftheexperimentalequipment,isdiscussedinthischapter.2.1SystemSelectionForthepresentwork,chromium(Cr,Z=24)wasselectedastheprojectileandtungsten(W,Z=74)wasselectedasthetarget.TheresultsfromtheCr+W,mediummasssystemproviderelevantinformationimportantforfuturemediummassmeasurementswithradioactiveionbeamsthatwillbeavailableatnextgenerationfacilities.Onlyeven-evenisotopesofCrandWwereconsideredheretominimizepairingTable2.1liststhenaturalabundancesandhalf-livesofallisotopesusedinthepresentwork.Therearetwostableandoneverylong-lived,evenisotopesofCr:54,52,and50,respectively.Naturalchromiumwasusedasthesourcematerialforthemeasurementsinvolving52Crbecauseitisthemostabundant32isotope.Isotopically-enrichedsamplesof50;54Crwereobtainedfromwith97.4%and99.20%purity,respectively,forthemeasurementswiththeseisotopes.Whasoneverylong-livedandthreestable,evenisotopes:180,182,184,and186,respectively.Isotopically-enrichedtargetsofeachWisotopewerepreparedatArgonneNationalLaboratoryandthepreparationofthetargetsisdescribedin[84].EachWtargetwasbackedwithcarbontosupportthethindepositoftheheavyelement.Table2.2containsalistofWandCthicknessesforeachtarget.IntheseriesofCr+Wreactionsconsideredinthepresentworkthefollowingitemsneedconsideration:(a)Onlyoneisotope,52Cr,hasaclosednuclearshell(N=28);(b)TheCr+Wreactionshavethesameentrancechannelchargeproduct,ofcourse(ZpZt=1776);(c)TheWisotopesarealltlydeformed,butwithsimilarvaluesof2intherangeof0.23-0.26;and(d)AlargerangeinneutronnumberwasavailablebetweentheCr+Wsystemsbecauseofthemanyavailableisotopes.Themostneutreaction(52Cr+180W!230Cf)andthemostneutron-richcombination(54Cr+186W!240Cf)by10neutrons.Thecombinationofawiderangeinneutronnumberinthecompoundnucleuswithlimitedvariationinmagicity,ZpZt,anddeformationmakesCr+Wanidealsystemforexploringthetheofneutron-richnessoninmediummassreactions.Additionally,withachargeproductof1776andcompoundnucleuschargeof98,thechromiumandtungstensystemfallsontheboundarydeterminedbyDuRietzetal.[40]betweenTypeIIandIIIsystemsasdiscussedinSection1.3.3.1.2.1.1TwoEnergyRegimesAsdiscussedinSection1.3.4theentrancechannelenergyofthereactionplaysakeyroleinandcompetition.Theexcitationenergyofthecompoundnucleus33Table2.1:Chromiumandtungstenisotopicinformationincludingpercentabundances(half-lives),2values,andanymagicnumbersinthenucleus.IsotopePercentAbundance(half-life)[85]2[86]MagicNumber50Cr4.345%(1.3x1018y)0.0No52Cr83.789%0.0Yes,N=2854Cr2.365%0.0No180W0.12%(6.6x1017y)0.258No182W26.50%0.259No184W30.64%0.24No186W28.43%0.23NoTable2.2:Tungstentargetandcarbonbackingthickness,andreaction[84]IsotopeThickness(gcm1)CarbonBacking(gcm1)ProjectileandELab(MeV)180W486050Cr,284.6;50Cr,268.3;52Cr,285.0;52Cr,276.0180W466054Cr,280.0182W978054Cr,284.4;50Cr,277.2184W644052Cr,282.3;52Cr,269.0;54Cr,283.1;50Cr,274.0186W434050Cr,280.4;50Cr,255.5;54Cr,281.7;54Cr,270.334andtheratioofthecenter-of-massenergytotheinteractionboththereactionchannel[57,51,58,59,41,39,60,61,62,63,64,65].TohelpdisentanglethesetwoeachreactionsystemwasmeasuredattwoEc:m:values:Ec:m:/VB=1.13andECN=52.0MeV.TheconstantfractionabovetheCoulombbarrierofEc:m:/VB=1.13hasbeenshowntobehighenoughabovethebarrierthatdeformationectsshouldbeminimal[46].TheconstantcompoundnuclearexcitationenergyofECN=52.0MeViscomparabletohotfusionreactions,wherethreetofourneutronsareevaporatedfromveryheavycompoundnucleiinattemptstoformnewelements.Additionally,ECN=52.0MeVistlyhigherthanthe20MeVgenerallyrequiredtominimizeshellinthedinuclearsystem.Bystudyingthesesystemsinbothenergyregimes,theofneutron-richnesscanbeexploredindependentoftheenergyTheenergeticsofthesetofreactionstomeettheEc:m:requirementsaregiveninTable2.3.2.1.2Cr+WSystemsEightCr+WsystemsweremeasuredinthetwoerentenergiesregimesattheAustraliaNationalUniversity(ANU)HeavyIonAcceleratorFacility.TheHeavyIonAcceleratorFacilityatANUprovidedanideallocationfortheseriesofCr+Wmeasurementssincealargenumberofsystematicstudiesofheavy-ionfusionreactionshavepreviouslybeencompletedattheHeavy-IonAcceleratorFacilitybythereactiondynamicsgroupatANU,ledbyDr.DavidHinde.Thepresentworkbfromthepreviousexperienceofthelocalgroup,andthewell-establisheddetectorsystemsforheavy-ionfusionstudies[41,39,87,60,39,40,65,64,7,83].TheCUBEdetector[41,40](seeFigure2.3)wasspdesignedtomeasuremassandangledistributionsofionfragmentsfromheavy-ioninducedreactions.TheCUBEiscomposedoftwolargearea,positionsensitivemultiwireproportional35counters(MWPC)andresidesinavacuumchamberonadedicatedbeamlinedownstreamofthe14UDtandemacceleratorandtheSuperconductingLinearAccelerator(LINAC).TheANUfacilityprovidedbeams(1091010pps)oftheCrisotopesattheenergieslistedinTable2.3duringthecourseofaboutoneweek.Todemonstratethatthisworkcanexploretheprobabilityofformingthecompoundnucleus,itisimportanttoexcludetheofthecapturecrosssectionortheevaporationresiduecrosssection.ThecapturecrosssectionandlcritwerecalculatedusingthePACE4codeinLise++[88]andarelistedinTable2.4.Asthesequantitiesareenergydependent,Table2.4isseparatedintotwosectionsbasedontheentrancechannelenergy.PACE4alsocalculatedanevaporationresiduecrosssectionof0mbforeachCr+Wsystem.Thevaluesoflmaxwasalsocalculatedforeachsystemaslmax=r˙capˇ2+1(2.1)andarelistedinTable2.4.TheremainderofthischapterdescribestheequipmentusedtomeasurethemassandangledistributionsfortheCr+Wreactions.2.2TheANUHeavy-IonAcceleratorFacilityTheANUHeavyIonAcceleratorFacilityconsistsofa14UDPelletrontandemacceleratorandasuperconductingLINAC,shownschematicallyinFigures2.1and2.2,respectively.Thefollowingsectionsdescribeeachoftheprimarycomponentsofthepresentmeasurements:ionsource,tandemaccelerator,superconductingLINAC,CUBEdetectorsystem,anddataacquisition.36Figure2.1:SchematicdiagramoftheANUheavy-ionacceleratorfacility.Theionsourceisshownatthetop(moredetailinFigure2.3).The14UDPelletronTandemacceleratorisinthecenter,followedbyananalyzingmagnetandtheconnectiontotheCUBEbeamline.OnlytheLINACmagnetisindicatedhereandaschematicdiagramofthecompleteLINACisshowninFigure2.237Figure2.2:SchematicdiagramoftheANULINAC.Thecryostatsaredepictedaswellasmanybeamlinecomponentsincludingthetwoachromatsandthepreandpostbunchers.38Table2.3:Cr+Wsystems,compoundnuclei,relativechangeinneutronsfusionQvalue(Qfus),Bassinteractionbarrier(VB)[9],Ec:m:forbothenergyregimesEc:m:/VB=1.13ECN=52.0MeVReactionQfus(MeV)VB(MeV)Ec:m:(MeV)ECN(MeV)Ec:m:(MeV)Ec:m:/VB50Cr+180W!230Cf0-158.0196.95222.664.6210.01.0750Cr+186W!236Cf6-149.3195.59221.071.7201.41.0352Cr+180W!232Cf2-162.1195.75221.259.1214.11.0952Cr+184W!236Cf6-157.7194.80220.162.4209.71.0854Cr+180W!234Cf4-163.1194.56219.856.7215.41.1154Cr+182W!236Cf6-161.8194.12219.357.6213.81.1054Cr+184W!238Cf8-159.8193.67218.959.0211.81.0954Cr+186W!240Cf10-157.5193.22218.373.1207.51.082.2.1IonSourceTheionsourceusedforthepresentworkwasaNationalElectrostaticsCorporation(NEC)sourceofnegativeionsproducedbycesiumsputtering(SNICS)ofthesolidchromiumma-terial.Thesourceislocatedatthetopofthe14UDtower[89].AschematicdiagramofthesourceisshowninFigure2.3.Theactivevolumeofthesourceisachamberwithcesiumvapor.ThecesiumvaporisproducedbyliquifyingCsat100to120Cinareservoirthatisseparatedfromthechamber.TheCsisallowedtopassintotheactivevolumeofthesourcethroughadeliverytubethatisheldat200C.ThesolidCrmetalwasplacedinavialinthecathodeattheendoftheactivevolumeofthesource.Recallthatthreetsourcematerialswereusedfortheseexperiments:nat;50;54Cr.Inthemiddleofthesource,therearetwoionizersforthecesium.Eachionizerhasatungstenionizingsurfaceheatedto1000C.WhenCsatomscomeintocontactwiththeionizertheyloseanelectronbecausethetungstenhasahigherelectronythancesium.Positively-chargedCsions39Table2.4:Cr+Wsystems,compoundnuclei,relativechangeinneutronsEc:m:,ECN,interactioncrosssection(mb)[88],lmax,andlcrit[88]forbothenergyregimesReactionEc:m:(MeV)ECN(MeV)˙cap(mb)lmaxlcritEc:m:/VB=1.1350Cr+180W!230Cf0222.664.6629.0908150Cr+186W!236Cf6221.071.7628.9908252Cr+180W!232Cf2221.259.1626.4918352Cr+184W!236Cf6220.162.4625.3918354Cr+180W!234Cf4219.856.7623.1928454Cr+182W!236Cf6219.357.6623.3928554Cr+184W!238Cf8218.959.0623.2928554Cr+186W!240Cf10218.360.85622.79285ECN=52.0MeV50Cr+180W!230Cf0210.052.0365.3675850Cr+186W!236Cf6201.452.0166.6443952Cr+180W!232Cf2214.152.0452.0767152Cr+184W!236Cf6209.752.0403.4726454Cr+180W!234Cf4215.452.3536.6857654Cr+182W!236Cf6213.852.0491.8817554Cr+184W!238Cf8211.852.0445.5767254Cr+186W!240Cf10207.552.0397.6726940Figure2.3:SchematicdiagramoftheoperationoftheSNICSshowingtheactivevolumeofthesource,theionizers,thecathode,thepathofionizedCsandthepathofsputteredsamplematerial.arethendrawntowardstheCrbya5kVchargeonthecathode,asdepictedinFigure2.3.Thecathodeiscooledto20CsoalayerofcondensedCsatomsformsonthesurfaceofthecathodeandservesasasourceofefortheproductionofnegativeionsofthesourcema-terial.TheionizedCssputtersthesourcematerialonimpactandsomenegativechromiumionsareformedbyelectrontransferfromtheneutralcesium.TheCrionswereextractedasmolecularionsbecauseoftheirelectrony[90].Crhydrideswereproducedbyintroducingammoniagasintotheionsourcevolumenearthecathode.Thenegativehydrideionswererepelledbythe5-kVchargeofthecathodeandacceleratedoutoftheionsource.AftertheCrH-molecularionswereextractedfromthesource,theywereacceleratedbya150kVpotentialNext,a90magnetwasusedtoseparatethevariouscomponentsofthebeamfromtheionsource.Themagnetic(B)neededtoselectthe41masstochargeratiooftheiontobeacceleratedcanbecalculatedfromtheexpression:Bˆ=p2mEq(2.2)wheremisthemassoftheionofinterest,Eisthekineticenergyoftheionsafterthe150kVacceleration,ˆistheradiusoftheionsthroughthemagnet,andqisthechargestateoftheionofinterest.Forexample,selectionof50CrHbeamfromtheionsourceundertheseconditionswouldrequireBˆ=p250:954amu931:5MeV=c2amu:150MeV1:6021019Coul=0:398Tm(2.3)2.2.214UDPelletronNECalsomadethe14UDTandemVandeaccelerator[91,92,93]thatistheprimaryacceleratoratthefacility.TheoperatingprinciplesoftheacceleratorweredescribedindetailinRefs.[94,95].Negatively-chargedionsfromtheionsourceareacceleratedbyalargepositiveelectrostaticpotentialtotheterminal;theretheyarestrippedofsomeelectronsandacceleratedawayfromtheterminal.Themaximumterminalvoltageavailablefromthe14UDacceleratoris15.5millionvolts[93].Inthecaseofthe14UDtandemaccelerator,thepositively-chargedterminalinthecenteroftheacceleratingtubeischargedbyathreechainPelletronchargingsystem[92],composedofcylindricalmetalpelletsseparatedbyinsulatingnylonlinks.Eachpelletispositivelychargedthroughinductivechargetransferatthebottomoftheacceleratortubetoprovideanetpositivechargetothepellet,whichisthenmovedtotheterminalbyamotorandpulleysystem.Attheterminal,eachmetalpelletisbroughtincontactwiththeterminalandthepositivechargebecomesdistributed42onthewholeterminal.Theacceleratortubeiswithsulfurgas(SF6)at6bartominimizeelectrostaticdischarges.Inthestepofaccelerationinthe14UDtandem,negativeionsareacceleratedfromgroundpotentialtothepositivelychargedterminalofvoltageVT.Thisstageofaccelerationprovidesanenergygainof(eVT),whereeistheelectronicchargeoftheionandis1efortheionsoutoftheSNICSsource(eisthechargeoftheelectron).Insidetheterminal,theionspassthrougha4gcm2carbonstripperfoiltobreakuptheCrHandremovesomeelectrons[96]fromthemetalatom.Thenewchargeqstateoftheionscanbecalculatedfromtheempiricalexpression[97,98]q=Z1+Z3=43:86EA1:670:6;(2.4)whereEisthekineticenergyoftheatom,Aisthemassnumber,andZistheatomicnumber.Forexampleinthepresentcase,50Crat14.4MeV,onewouldexpectq=5+.Thepositively-chargedionsarethenacceleratedbacktogroundpotentialforanenergygainofqiVTforionsofchargestateqi.Intotal,theenergygainedinthetwostagesofaccelerationcanbecalculatedasE=qiVT+VT+0:150MeVdEdx(2.5)Afteracceleration,thedesiredbeamisselectedbyahighresolution90analyzingmagnetbasedonthechargetomassratio.Noticethattheenergiesrequiredforthisexperimentwerelargerthanthosethatthe14UDacceleratorcouldprovide,sothesuperconductingLINACboosterwasusedaswell.ForexampleinthemeasurementoftheCr+Wreaction,themaximumenergyavailablefromthetandemwas273MeVinthelabframe.Inthecenter-43of-massframeforthe50Cr+180Wthisisabout214MeVandislowerthantheenergieslistedinTable2.3.2.2.3SuperconductingLINACThebeamfromthetandemiscontinuousintime.ALINAC,ontheotherhand,onlyworkswithpulsedbeams.BeforeinjectionintotheLINAC,thebeamfromthetandemisbunchedinto100psFWHMbucketsbyaSuperbuncherQuarterWaveResonator.TheLINACconsistsof12AppliedSuperconductingIncorporatedSplitLoopResonatorsinfourcryostatsasindicatedinFigure2.2.The12resonatorsworktogethertoprovidea6MeV/qenergygain.Afteracceleration,thebeamisrebunchedtominimizespreadatthetarget.Thebeamlineusesa180achromaticsectionandthentheCUBEbeamlineasshowninFigure2.2.2.3TheCUBEDetectorSystemTheCUBEdetectorsystemhasservedastheprimarydetectorforreactiondynamicsexper-imentsatANU[40,41].Thedeviceishousedinavacuumchamberthatismaintainedat˘2105Torrduringoperation.TheCUBEconsistsoftwoMWPCswithanactiveareaof2836cm2each.EachMWPCprovidesapositionandtimingmeasurement,sothatthemassratioandcenterofmassangleforfragmentscanbededucedbyusingthekinematiccoincidencemethod[41],describedintheSection3.4.TheFrontMWPCcoveredlabanglesbetween5<lab<80andtheBackMWPCcoveredlabanglesbetween50<lab<125duringthepresentwork.IntheFrontandBackMWPCswerecenteredatlab=0andlab=180,respectively.ThefrontwireplaneofeachMWPCwas18cmfromthecenter44Figure2.4:SchematicscalediagramofthelayoutofthedetectorsinsidetheCUBEdetectorsystemasviewedfromabove.Onemonitordetectorisabovethebeampathandtheotherisbelow,seetext.ofthetarget.Thesepositionswereselectedtoprovideoptimalcoverageofthefoldinganglesforefragmentsemittedperpendiculartotheplaneofthetargetinthesereactions.AschematicdrawingofdetectorsthatmakeupthedeviceisshowninFigure2.4.TheCUBEtargetladdercanholdseven1.9mmdiametertargetsinadditiontoonetuningapertureandwasmountedinthecenterofthechamberasshowninFigure2.5.TheWtargetswererotated30withrespecttothebeamaxisasshowninFigure2.4.TwosiliconsurfacebarrierdetectorswereusedtomeasureRutherfordscatteringalongthebeamdirection.TheyarehighlightedbytheredcirclesinFigure2.5.TheSimonitormountprovidesthreeoptionsfortheplacementasshowninFigure2.5.Forthepresentwork,theywereplaced18cmbehindthetargetatlab=22.5andlab=90and270.452.3.1MWPCsMWPCsutilizetheionizationcreatedbychargedparticlespassingthroughagastoprovideameasureofthetimeandpositionofthatparticle[99,100,101].ArenderingofthedesignofthetwoMWPCsinsidetheCUBEchamberisshowninFigure2.5.MWPCs,likeotherproportionalcounters,relyonchargemultiplicationinthegas(calledaTownsendavalanche)toamplifytheelectronsfromtheprimaryionizationproducedbytheinteractionofthechargedparticlewiththegas[102].InaTownsendAvalanche,electronsareacceleratedbyastrongelectricoveradistanceofonemean-freepathandgainenoughenergytocauseadditionalionization[102].Thisprocessisrepeateduntiltheelectronsarecollectedontheanode.MWPCsaresimilartootherproportionalcounterswithanodewires.Thinwiresareusedsothatelectronsthatarefarfromtheanodewillndthattheelectricisfairlyuniform,butwhentheelectronsapproachtheanodewiretheyencounterasteeplyrisingelectric.Therefore,theelectronsareacceleratedtowardsthenearestwireandtheavalanchesproducednearanindividualwireinducelargesignalsonthewireandgiveapositionresolutionbasedonthespacingofthewiresandthetimedelayofthesignals[102].2.3.2StructureoftheCUBEMWPCsInaCUBEMWPC,thelayerofthedetectornearesttothetargetwasa0:9mthickMylarpressurewindow(toreduceofthegasthroughthewindow)andwascoatedwithcoppertolimitchargebuildupontheMylar.Thepressurewindowthusthegaseousvolumeofthedetector.Eachdetectorwaswithpropanegastoapressureof3.5Torrrelativetothechamber.Eachpressurewindowwasretainedbyfourverticalandthreehorizontal0.45mmdiameterstainlesssteelwirestomitigatethebowingofthefoildueto46Figure2.5:RenderingoftheCUBEdetectorsetupasusedinthepresentwork.TheFrontandBackMWPCs,thebeamdirection,thetargetladdersupport,andthetwoSimonitordetectorsareindicated.47thepressuretial.InsideeachMWPCaretwoorthogonalanodewireplanescomposedofgold-coatedtungstenwires,20mindiameterandspacedat1mmintervals.Theverticalplanewasmadeupof357wiresandthehorizontalhad284wirestoprovidetwodimensionalpositionsensitivity.Signalsfromtheanodewireswerereadoutusing10-tappassivedelaychipsthatwereconnectedinseries.Eachanodewirewasconnectedtoa1nstapofadelaychip.Thetwoanodeplaneswere6mmapartandseparatedbyacentralcathodefoil(3mmfromeachanode).Thecathodewasa0.9mthickMylarfoilthathad40gcm2ofAuoneachside.Thegoldwassegmentedinto4quadrantsoneachsidetolimitthecapacitanceofthefoil.Thecathodewaschargedto-490Vduringthisexperiment.Thebackplaneofthedetectorwasasolidplatethatheldthetimedelaylines.AfragmentobservedintheoneoftheMWPCsproducesanenergysignalthattravelsthroughthetimedelaylines.Therelativetimebetweenthesignalsateachendofthedelaylinecablesprovidesameasurementofthepositionatwhichtheeventoccurred.Eachtimedelaysignalswassentintoa11-bitSilena7423UHSanalog-to-digitalconverter.Thepositionresolutionwaslimitedbythe1mmradiusofthebeamspotonthetarget[103].ThepositionandtiminginformationrecordedfromtheCUBEwasthenusedtoprovidemassandangleinformationforeacheventasdescribedinthenextchapter.48Chapter3DataAnalysisTechniquesThischapterdescribesthetechniquesusedtodeterminethemassratiosandcenter-of-massanglesfromthetimingandpositionsignalsobservedforcoincidenttwo-bodyeventsintheCUBEdetectorsetup.Thecoordinatesystemsusedinthepresentworkaredescribed.ThecalibrationofthepositionandtimingsignalsobservedintheMWPCsinthepresentworkarediscussed.Thekinematiccoincidencemethod[4]wasusedtodeterminethevelocityvectorsforeachdetectedfragmentfromthepositionandtimingsignalsandisdescribedinSection3.4.AC++basedprogramusingtheRootDataAnalysisFramework[104],developedbythereactiondynamicsgroupatANUforCUBEmeasurements,calledDagui,wasusedfortheanalysis.3.1CoordinateSystemInthissection,thecoordinatesystemsusedinthepresentworkareEachMWPChasacoordinatesystemwithinitsactivedetectionareaasillustratedinFigure3.1.Theshorterlengthwasparalleltothebeamaxisduringthemeasurementsandasthexdimension.Thelongerdimensionwasperpendiculartothebeamdirectionandastheydimension.Thecoordinatesinunitsofmmofthecenterofeachedgeareindicated.Notethatthereisanbetweentheelectroniccenterandthephysicalcenterofthedetectors.Inthepresentwork,thecenterofthedetectorreferstotheelectroniccenter,49Figure3.1:SchematicscalediagramoftheindividualMWPCcoordinatesystemsusedinthepresentwork.ThegraybordersrepresenttheMWPCsupportstructureandthewhiteinnerregionsrepresenttheactiveareaoftheMWPCs.ThefourpositionquadrantsoftheMWPCscathodesareindicated.Thecoordinatesatthecenterofthedetectorandthecenterofeachedgeoftheactiveareaareindicatedinunitsofmm.as(0,0)inmminthe(x;y)plane.ThetwoMWPCsareincludedwithinthefullCUBEdetectorsetupCartesiancoordinatesystemasshowntoscaleinFigure3.2.Notethattheshapesrepresentingthetargetaretoscalewiththesizeofatargetframetomakethemmorevisibleinthediagram.ThecenterofCUBECartesiancoordinatesystem,where(X;Y;Z)=(0,0,0),isatthecenterofthetarget.TheZdimensionisalongthebeamaxis.TheXdimensionisperpendiculartothebeamaxisandthroughthecenteroftheBackMWPC.TheYdimensionisperpendiculartotheXandZdimensions.Ascalediagramofthe(X;0;Z)planeintheCUBEdetectorsetupisshowninPanelAofFigure3.2fromatop50downview.The(X;0;Z)planeisbetweenthecenterofthetargetandthecentersoftheMWPCs.PanelBshowsascalediagramofthe(X;Y;0)planeintheCUBEsetupfromthepointofviewofthebeamupstreamofthetarget.The(X;Y;0)planeisbetweenthecenterofthetargetandthecenterBackMWPC,normaltothebeamdirection.InFigure3.2,the(X;Y;Z)coordinatesatthecentersofthetwoMWPCsareindicated.ThiscoordinatesystemcanthenbeconvertedtothesphericalcoordinatesystemillustratedinFigure3.3.ThesameschematicdiagramsoftheCUBEdetectorsetupareillustratedinPanelsAandBinFigure3.3asinFigure3.2.Theand˚wereselectedtobeconsistentwithpreviousmeasurementsfromtheCUBEdetectorsetup.Inthepresentwork,isintheplanebetweenthecenterofthetargetandthecentersoftheMWPCsasillustratedinPanelBinFigure3.3.=0isatthebeamaxisdownstreamofthetarget,=180isatthebeamaxisupstreamofthetargetandisalwaysbetween0and180.isalongacirclecenteredonthebeamaxisinanyplanenormaltothedirectionofthebeam,liketheexampleillustratedinPanelBinFigure3.3.=0atthecenteroftheFrontMWPCandas=180atthecenteroftheBackMWPC.istobebetween0and180abovethebeamaxisandbetween180and360belowthebeamaxis.Theradius,r,isasthedistancefromthecenterofthetargettoagivenpositionwithintheCUBEsetup.ThecenterofeachMPWCwas180mmfromthecenterofthetarget.ThesphericalcoordinatesatthecenterofthetwoMWPCsareindicatedinFigure3.3.Table3.1liststhecoordinatescorrespondingtothecenterofthedetectoractiveareaandthecenterofeachedgeofthedetectorsinthethreecoordinatesystem.51Figure3.2:SchematicscalediagramoftheCartesiancoordinatesystemusedinthepresentworkinrelationtotheCUBEdetectorsetup.PanelAshowsadiagramoftheCUBEdetectorssetupfromaboveillustratingthe(X;0;Z)plane.PanelBshowsadiagramoftheCUBEdetectorsetupfromthebeamaxisupstreamofthetargetillustratingthe(X;Y;0)plane.ThecoordinatesatthecenteroftheCUBEandatthecenterofthetwoMWPCsareindicated.Figure3.3:SchematicscalediagramofthesphericalcoordinatesystemusedinthepresentworkinrelationtotheCUBEdetectorsetup.PanelAshowsadiagramoftheCUBEdetectorsetupfromabove.Theofandrareindicated.PanelBshowsaviewfromthebeamaxisupstreamoftheCUBEandtheofisindicated.ThecoordinatesatthecenteroftheCUBEandatthecenterofthetwoMWPCsareindicated.52Table3.1:CoordinatesineachofthethreesystemsinthisworkforthecenterandfourpositionsaroundtheedgeofthetwoMWPCs.Theedgepositionslistedareatthecenteroftheedgesofthetop,bottom,left,andrightsidesoftheactiveareaofthetwoMWPCs.IntheCartesiansystemsandinrinthesphericalsystemthevaluesaregiveinmm.Inthesphericalcoordinatesystemthevaluesandaregivenindegrees.DetectorCoordinatesCUBECoordinatesSphericalCoordinates(x;y)(X;Y;Z)(r,Center(0,0)(-180,0,0)(180,90,180)BackTop(0,17.5)(-180,177,10)(253,90,135)MWPCRight(14,0)(-180,0,150)(235,50,180)Bottom(0,-17.5)(-180,-163,10)(243,90,-135)Left(-14,0)(-180,0,-130)(222,125,180)Center(0,0)(127,0,127)(180,45,0)FrontTop(0,17.5)(120,175,134)(251,45,45)MWPCRight(14,0)(219,0,36)(222,80,0)Bottom(0,-17.5)(120,-175,134)(253,45,315)Left(-14,0)(22,0,232)(234,5,0)3.2PositionInformationThefollowingsectionsdescribetheprocessforcalibratingtheMWPCsandconvertingamongthecoordinatesystems.AsdiscussedinSection2.3,eachfragmentobservedinanMWPCduringaCUBEmeasurementresultsinapositionsignal.Thereactionof50Cr+180WatELab=284.0MeVisusedthroughoutthediscussionasanexample.Thisprocesswasappliedconsistentlytothewholedatasettoobtaintheresultsforeachreactionpresentedinthiswork.3.2.1PositionCalibrationsTheedgesoftheactiveareaoftheMWPCsweredeterminedtocalibratetheobservedpositioninformationtothecoordinatesystemsinSection3.1.Duringtheexperiment,53acalibrationmeasurementwascarriedoutinwhichtheentireactiveareaoftheBackMWPCwasilluminated.Inthiscalibrationmeasurement,50Crwasreactedwith184WatELab=186.0MeV.Atthisenergy,thereactionof50Cr+184Wwaswellbelowthetheinteractionbarriersoonlyelasticscatteringoccurred.Thedataacquisitionsystemwasrunin\singlesmode"whereonlyaneventintheBackMWPCwasrequiredtotriggerthedataacquisitionsystem.Thisallowedforthecollectionofindividualeventsacrosstheentireactiveareaofthedetector.Thesignalamplitudesfromtheadcwerethennormalizedtothephysicaledgesofthedetectortoprovidealineartransformationtoposition.ThepositionspectrarecordedduringthecalibrationmeasurementareshowninFig-ure3.4.TheedgesoftheBackMWPCweredeterminedfromthespectrashowninPanelsAandBofFigure3.4bythesharpinthepositiondistributions.TheactiveareaedgescanbeobservedinPanelAofFigure3.4inthexdimensionatchannelnumbers215and915inx.TheactiveareaedgecanbeobservedinPanelBofFigure3.4intheydimensionatchannelnumbers358and795.ThesevaluesareconsistentwithpreviousCUBEmea-surements.IntheFrontMWPC,theedgesoftheactiveareawerelessclear.ThepositiondistributionsinthexandydimensionsmeasuredintheFrontMWPCareshowninPanelCandD,respectively,inFigure3.4.Theedgesweredeterminedtobeatchannelnumbers240and1050inthexdimensionand142and1020intheydimensionbasedonpreviousmeasurementswithfullilluminationofthefrontMWPC.ThechannelnumbersconsideredtobetheedgeofthetwodetectoractiveareasarelistedinTable3.2withthecorrespondingpositioninmmforthedetectorcoordinatesystem.ThereareadditionalpointsofinterestinthefourspectrashowninFigure3.4.IntheBackMWPCatimedelaymodulewasnotfunctioningcorrectlyandcausedagroupofeventstobeobservedatlowerchannelnumbersthantheyshouldhavebeen.InPanelBof54Table3.2:TheexperimentallydeterminedpositionsinchannelnumbersandthedpositionsinmmfortheedgesoftheactiveareaoftheFrontandBackMWPCs.BackMWPCFrontMWPCPositionChannelNumbermmChannelNumbermmXLeft215-130.0240-149.0XRight910149.01050130.0YTop358178.5142178.5YBottom795-178.51020-178.5Figure3.4,theseeventscanbeobservedaroundchannelnumber100.Also,apulsersignalwasintroducedtothedataacquisitionsystemforeachdetectorandcanbeobservedinthespectra.IntheBackMWPC(PanelsAandBofFigure3.4),thepulsersignalswereobservedaroundchannelsnumbersx=976andy=385.IntheFrontMWPC(PanelsCandDofFigure3.4),thepulsersignalswereobservedaroundchannelsnumbersx=256andy=1069.ThetwodimensionalpositionspectrafortheBackandFrontMWPCsareshowninFigures3.5and3.6,respectively,todemonstratethegatesthatwereappliedtothedatasetinthepresentwork.ErroneouseventscanresultfromedgenoiseintheMWPCs,anddataconversionerrors.AdditionalerroneouseventsincludethosemisplacedbythetimedelaymodulethatwasnotfunctioningcorrectlyintheBackMWPC.Theseeventswereremovedfromthedatasetbygatesrepresentedbythesolid,blackrectanglesinPanelAofFigures3.5and3.6for50Cr+180WatELab=284.0MeV.ThetwodimensionalpositiondistributionsobservedintheBackandFrontMWPCsareshowninPanelBinFigures3.5and3.6,respectively,afterthegateswereapplied.NotethatthevariationoftheintensityisclearlyvisibleinthegatedspectrashowninPanelBofFigures3.5and3.6.TheintenseregionsresultfromthelimitedangularcoverageofthetwoMWPCsinthecenter-of-mass55BackMWPCXPositionDistributionBackMWPCYPositionDistributionFrontMWPCXpositionDistributionFrontMWPCYpositionDistributionFigure3.4:Positiondistributionsinthexandydimensionsinchannelnumberobservedfromthecalibrationmeasurementof50Cr+184WatELab=186.0MeVthatwasusedtodeterminethedetectoredgesinFrontandBackdetectors.PanelsAandBcorrespondtothexandypositiondistributionsfortheBackMWPCandPanelsCandDcorrespondtothexandypositiondistributionsfortheFrontMWPC.56frame.Theforwardfocusingresultingfromthemomentumofthecompoundnucleuscausesthenon-rectangularshapeobservedinthepositionspectrafromtheFrontMWPC.AnadditionalfeatureofnoteintheFrontMWPCpositionspectraistheangledlineswhichlikelyresultfromanambiguityinthepositiondeterminationatpositionswherethexpositionequalstheyposition.Thiscouldbecorrectedifathirdpositionsensitivelayerwasaddedtothedetectortoremovethisambiguity.Additionally,noiseinthespectracomesfromRFsignalspickedupbythepre-amTheofthisnoiseissmallandonlycausedabouta1mmmodulationinthepositionsignals.ThewiresoftheMWPCcanbeseeninthepositionspectraaswell.InthecenterofbothdetectorsintheYdimensionthereisalargedipinthepositionspectraatYequals0.Thisisduetotheplacementofapressurewindowsupportwireinthecenterofthedetector.Thecalibrationparametersforthedetectoredgesallowedfortheconversionfromchannelnumbertomillimeters.ForthelineartransformationfromchannelnumbertomminthexdimensiontheslopewascalculatedasSlopex=xLeft(mm)xRight(mm)xLeft(ch)xRight(ch)(3.1)wherexLeft(mm)andxRight(mm)aretheknownpositionsofthedetectoredgesinmm,andxLeft(ch)andxRight(ch)arethechannelnumbersdeterminedtobetheedgeofthedetectors.TheinterceptwasdeterminedfromthesameinformationasInterceptx=xRight(mm)xLeft(ch)xLeft(mm)xRight(ch)xLeft(ch)xRight(ch):(3.2)Theslopeandinterceptintheydimensionweredeterminedinthesamemannerusingthe57Figure3.5:TwodimensionalpositionspectrafortheBackMWPC.PanelAshowstherawpositioninformationandthesolidblackrectanglethegateappliedtothedatasets.PanelBshowsthepositionspectraafterthegatewasapplied.Botharefor50Cr+180WatELab=284.0MeVasanexample.58Figure3.6:TwodimensionalpositionspectrafortheFrontMWPC.PanelAshowstherawpositioninformationandthesolidblackrectanglethegateappliedtothedatasets.PanelBshowsthepositionspectraafterthegatewasapplied.Botharefor50Cr+180WatELab=284.0MeVasanexample.59Table3.3:SlopesandInterceptsdeterminedforthelinearconversionfromchannelnumbertomillimetersfortheMWPCs.Detector0Detector1DimensionSlope(mm/ch)Intercept(mm)Slope(mm/ch)Intercept(mm)x0.401-216.30.344-231.7y-0.817471.0-0.407236.2channelnumbersandknowndetectoredgesintheydimension.TheslopeandinterceptvaluesinxandyfortheMWPCsarelistedinTable3.3.FromtheslopeandinterceptvalueseachpositioncouldbedeterminedinmmasPositionx=y(mm)=Slopex=y(mm=ch)Postionx=y(ch)+Interceptx=y(mm)(3.3)whereeachvariablecorrespondstotheappropriatexorydimensionvalue.Thepositionsignalsinmmfor50Cr+180WatELab=284.0MeVintheBackandFrontMWPCsareshowninPanelsAandBofFigures3.7,respectively.3.2.2TransformationAmongtheCoordinateSystemsOneoftheprimaryquantitiesofinterestinthepresentworkisthecenter-of-massangleatwhichthefragmentswereemitted.Todeterminethisangle,the(x;y)positioninformationobservedintheMWPCsneededtobetransformedtothefullCUBEsetupCartesianco-ordinatesystemandthentransformedtosphericalcoordinates.ThissectiondescribestheprocessusedinthepresentworktotransformthetwodimensionaldetectorpositionsignalstothefullCUBEsystemcoordinates.AsdiscussedinSection3.1,thecenterofeachMWPCwasinbothCartesianandsphericalcoordinates,thusallotherpositionsobservedintheMWPCsweredeterminedrelativetothecenterofthedetector.Allpositionsinthe60Figure3.7:TwodimensionalpositionspectrafollowingtheconversionfromchannelnumbertommfortheBack(A)andFront(B)MWPCsobservedduringthemeasurementof50Cr+180WatELab=284.0MeVasanexample.61CUBEcoordinatesystemwereinitiallydeterminedinchannelnumbers.TheYcoordinateintheCUBECartesiancoordinatesystemwasdeterminedfromthecenterofthedetector(Ycenter)intheCUBECartesiancoordinatesystem,aszero,andthechannelnumberofagivenevent(yevent)intheMWPCcoordinatesystemsasY(ch)=Ycenter(ch)+yevent(ch)(3.4)TheXvalueintheCUBECartesiancoordinatesystemwasdeterminedfromtheXandvaluesatthecenterofthedetectorintheCUBECartesiancoordinatesystemandthexpositionobservedfortheevent(xevent)inchannelnumbersasX(ch)=Xcenter(ch)+xevent(ch)cos(center;i):(3.5)Finally,theZvalueintheCUBECartesiancoordinatesystemwasdeterminedfromtheZandvaluesatthecenterofthedetectorintheCUBECartesiancoordinatesystemandthexpositionobservedfortheevent(xevent)inchannelnumbersasZ(ch)=Zcenter(ch)+xevent(ch)sin(center;i):(3.6)After(X;Y;Z)positionsweredeterminedasimpleCartesiantosphericalcoordinatestrans-formationwasusedtodeterminethesphericalcoordinatesforanobservedevent.TheconversionfromCartesiantosphericalcoordinateswasdonebyusingtherootTVector3class[104].Theangularcoverageasafunctionof)oftheBackandFrontMWPCsareshowninPanelsAandBinFigure3.8,respectively,foreventsrecordedin\singlesmode"fromthecalibrationmeasurementof50Cr+184WatELab=186.0MeV.62Figure3.8:AngularcoverageoftheBack(a)andFront(b)MWPCsshownasLabonthex-axisandonthey-axisfromthemeasurementof50Cr+180WatELab=284.0MeV.633.3TimingInformationInadditiontothepositioninformationdiscussedabove,atimingsignalwasalsorecordedforeventsobservedintheCUBEMWPCs.Theraw,uncalibratedtimedistributionofthecoincidenttimingsignalsobservedinthemeasurementof50Cr+180WatELab=284.0MeVforthetwoMWPCsisshowninPanelAinFigure3.9.ThesolidblackpolygoninPanelAinFigure3.9representsthegateappliedtothedatasettoremoveeventsincorrectlyassociatedwithabeampulse.Eventsoutsideofthegatedregionareduetoeventsfromneighboringbeambunchesfromthebeamchopper.ThedoublepeakintheelasticscatteringeventsintheBackMWPC(time0)resultsfromatimebetweenthequadrantsintheydimension.ThecoincidenttimesignalsfollowingconversionfromchannelnumbertonsareshowninPanelBinFigure3.9.Toconvertthesignalsfromchannelnumbertons,acalibrationofthetimetoanalogconversion(TAC)wasdonewithanOrtec462TimeCalibratortodeterminethechannelnumbertonscalibrationfortheMWPCs.Thetimecalibratorwassetuptoproducepulsesspacedby10nsandthetimespectraobservedduringthiscalibrationmeasurementareshowninFigure3.10.Eachpeakcorrespondstoapulsefromthetimecalibrator.Thecenterofeachpeakwasdeterminedandtheaveragespacingbetweeneachpeakprovidedthechannelnumbertonsconversion.IntheBackMWPC,themeanspacingwas66channelsandthetimeslopewas0.1516ns/ch.IntheFrontMWPC,themeanspacingwas113channelsandthetimeslopewas0.088ns/ch.ThelargerspacingintheFrontMWPCTACcalibrationtimingspectracomparedtothespacingintheBackMWPCTACcalibrationtimingspectrawasduetoavariationinthesettingsbetweenthetwodetectors.Anexampleillustrationofthetimingstructureofthe14UDTandemAcceleratorand64Figure3.9:PanelAshowstherawtimingsignalsobservedforcoincidentfragmentsintheFront(x-axis)andBack(y-axis)MWPCsfromthemeasurementof50Cr+180WatELab=284.0MeV.PanelBshowstheobservedtimingsignalsfollowingconversiontons.Seetextfordetailsonthisconversion.65Figure3.10:TimespectrainchannelnumbersobservedintheBack(A)andFront(B)MWPCsfromtheTACcalibrationswith10nspulses.66CUBEsetupatANUisshowninFigure3.11.Thelengthofthetpathfromtheacceleratortothetargetandthetargettothedetectorswerewellknownandconstant.AnexampleoftwoRFpulsesisillustratedinPanelAofFigure3.11.Inthepresentwork,theRFsignalfromtheacceleratorwasutilizedasareferencetimesignalandwaspulsedatintervalsof106.7ns.AnexampletimingsignalobservedintheBackMWPC,whichwasusedasthe\start"signalforthedataacquisition,isshowninPanelBofFigure3.11.AnexamplesignalobservedintheFrontMWPC,whichwasusedasthe\stop"signal,isillustratedinPanelCofFigure3.11.FortheseexamplesignalsintheMWPCs,theleftmostRFpulsewouldbethereferencetime,andtherightmostpulsecorrespondstothenextbeampulse.ThetimebetweentheobservedtimesignalintheBackdetectorandthereferenceRFsignalcorrespondstothetransmissiontimethroughtheacceleratorandbeamlinetothetargetandthenfromthetargettothedetector(t0).ThetimebetweentheobservedsignalsintheBackandFrontMWPCsistheelectronicdelaytime(t).Theelectronicdelaytime(t)betweentheBackandFrontMPWCtimingsignalsdependsonthecablelengthsandthetransmissiontimesoftheelectronicssignalsoftheMWPCs.Smallvariationsintimemaybecausedbytemperaturedriftsoftheelectronicssystem.twasoptimizedbyrequiringthatthebinaryfragmentsweresymmetricaboutalineatmassratioequalto0.5.Thetransmissiontime(t0)dependsonthebeamspeciesandenergy.t0wasoptimizedbyrequiringthatonlybinaryeventswereincluded.FortheMWPCs,thecalibratedtimeswerecalculatedasT(Back)Calibrated=TimeSlopeT(Back)Raw+t0(3.7)67Figure3.11:Illustrationofanexamplesetoftimingsignalsincluding,RFsignalsinthetoppanel,atimingsignalfromtheBackMWPCinthemiddlepanel,andatimingsignalfromtheFrontMWPCinthebottompanel.t0andtarethetimeparametersusedintheCUBEcalibration.Seetextfordiscussion.68T(Front)Calibrated=TimeSlopeT(Front)Raw+t0+t(3.8)Afterthepositionandtimingsignalswerecalibratedtheywereusedtodeterminethevelocityvectorsneededinthekinematiccoincidencemethod.3.4KinematicCoincidenceMethodThewell-establishedkinematiccoincidencemethod[41,4]isatechniqueusedtodeterminethemassratiosofcoincidentfragmentsandhasbeenappliedextensivelytoandlikereactions[4,41,5,87,46,40,105,106,64,65].Inthekinematiccoincidencemethod,themeasuredpositionandtimingsignalsareusedtodeterminethelaboratoryframevelocityvectorsforapairofcoincidentfragments.Thevelocityvectorsarethenconvertedintothecenter-of-massframeandusedtodeterminetheMRofeachfragment.Thekinematiccoincidencemethodreliesontheassumptionofbinaryreactionkinematicstoensurethatthemassratioscanbedeterminedfromthecenter-of-massvelocityvectors.TwotestswereperformedtoensurethatthisassumptionwasvalidforthedatasetinthepresentworkandarediscussedinSection3.5.1.Inthekinematiccoincidencemethod,thetwoemittedfragmentsarecharacterizedbytheirvelocityvectors.AnexampleofaneventobservedinthepresentworkisillustratedinFigure3.12andthepertinentvectorsareindicated.Followingseparation,eachfragmentwillhaveathreedimensionalvelocityvectorinthelabframe(v3D;i;lab).Additionally,themotionofthefragmentscanbeconsideredinthecenter-of-massframe,withthethreedimensionalvelocityvectorsV3D;i;c:m:.Thelabframeandcenter-of-massframevelocityvectorscanbeprojectedontothe(X;0;Z)planeasintheCUBECartesiancoordinatesystemin69Figure3.12:Illustrationoftheprimaryvectorsconsideredinthekinematiccoincidencemethodfortwoemittedfragments.PanelAshowstheprojectionofonepossiblecombi-nationofvectorsontoaplane(X;0;Z)alongthebeamaxis.TheZ-axisrepresentsthebeamaxis.Thesolid,blackvectorsrepresentapossiblesetofVi;c:m:fortwofragmentsi.Thedashed,purplevectorsrepresentonepossiblesetofvi;lab.Asanexample,thetwocomponentsofthetwoVi;c:m:areshown.Thedotdashed,redvectorsrepresentui;c:m:andthedotdashed,bluevectorsrepresentwi;c:m:.i;labisshownasanexampleoftheof.PanelBshowsaprojectionofonepossiblecombinationofvelocityvectorsontoaplane(X;Y;0)perpendiculartothebeamaxis.Thedashed,blackvectorsrepresentonepossiblecombinationofVi;c:m:forfragmentsi.Thedotdotdashed,skybluevectorsrepresentpossi-bleVi;dev.TheprojectionofeachVi;devonthez-axisisrepresentedbythedotdotdashed,darkpurplevectors(shownjustthezaxisforclarity).Thesolid,orangevectorsrepresentvperp,whichshouldbezeroinbinarykinematics.˚i;devarealsoindicated.70Table3.4:Componentdfortheprojectionsvi;labalongtheXandZaxesinthe(X;0;Z)planeandalongtheXaxisinthe(X;Y;0)plane.Thecomponentsinthe(X;0;Z)planearerelativeto,whileXisinthe(X;Y;0)planerelativetoSeetextforfulldescriptionsofplanesandangles.vi;labVi;c:m:Xcomponentwi;lab=vi;labcosi;labwi;c:m:=Vi;c:m:cosi;c:m:Ycomponentui;lab=vi;labsini;labui;c:m:=Vi;c:m:sini;c:m:X˚componentsi;lab=vi;labi;labsi;c:m:=Vi;c:m:i;c:m:Section3.1.The(X;0;Z)planeisillustratedinPanelAofFigure3.12wherethelabframeandcenter-of-massframevectorprojectionsareindicatedbyvi;labandVi;c:m:,respectively.EachprojectedvectorcanbedecomposedintoitscomponentsalongtheXandZaxes.Thecomponentsofthecenter-of-massframevectorprojectionareillustratedinPanelAofFigure3.12,asanexample.ThecomponentintheZdimensionisindicatedbyuandthecomponentintheXdimensionisindicatedbyw.TheforthecomponentsarelistedinTable3.4.InPanelAofFigure3.12theangleatwhichthefragmentswereemittedinthelaboratoryframeisrepresentedbythecurved,purplearrows.Additionally,inPanelAofFigure3.12thevectorrepresentingtheconversionfromVi;c:m:tovi;labisindicatedbythegreenarrowandlabeledvpar.vparrepresentsthevelocityofthecompoundsysteminthedirectionparalleltothebeam.AnexampleeventviewedfromupstreamofthetargetisillustratedinPanelBinFig-ure3.12inthe(X;Y;0)plane,asinSection3.1.Thetwodashed,blackvectors(Vi;c:m:)representthevelocityvectorsprojectionsofthetwofragmentsontothe(X;Y;0)planeinthecenter-of-massframe.Theprojectilebeamshouldhavenomomentuminthisplane,sotheprojectionsofvi;labandVi;c:m:shouldbeequivalent.Further,conservationofmomentumrequiresthatthetwonucleibeemittedbacktobackwith˚1-˚2=18071inthecenter-of-massframe.Thisistrueoftwo-body,fullmomentumtransfereventsandisrequiredfortheassumptionsofthekinematiccoincidencemethodtohold.Thiswillnotbeobservediflightparticle(alpha,neutron,orproton)emissionortransfer-inducedoccurinaspeventbutonlyonaverageforanensembleofevents.Suchprocesseswouldresultintheobservedvi;labnotbeingequivalenttoVi;c:m:inthe(X;Y;0)plane.Thedot-dotdashed,lightbluevectors(Vdev;i)representthevelocityvectorsofthefragmentobservedinthelabframeafteraneventlikelightparticleemissionthatwouldalterthevelocityofthefragments.InPanelBofFigure3.12theangleiatwhichthefragmentswereemittedisrepresentedbythelightblue,curvedarrows.Thedotdashed,purplevectorslabeledsdev;irepresentthecomponentofVdev;ialongtheXaxisdeterminedwithrespecttoi.Themathematicalofsdev;iisincludedinTable3.4.ThedeviationbetweenVi;c:m:andVdev;iisrepresentedbytheorangevectorslabeledvperpandencompassesthevelocityperpendiculartothebeamdirection.Bothvperpandvparareusedtoensurethattheeventsincludedinthedatasetweretwobodyevents.vperpcanbecalculatedfromthezcomponentsofVdevfromeachfragmentasvperp=sdev;1sdev;212qs2dev;1+s2dev;22sdev;1sdev;212:(3.9)where1;2is˚1-˚2.Itisclearthatwhenthetwofragmentsareemittedbacktoback(12=180)vperpwillbezero.Whenvperpiszero,thenallofthecompoundnuclearmomentumisaccountedforinvparandV1;c:m:willbeequivalenttoV2;c:m:.AratiooftheVi;c:m:componentsandvparcanthenbewrittenasu1;c:m:w1;c:m:vpar=u2;c:m:w2;c:m:vpar(3.10)72Theminussignsresultsfromthefactthatuwillonlybepositive,whilewcanbepositiveornegative.Wheneq.3.10issolvedforvparusingthecomponentinTable3.4andthetrigonometricangleadditionrule,thefollowingequationresults,vpar=u1w2+u2w1u1+u2=v1v2sin(1+2)v1sin1+v2sin2(3.11)whereallcomponentsarerelativetothecenter-of-massframevelocityvectors.Whenvperpiszero,thenvparshouldbeequivalenttothecompoundnucleusvelocity(vCN),whichcanbecalculatedasvCN=1:389sELabApApAp+AT(cm=ns):(3.12)whereELabistheincidentbeamenergyinthelabframeinMeVandApandATarethemassesoftheprojectileandtarget,respectively.3.5VelocityDeterminationInthepresentwork,thelabframevelocitiesweredeterminedfromtheobservedpositionandtimingsignalsasvi;lab=rTCalibrated(3.13)whereristhemagnitudeofthepositionvectorinsphericalcoordinatesinmm,andtimeisthetimeinns.Eachvi;labwasconvertedtothecenter-of-massframebyVi;c:m:=qv2i;lab+v2CN2vi;labvCNcos():(3.14)733.5.1UsingtodemonstratevperpiszeroAsdiscussedinSection3.4,thekinematiccoincidencemethodreliesontheassumptionthatvperpbezero.Thisassumptionshouldbevalidinthepresentworkbecausethesystemsweremeasuredatcenter-of-massenergieswellbelowthebarriersfortheWtargetsandoneexpectsonlytwomassivefragmentsintheexitchannel.Therefore,three-bodyeventsarisingfromtransferinducedofthetargetshouldberare.Toappropriatelyusethekinematiccoincidencemethodalleventsviolatingtheassump-tionofbinarykinematicswereremovedfromthedataset.ThiswasdonebyremovingeventsfromthedatasetwherevperpwasnotzeroandvpardidnotequalvCN.ThevperpvaluesareshowninPanelAinFigure3.13asafunctionofvpar-vCNdeterminedfortheeventsobservedduringthemeasurementof50Cr+186WatELab=284.0MeV.Thegroupofeventswithvpar-vCNbetween10and15mm/nscomefromreactionswiththecarbonbackingonthetarget.Lightparticleemissionwilloccurafterthetwofragmentsseparate.ThiscausesthewidespreadintheeventscenteredatzeroinPanelAofFigure3.13.Thegateappliedtothedatawasacirclewitharadiusof1mm/nsandisrepresentedbytheblackcircleinFigure3.13.The1cm/nsgatewasselectedsothatthethreebodyeventswereremovedwithoutngthetwobodyeventsthroughoutthedataset.Asaresultofthegateap-pliedtothedataonlyeventswheretheoflightparticleemissionaveragedtozeroareincludedinthedataset.AsdiscussedinSection3.4forbinaryevents,vpar-vCNmustequalzeroandvperpmustequalzero[41].ThevaluesofvperpareshowninPanelBinFigure3.13asafunctionvpar-vCNafterthegatewasappliedtothedataset.Thedistributionisnowcenteredonvperpofzerointheydimension,andvpar-vCNofzerointhexdimension.Notethatevenpriortoapplyingthegatethedistributionisstronglypeakedatvperpofzeroand74vpar-vCNofone,indicatingthatthetwo-bodyreactionsarethedominantexitchannel.vperpwillbezerowhenthetwofragmentsareemittedat180inthecenter-of-massframe.Toreiteratethatvperpcanbeassumedtobezerointhepresentwork,thebetween1and2isshowninFigure3.14for50Cr+180WatELab=284.0MeV.Thetwofragmentsareemitted180apart,thustheuseofthekinematiccoincidencemethodisinthepresentwork.3.5.2CalculatingMROneoftheprimarydeducedquantitiesfromCUBEmeasurementsisthemassratioofafragment,asMR;1=A1A1+A2,whereAiisthemassofoneofthefragmentsdetectedincoincidence.Thekinematiccoincidencemethodisusedtodeterminethemassratiosfromthecenter-of-massvelocityvectorsusingconservationofmomentum.Inthecenter-of-massframe,themomentumofthetwofragmentsisequal(p1=p2)andAT=A1+A2.Usingtheserelationsandtheonofmomentum,themassratioofafragmentcanbedeterminedfromthevelocitiesasp1=p2(3.15)A1V1;c:m:=A2V2;c:m:(3.16)(ATA2)V1;c:m:=A2V2;c:m:(3.17)ATV1;c:m:A2V1;c:m:=A2V2;c:m:(3.18)ATV1;c:m:=A2V2;c:m:+A2V1;c:m:(3.19)ATV1;c:m:=A2(V2;c:m:+V1;c:m:)(3.20)V1;c:m:V2;c:m:+V1;c:m:=A2AT=MR(3.21)75Figure3.13:Perpendicularvelocitydeterminedfor50Cr+180WatELab=284.0MeVasafunctionofthebetweenvparandvcn.Thesolid,blackcircleinPanelArepresentsthegateappliedtothedatasetandhasa1mm/nsradius.PanelAshowsthedistributionbeforethegatewasapplied.PanelBshowsthedistributionafterthegatewasappliedtothedataset.76Figure3.14:Thenumberofcountsobservedfor50Cr+180WatELab=284.0MeVshownasafunctionofthebetweenthedeterminedvaluesoffromtheBackdetectorandtheFrontdetectorforgatedcoincidentevents.Thedataisrepresentedasthesolidbluelineandshowsastrongpeakataof180.AGaussianfunctiontothedataisshownasthedashed,redlineandtheboxintheupperrightcornerprovidesthemeansandRMSfromthe77whereAiisthemassoffragmentiandVi;c:m:isthetotalvelocityvectorinthecenter-of-massframeforfragmenti.3.5.3EnergyCalculationThededucedvelocityvectorswerecorrectedforenergylossoftheprojectileinthetar-getandtargetbackingmaterialandfortheenergylossofthefragmentexitingthetargetbyestimatingtheenergylossrelativetotheenergylossofanalphaparticleinthesamematerial[102].Todeterminetheestimatedenergyloss,aninitialenergyEint;LaboftheemittedfragmentwasdeterminedasEint;Lab=0:00518MR(AP+AT)v2lab(3.22)thenvlaboftheemittedfragmentwasrecalculatedwiththenewenergyvaluesasvlab=13:89sEnew;LabMR(AP+AT)(mm=ns):(3.23)ThisprocesswasiterateduntilthechangeinElabwaslessthan10keV.Then,thecenter-of-massvelocitiesweredeterminedwitheq.3.14withthevlabcorrectedforenergylossinthetarget.Additionally,theenergyofeachemittedfragmentswasdetermined.TheenergywasestimatedasEfrag;i=MR;i(AP+AT)V2lab(3.24)ItisimportanttonotethattheCUBEdetectorsetupwasoptimizedforpositionandtimemeasurements,notformeasuringtheenergyoftheemittedfragments.Additionally,the78CUBEdetectorsetupwasoptimizedformassratiodeterminationanddoesnotaccountforneutronloss,whichcouldchangethemassandthereforethetotalenergy.Thus,thisisonlyanapproximation.Furthercorrectionswouldbenecessarytoaccuratelydeterminetheenergyofthefragments.3.5.4TotalKineticEnergyGatesThesumoftheEfrag;ivaluesfortwocoincidentfragmentsisthetotalkineticenergyofthesystem.TheratioofthededucedtotalkineticenergytoatheoreticaltotalkineticenergyisshowninFigure3.15.WherethetheoreticaltotalkineticenergyforfragmentsiscalculatedusingViolasystematics[107,108]TKE=0:11897Z2=A1=3+7:3MeV;(3.25)whereZandArefertothecompoundnucleus[108].Thededucedtotalkineticenergy(Efrag;1+Efrag;2)foreventsshouldbeequivalenttothatgivenbyeq.3.25.ThetotalkineticenergycalculatedwithViolasystematicsforthe50Cr+180Wsystemis193.8MeV.TheintensegroupsatMR=0:2and0:8inFigure3.15arescatteringevents.ThebandofeventsbetweenMR=0:35and0:65withatotalkineticenergyratioofapproximatelyoneareeevents.AsobservedinFigure3.15thetailoftheheavyscatteringeventsincludeseventsatMRvaluesneartotherangeoftheeevents.ThescatteringeventsinthatregionwereremovedfromthedatasetbyagaterepresentedbytheblackpolygonshowninPanelAofFigure3.15.ThedistributionafterthegatewasappliedtothedataisshowninPanelBofFigure3.15.79Figure3.15:Ratioofthededucedtotalkineticenergyfrombinaryfragmentstothetotalkineticenergycalculatedforfragmentsfor50Cr+180WatELab=284.0MeVshownasafunctionthedeterminedmassratios.Thesolid,blackpolygoninPanelArepresentsthegatesusedtoremovescatteringeventswithmassratiosintheeregion.PanelAshowsthedistributionbeforethegatewasapplied.PanelBshowsthedistributionafterthegatewasapplied.803.5.5DeterminationofMRandc:m:Afteraccountingforenergylossinthetarget,thefragmentvelocitieswereusedtodeterminethemassratiosandcenter-of-massangles.Themassratiosweredeterminedfromthecenter-of-massvelocitiesasMR;i=Vc:m:;jVc:m:;i+Vc:m:;j(3.26)whereicorrespondstothefragmentforwhichthemassratiowasdetermined,andjcorre-spondstothecoincidentfragment.Thesecondquantityofinterestinthepresentworkisc:m:,whichwasdeterminedfromthecomponentsofthecenter-of-massvelocityvectorsandvcnasc:m:=tanuiwivcn(3.27)Thechapterhasdiscussedthefullsetofcalibrationsandgatesappliedtothedatasetinthepresentwork.Theresultingmassratiosandc:m:determinedforthecoincidentfragmentsobservedinthepresentworkwillbediscussedinChapter4.81Chapter4ResultsThischapterpresentstheresultsoftheCr+WmeasurementspreformedattheAustraliaNationalUniversityinNovember2013.Massdistributions,angulardistributions,andmass-angledistributions(MAD)werededucedforeachoftheeightreactionsmeasuredinthepresentworkatbothEc:m:/VB=1.13andECN=52.0MeV.Thetechniquesforeachmassdistributiontodeterminethewidthandthedetailsofthecalculationofthetheoreticalpredictionsforpuremassdistributionsarediscussed.Thischapteralsodescribesthemethodfordeterminingtheangulardistributionsforeachsysteminthepresentwork.4.1Cr+W:Ec:m:/VB=1.13ThissectionpresentstheMADs,massdistributions,andangulardistributionsgeneratedfortheseriesofsystemsmeasuredatEc:m:/VB=1.13inthepresentwork.4.1.1Mass-AngleDistributionsAsdiscussedinSection1.3.3,MADshavebeenusedextensivelyinstudiesofreactiondy-namics[40,39,87].MADsareahistogramofthec:m:asafunctionofthedeterminedmassratios,whichconstitutesthefulldatasetofthepresentwork.AMADwasgeneratedforeachofthetwoMWPCsinthepresentwork.TheMADsgeneratedfromeventsintheBack8250Cr+180W!230Cf=052Cr+180W!232Cf=254Cr+180W!234Cf=450Cr+186W!236Cf=6Figure4.1:UnsymmetrizedMADsoftheeightCr+WreactionsintheBackMWPCatEc:m:/VB=1.13.nisthechangeinthenumberofneutronsinthecompoundnucleusrelativeto50Cr+180W,whereN=132.MWPCforeachsystemstudiedinthepresentworkareshowninFigure4.1.Coincidencebetweentwoobservedfragmentsineachdetectorwasrequiredforeacheventrecordedinthepresentwork.ThecomplementaryMADsobservedbytheFrontMWPCforthesys-temsmeasuredinthepresentworkareshowninFigure4.2.TheseMADsareobtaineddirectlyfromtheMWPCsandarereferredtoas\unsymmetrized."Asthetermimplies,theMADscanalsobeshowninasymmetrizedfashion.Thefollowingsectiondiscussessymmetrization.83Figure4.1:(cont'd)52Cr+184W!236Cf=654Cr+182W!236Cf=654Cr+184W!238Cf=854Cr+186W!240Cf=108450Cr+180W!230Cf=052Cr+180W!232Cf=254Cr+180W!234Cf=450Cr+186W!236Cf=6Figure4.2:UnsymmetrizedMADsgeneratedfortheCr+WreactionsintheFrontMWPCatEc:m:/VB=1.13.isthechangeinthenumberofneutronsinthecompoundnucleusrelativetothelightestsystem,50Cr+180W,whereN=132.85Figure4.2:(cont'd)52Cr+184W!236Cf=654Cr+182W!236Cf=654Cr+184W!238Cf=854Cr+186W!240Cf=10864.1.1.1SymmetrizationOfteninheavy-ionfusionreactionstudiesMADsaresymmetrized.ThismeansthatforhalfoftheeventsshownintheMADthemassratioandc:m:weredeterminedbasedontheassumptionthatforbinaryeventsdetectedincoincidence,anyfragmentdetectedat1,MR;1willhaveapartnerat1801,1MR;1inthecenter-of-massframe.AnimportantconsiderationwhenlookingatMADsthoughisthattheangulardimensionisgenerallyconsideredfrom0c:m:180onbothsidesofthebeamaxis,asshowninPanelAofFigure3.3.Ifweretobeshownas360,thenamoreexpandedMADcouldbeplottedlikethecartoonMADinFigure4.3PanelA.ThisillustrationofaMADdepictsthemassandangletrajectoriesofanexamplereactionasafunctionofcontacttime.Onepossiblecorrelationbetweenc:m:andMRforthelightfragmentisdepictedbythedotdashed,bluelinesandthecorrespondingcorrelationbetweenc:m:andMRfortheheavyfragmentisdepictedbythedashed,redlines.At45degreesincrements,illustrationsoftheseparatingsystemareshown.Forexample,alightfragmentobservedatc:m:of135ocorrespondstoaheavyfragmentobservedatc:m:of-45o.TomovebetweenthisexpandedMADandthegenerallyusedMADs,thenegativeanglesareeat0,toproduceMADsliketheoneshowninFigure4.3PanelB.Now,alightfragmentobservedatc:m:of135ocorrespondstoaheavyfragmentobservedatc:m:of45o.ThisdistinctionisimportanttokeepinmindwhenconsideringMADs.Thetwofragmentsareemitted180oapart,butaredepictedat1and1801.SymmetrizedMADsareusedthroughouttheliteraturetostudyandquasi-competitioninheavy-ionreactions.Inordertobeconsistentwiththeliterature,theMADsinthepresentworkwerealsosymmetrized.ThesymmetrizedMADsshownhere87Figure4.3:Evolutionofamassangledistributionthroughvariousseparationangles.PanelAshowsthefull360degreecoverage.PanelBshowsasymmetrizedMADwitha0-180degreescalein.weregeneratedfromtheBackMWPCMADs.ForeacheventintheBackMWPCMADacorrespondingeventwasplacedat1801and1MR;1.4.1.1.2SymmetrizedMADsforCr+WsystemsTherearethreekeyregionsinaMAD:theistheintenseregionofproductsnearthemassratiooftheprojectile(ˇ0.2inthepresentwork).Thesecondisthecomplementaryclusterofproductsnearthemassratioofthetarget(ˇ0.8inthepresentwork).Together,theeventsintheseregionsconstitutethelargestfractionofscatteringeventsdetectedinthemulti-wireproportionalcounters(MWPC)duringthemeasurements.Thethirdregioncontainstheeeventsatcentralmassratiosandisthefocusofthepresentwork.Theeregionistakentobebetweenmassratiosof0.35and0.65inthepresentworkand88isindicatedbythesolid,blackrectangleinFigure4.4.Thisregionwasselectedbecauseitconsistentlyexcludestheelasticeventsthroughoutthedataset.PreviousworkhasconcludedthatacorrelationbetweenmassratioandangleintheeregionofasymmetrizedMAD(asopposedtoaconstantangleandmassratio)isoneindicationofthepresenceof[5,4].Amass-anglecorrelationwasobservedineachexperimentalMADinthepresentworkatEc:m:/VB=1.13inthecentraleregion,indicatingthepresenceofTheMADgeneratedfromthereactionof50Cr+180WatElab=284:6MeVisshowninFigure4.4.TheobservedcorrelationishighlightedbythethreeregionsindicatedinFigures4.4and4.5.Thesolid,blackrectangleencompasseventsfromMR=0.35-0.65andspanstheangularcoverageofthedetectorstohighlighttheregionwhereefragmentsareexpected.OneregionofnoteiscenteredatMR˘0.4andc:m:ˇ45o.ThesecondcomplementaryregioniscenteredatMR˘0.6andbetweenc:m:ˇ135o.Eventswiththiscombinationofmassratiosandc:m:canlikelybeattributedtoduetorelativelysmallangularfromthegrazingangleandindicatesashortcontacttimeforthedinuclearsystem.Theseregionsindicatethattheheavyfragments(MR>0.5)werepreferentiallyemittedatbackwardangles(c:m:>90),whilethelightfragments(MR<0:5)werepreferentiallyemittedatforwardangles(c:m:<90),whichistermedamass-anglecorrelation.Forexample,notethatthelightfragmentsarepreferentiallydetectedintheFrontDetector(Figure4.2)atsmallc:mandMR,whiletheheavyfragmentsareobservedintheBackMWPC(Figure4.1).Onlyinthesymmetrizedaretheybothpresent(Figure4.6).Themassdistributiongeneratedfromthereactionof54Cr+186WatElab=287:6MeV,Figure4.5,showsthattheregionsatasymmetricmassratiosarelessenhancedrelativetothemasssymmetricregioninFigure4.4.Theenhancementofthesymmetricmassratioeventsrelativetotheasymmetricmassratioeventsindicatesthatless8950Cr+180W!230Cf=0Figure4.4:Themassangledistribution,wherec:m:isshownasafunctionofmassratio,forcoincidenteventsfromthereactionof50Cr+180WatElab=284:6MeV.Thesolid,blackrectanglehighlightsthemasssymmetricregion(MR=0.35-0.65)acrossthefullangularcoverageofthesymmetrizedMAD.Seetextfordiscussion.isthechangeinthenumberofneutronsinthecompoundnucleusrelativetothelightestsystem,50Cr+180W,whereN=132.ofthereactionislosttointhereactionwiththelargestneutronnumber.ThesixotherMADsgeneratedfromtheCr+WsystemsatEc:m:/VB=1.13areshowninFigure4.6.AllaxisscalesandlabelsarethesameinFigures4.6asthoseinFigure4.4and4.5.NoticethatineachMADinthepresentworkamassanglecorrelationwasobserved.Thechangeintheangularcorrelationwithincreasingneutron-richnesswillbeaddressedquantitativelyinthemassdistributionsandisdiscussedinSection4.1.2below.9054Cr+186W!240Cf=10Figure4.5:ThesymmetrizedMADfromthereactionof54Cr+186WatElab=281:7MeV.AsinFigure4.4,thesolid,blackrectanglewasdrawntohighlighttheregionofmasssymmetriceventsbetweenMR=0.35-0.65acrosstheangularcoverageoftheMWPCs.9152Cr+180W!232Cf=254Cr+180W!234Cf=450Cr+186W!236Cf=652Cr+184W!236Cf=654Cr+182W!236Cf=654Cr+184W!238Cf=8Figure4.6:SymmetrizedMADsoftheremainingsixCr+WreactionsatEc:m:/VB=1.13.isthechangeinthenumberofneutronsinthecompoundnucleusrelativeto50Cr+180W,whereN=132.924.1.2MassDistributionsThemassdistributionsfromthesymmetrizedMADsfortheeightCr+WreactionsmeasuredatEc:m:/VB=1.13areshowninFigure4.7.EachmassdistributionisasimpleprojectionofthecorrespondingsymmetrizedMADontoMR.Theentireangularrangewasincludedinthemassdistributions.ThelargepeaksatMR=0.2and0.8arethequasielasticscatteringeventswithmassratiossimilartothatofCrtoWintheentrancechannel.ThescatteringpeaksextendabovetherangepresentedinFigure4.7,asthey-axisrangewasselectedtoclearlyseetheshapeofthedistributionintheeregion.Themassdistributionshaveamaximumatmassratiosof0.5andaseeminglybroadpeak,whichindicatesthattheyarelikelyTypeIIsystemsaccordingtothedistinctiondiscussedinSection1.3.3.1[40].4.1.2.1DeterminationofMassWidthfromMassDistributionThemass-anglecorrelationintheMADsprovidedaqualitativemeansofcomparingthereactiondynamicsofthesystems,however,itisusefultohaveaquantitativemeansofcomparison.Therefore,thewidthofthemassdistributionintheeregionwasobtained.Asdiscussedpreviously(1.3.1)anarrowmassdistribution,similartothatobtainedinlowenergyindicateswhileabroadmassdistributioniscommonlyconsideredtobeanindicationofthepresenceofInsinceequilibriumisreachedinthemassdegreeoffreedom,themostprobablefragmentshaveasymmetricmassratio.ThisresultsinaconcentrationoffragmentswithmassratiosnearMR=0.5andthusasharppeakinthemassdistribution.Thewidthofthemasspeakisindicativeoftheexcitationenergyofthesystem.However,inssionthedinuclearsystemseparatesbeforereachingfullequilibrium,includinginthemassdegreeoffreedom.Largerimpactparametercollisionswithhigher9350Cr+180W!230Cf=052Cr+180W!232Cf=254Cr+180W!234Cf=450Cr+186W!236Cf=6Figure4.7:MassdistributionsforalleightCr+WsystemsfromthepresentworkatEc:m:/VB=1.13.ThesolidredlinerepresentaGaussiantothedata.ThedashedbluelinerepresentsaGaussianfunctionwiththewidthscalculatedfromastatisticalapproximationsforpureFThisGaussianfunctionhasbeennormalizedtothepeakoftheexperimentalmassdistribution.nisthechangeinthenumberofneutronsinthecompoundnucleusrelativeto50Cr+180W,whereN=132.94Figure4.7:(cont'd)52Cr+184W!236Cf=654Cr+182W!236Cf=654Cr+184W!238Cf=854Cr+186W!240Cf=1095orbitalangularmomentumresultinre-separationofthedinuclearsystemonashortertimescale,beforefullmasstransferhasoccurred.Thisresultsinefragmentswitharangeofmassratios,thusbroadeningthemassdistributionforthesystemrelativetothemassdistributionofasystemwithoutInordertodeterminethewidthofthemassdistributions,eachexperimentalmassdis-tributionwaswithaGaussianfunctioncenteredonMR=0.5.ItisimportanttonotethatthedistributionsarenotexpectedtobepurelyGaussian[43]However,theyweresimilarenoughtoaGaussiandistributioninshapethattheycouldbewithaGaussianfunctionasameansofextractingthewidthoftheexperimentaldistributions.Themassdistributionswereonlybetweenthemassratiosof0.35and0.65touniformlyexcludeelasticanddeep-inelasticscatteringevents.TheresultingGaussianfunctionsareshownasthesolid,redlineineachpanelofFigure4.7.ThewidthofthedistributionwasmultipliedbyACNtogivethemasswidth(˙exp).ThemassdistributionwidthsforeachsystemarelistedinTable4.4.TheuncertaintyonthewidthoftheGaussianfunctiontothedatawasdeterminedfromachi-squaredminimizationandislistedinTable4.4.Eachexperi-mentalwidthcanbecomparedwithastatisticalapproximationofpure(˙)toaccountforanysmallchangesresultingfromthesubtleamongthesystems.Amethodtocalculatetheexpectedwidthforispresentedinthenextsection.4.1.2.2StatisticalApproximationofPureFusion-FissionThewidthofthemassdistribution,˙,frompurecanbeestimatedbythestatisticalapproximation˙2=Tk=1krEscia;(4.1)96whereTisthenucleartemperatureatthescissionpoint[5,46],kistheparameter,0:0048MeV=u2,Esciistheexcitationenergyofthecompoundnucleusatthescissionpoint,andaistheleveldensityparameterasa=A/8.5MeV1.Linetal.suggestthatthenuclearexcitationenergyatscissioncanbecalculatedasEsci=E+QsymTKEhEscipreiEscirotEdef:(4.2)whereQsymistheQvalueforsymmetricofthecompoundnucleus,TKEisthetotalkineticenergyreleasedinfromtheViolasystematics[108](Seeeq.3.25).TheaverageenergycarriedawaybyprescissionneutronemissionhEscipreiisestimatedfromtheneutronmultiplicity(hprei)scaledbytheenergyremovedbyeachneutronemitted,hEnprei.Theneutronmultiplicitywasestimatedasin[109]wherehprei=1:980:0133ACN0:0376E+0:00042ACNE:(4.3)Theaverageenergyremovedbyeachemittedneutronwasestimatedinthesamemanneras[110]wherehEnprei=hEni+hBni,withhBniistheaverageneutronbindingenergy,8.027MeV,hEni=2.0TnandTn=pE=a.Thedeformationenergy(Edef)wassetto12MeVbecauseitisacommonlyusedvalueinactinide[5].TherotationalenergyatscissionEscirotwascalculatedasdescribedin[109],whereEscirot=(E0rot/4.3)+(T/2.0).E0rotwasasE0rot=34.54l2=ACN2,wherelistheaverageentrancechannelangularmomentum.Anaveragelvalueof25.19hfortheCr+WsystemswascalculatedfromCCFULL[111,112].EscirotandThadtobecalculatediterativelysoforeachsystemconvergencewasasachangeinEscix0:001andwasreachedaftertwoiterations.Thecalculated˙arelistedin97Table4.1:CalculatedvaluesusedinthedeterminationofEsci.SystemE*QsymTKEEscipreEscirotEdefEsci(MeV)(MeV)(MeV)(MeV)(MeV)(MeV)(MeV)50Cr+180W64.3236.1187.331.21.481268.250Cr+186W71.4231.5185.937.71.431265.752Cr+180W59.0233.5186.927.61.451264.652Cr+184W62.2231.5185.930.41.421263.854Cr+180W56.9234.9186.426.21.441265.754Cr+182W57.2231.5185.926.61.411262.754Cr+184W59.0232.4185.528.21.411264.354Cr+186W61.1228.5185.029.61.381261.05Table4.4.AGaussianfunctionwithitswidthsettothecalculatedwidthforpureforeachsystemisshownasthedashedbluelineforeachrespectivemassdistributioninFigure4.7.EachtheoreticalGaussianfunctionwascenteredatMR=0.5andnormalizedtotheexperimentaldatapointatMR=0.5.Itwasnotexpectedthatpurewouldaccountforthefullexperimentalmassdistributionatsymmetricmassratios.Thecontribu-tiontothemassdistributionforpurefwouldlikelybesmaller.Evennormalizedtotheexperimentaldata,itisclearthatthepurefusionwidthunderestimatestheexperimentalmassdistribution.TheadditionalcontributiontothemassdistributionmustcomefromotherprocessesandquisthemostlikelycauseofthisdeviationfrompureTheabsoluteheightofthemassdistributionforpurecouldnotbedeter-minedfromtheexperimentaldata,soonlyanupperlimitofPCNisreportedinthepresentwork.TheupperlimitoftheprobabilityofformingacompoundnucleusPCNforeach98Table4.2:CalculatedvaluesusedinthedeterminationofEscipre.SystemhpreihEnpreihEniTnhBni(MeV)(MeV)(MeV)(MeV)50Cr+180W2.711.53.51.78.06550Cr+186W3.211.73.61.88.06552Cr+180W2.411.43.31.78.06552Cr+184W2.711.43.41.78.06554Cr+180W2.311.33.21.68.06554Cr+182W2.411.33.21.68.06554Cr+184W2.511.33.31.68.06554Cr+186W2.611.43.31.78.065Table4.3:CalculatedvaluesusedinthedeterminationoftheEscirot.SystemE0rotTl(MeV)(MeV)h)50Cr+180W2.541.7925.1950Cr+186W2.431.7325.1952Cr+180W2.501.7325.1952Cr+184W2.431.7125.1954Cr+180W2.471.7425.1954Cr+182W2.431.6925.1954Cr+184W2.401.7025.1954Cr+186W2.361.6525.1999Table4.4:Experimentalmasswidths˙exp,statisticalestimateforthepuremasswidth˙,andtheratioof˙exp=˙(upperlimitofPCN)forall8systemsmeasuredatthesameEc:m:/VB=1:13SystemN˙experror˙PCN(UL)=˙=˙exp50Cr+180W098.016.418.190.18650Cr+186W643.81.317.740.40952Cr+180W265.44.018.110.27452Cr+184W634.10.517.680.52154Cr+180W455.82.117.960.32154Cr+182W638.30.717.690.46254Cr+184W839.90.817.770.44654Cr+186W1037.40.717.500.468Cr+WsystemwastakentobetheratioofthecalculatedmasswidthfortotheexperimentalmasswidthsasUpperLimitPCN˙˙exp:(4.4)ThefractionalvaluesoftheupperlimitofPCNdeterminedforeachsystemarelistedinTable4.4.4.1.3AngularDistributionsTheangulardistributions(W())weredeterminedfortheeightCr+Wreactionsmeasuredinthepresentwork.EachdistributionwassummedoverallEachangulardistributionwasexpressedasthetialfragmentcrosssectionatagivenangle(d˙()).Theangular100distributionandthetialfragmentcrosssectionarerelatedby[51]d˙()=W2ˇ()˙:(4.5)SeeSection1.3.2formorediscussion.d˙()wasdeterminedwithamethoddevelopedbythereactiondynamicsgroupatANU.ThemethodusesanormalizationtoanelasticscatteringcalibrationmeasurementtodeterminetheangulardistributionwhileaccountingforthethicknessofthetargetandtheoftheMWPCsandSimonitordetectors.Theangulardistributionwasonlydeterminedforc:m:between101oand141osoonlyangleswheretheBackMWPCcoveredallmassratiosintheeregionwerecon-sidered.TheangularregionishighlightedinFigures4.8and4.9bythedashedblackbox.d˙()wasdeterminedforangularbinsthatwerefourdegreeswideacrossthisregion.Thec:m:valuesreportedinFigure4.15correspondtothecenterofeachbin.AsdescribedinSection3.2.1,duringtheexperimentatANU,anelasticscatteringcali-brationmeasurementwasrunwiththereactionof50Cr+184WatElab=186.0MeV.TheenergyofthecalibrationrunwasselectedtobebelowtheBassinteractionbarrier[9]of50Cr+184Wof196.04MeV.Atthisenergy,thenuclearreactioncrosssectiongoestozero,soallofthereactionshouldbeelasticscatteringevents.TheunsymmetrizedMADobservedintheBackMWPCforthecalibrationmeasurementof50Cr+184WatEc:m:=186.0MeVareshowninFigure4.8.Onlyfragmentswithlightmassratiosat0.2areobservedintheBackMWPCbecausetheheavyfragmentdidnothavetenergytogetoutofthetarget.TheunsymmetrizedMADobservedintheBackMWPCfor50Cr+180WatElab=284.6MeVisshowninFigure4.9asanexample.TheMADafterthemassratiogatewasapplied101Figure4.8:Unsymmetrizedmassangledistributionforcalibrationrunof50Cr+184WatElab=186.0MeV.Thedashed,blackboxindicatestheangularregionincludedintheangulardistributioncalculations.102Figure4.9:Unsymmetrizedmassangledistributionfor50Cr+180WatElab=284.6MeVasanexampleoftheeventsincludedinthedeterminationoftheangulardistribution.Thesolid,blackboxrepresentsthegateusedtoexcludealleventsoutsidetheeregion.isshowninFigure4.10andtheincludedangularregionishighlightedbythedashed,blackbox.4.1.3.1NormalizationoftheAngularDistributionTheequationusedforthenormalizationisd˙(MWPC;E)dMWPC=YFFMWPC1YElasticsMWPC;Cald˙(MWPC;Ecal)MWPC1YElasticsMond˙(Mon;E)MonYElasticsMon;CalMond˙(Mon;ECal):(4.6)103Figure4.10:Unsymmetrizedmassangledistributionafterthegateontheeregionwasappliedtothedatasetfor50Cr+180WatElab=284.6MeVasanexampleoftheangularregionincludedinthedeterminationoftheangulardistribution.Thedashed,blackboxrepresentstheangularregionincludedintheangulardistributioncalculations.104whereYFFMWPCwastheyieldintheMWPCsduringthereactionofinterest,YElasticsMonistheyieldintheSimonitordetectorsduringthereactionofinterest,YElasticsMWPC;CalistheyieldintheMWPCsduringthecalibrationrun,andYElasticsMon;CalistheyieldintheSimonitordetectorsduringthecalibrationrun.ThreeRutherfordscatteringcrosssectionswerealsonecessary.(1)d˙(Mon;E)=disthededucedRutherfordscatteringcrosssectioninthemonitorsattheenergyoftherun.(2)d˙(lab;Ecal)=distheRutherfordscatteringcrosssectionattheenergyofthecalibrationrunataparticularangle(lab)intheMWPCs.(3)d˙(Mon;E;Cal)=disthededucedRutherfordcrosssectionattheinthemonitorsatthecalibrationenergy.Notethatallanglesareinthecenter-of-massframe.Toquicklydemonstratethateq.4.7isdimensionallycorrect,considerthegeneralcasewheretheyieldofagivenreactionproductinadetectorcanbecalculatedasY=IˆNxt˙whereIisthebeamintensity,ˆNistheparticledensityofthetarget,xistheectivetargetthickness,tisthetimeofthemeasurement,˙isthecrosssectionofthereactionchannelofinterest,andisthedetector.Therefore,˙canbedeterminedfortheexperimentalyieldasYIˆNx.Thetialcrosssectioncanthenbedeterminedasd˙(;d˘YIˆNx1whereisthesolidangleofagivendetector.Theyieldisde-terminedfromthemeasurementasdiscussedlaterandI;ˆN;x;t;andconstantsrelatedtothemeasurements.Whileallthesequantitiesshouldbeknowntheycanintroducelargeerrorintotheangulardistributionifnotknownwell.Theparametersinparticularthataretoknowinthepresentworkarethethicknessesandparticledensitiesofthetungstentargets.Thed˙(;d1Ytermsarereplacedwiththeirrespectivecomponents,1IˆNx1,asbelow105d˙(MWPC;E)dMWPC=YFFMWPC1ˆN(Cal)xCalIcaltCalMWPCMWPC1ˆNxIMonMonˆN(Cal)xCalICaltCalMonMon:(4.7)andcancelingtermsleavesd˙(MWPC;E)dMWPC=YFFMWPC1MWPCMWPCˆNxIt:(4.8)4.1.3.2QuantitiesneededinAngularDistributionDeterminationThissectiondescribeshowthevariousquantitiesrequiredforthedeterminationofthean-gulardistributionwerededuced.Thevaluesrelatingtothemonitorsremainedconsistentforagivensystem,sotheyaredescribedst.Theyieldinthemonitors,YElasticsMonorYElasticsMon;Cal,wasdeterminedfromthesumoftheintegratedcountsinthemonitorenergydistributions.Themonitorenergydistributionsfortheexamplesystemof50Cr+180WatElab=284.6MeVareshowninFigure4.11.ThenormalizationalsorequiredthattwoRutherfordscatteringcrosssectionsatthemonitorangles(22:5o)werecalculated,onecorrespondingtotheenergyofthereactionofinterestandonecorrespondingtotheenergyofthecalibrationrun.TheRutherfordcrosssectionswerecalculatedasd˙d=Z1Z2e24ˇ0Epc:m:21sin4(=2)(4.9)whereZireferstotheexitchannelfragments,eisthechargeofanelectron,0isthe106Figure4.11:Countsinthetwomonitordetectorsforthereactionof50Cr+180WatElab=284.6MeVshownasafunctionofchannelnumber.permittivityoffreespace,andistheangularlocationofthedetectorinthecenter-of-massframe.TheSimonitordetectorswerelocatedatlab=23forallmeasurements.ForelasticscatteringeventsinthemonitordetectorsEpc:m:isthecenter-of-massenergyoftheprojectile.Therestofthequantitiesneededineq.4.6weredeterminedforagivenfour-degreerangeofthecenter-of-massangle.Thedistributionofeeventsoverthecenter-of-massangles(c:m:)coveredbytheBackMWPCisshowninFigures4.12.ToaccountforthesintheMWPC,whichsitsinthelabframe,thecenter-of-massanglesoftheion-likefragmentsneededtobeconvertedtothelabframeangles(Jlab)sotheycouldbenormalizedtotheelasticscatteringeventsatthesameJlab.Thec:m:valuesdeducedforkefragmentsfor50Cr+180WatElab=284.6MeVasafunctionoftheircorrespondingJlabareshowninFigure4.13.ThespreadinJlabforeachc:m:resultsfromtherangeofmassratiosfortheefragments.TheintensityscaleinFigure4.13representsthenumberofeventswithagivencombinationofc:m:andJlab.Thec:m:versuslabdistributionwaswithafourthdegreepolynomial.Theresultofthat107Figure4.12:c:m:distributionsforthereactionof50Cr+180WatElab=284.6MeV.fortheexamplesystemof50Cr+180WatElab=284.6MeVisrepresentedbytheredlineinFigure4.13.Thenormalizationineq.4.6wascompletedonabinbybinbasisforthedistributioninFigure4.13.Foreachc:m:ofefragmentsthecorrespondingJlabwasdetermined.ThisvalueofJlabwasthenconvertedbackintoc:m:(Elas)forelasticscatteringbytheequationc:m:(Elas)=lab+180:0ˇasin ApAtsinlabˇ180:0!(4.10)whereAPisthemassoftheprojectile,ATisthemassofthetarget,Aiisthemassofanemittedfragment,andTKEisthetotalkineticenergycalculatedfromViolasystematics(seeeq.3.25).c:m:(Elas)wasthenusedinthedeterminationoftheRutherfordcrosssectiond˙(MWPC;Ecal)MWPCandtheyieldofelasticsatagivenangleintheBackMWPC(YElasticsMWPC;Cal).Thec:m:(Elas)distributionfortheelasticscatteringcalibrationmeasurementisshownin108Figure4.13:Distributionofc:m:foreachdeducedlabforthe50Cr+180WatElab=284.6MeV.Thesolid,redlinerepresentsafourthdegreepolynomialtothedistribution.Figure4.14.Nowthatallofthequantitieshavebeendeterminedforagivencombinationofc:m:andJlabapartialvalueofd˙(E)dMWPC(c:m:;lab)canbecalculated.ThisprocesswasrepeatedforeachpossibleJlabforagivenc:m:.Thenallofthed˙(E)dMWPC(c:m:;lab)weresummedtodeduced˙(MWPCE)dMWPCforgivenMWPCintheBackMWPC.RepeatingtheprocessforeachMWPCregionledtothedeterminationofthenalangulardistributionsshowninFigure4.15afterthevalueswerecorrectedfortherelativedetector4.1.3.3RelativeDetectorDuringtheprimaryCr+Wmeasurementsandthecalibrationrunapulsersignal(P;PCal)wasaddedintothedataacquisitionsystemfortheMWPCsatsignalamplitudesthatcorre-109Figure4.14:c:m:distributionsforthecalibrationmeasurementof50Cr+184WatElab=186.0MeV.spondtochannelnumberscombinationsinXandYoutsidetheactivedetectorarea.Scalervalueswererecordedforthepulser(Pscal;Pscal;Cal)andthetwoSimonitordetectors.ThescalersfromthetwoSimonitordetectorsweresummedtodetermineMscalandMscal;CalfromtheprimaryCr+Wmeasurementsandthecalibrationrun,respectively.Therelativeintrinsicpeak(Relpeak;int)oftheFrontMWPCwasdeterminedbetweenthereactionofinterestandthecalibrationrunof50Cr+184W!234CfatElab=186:0MeV.TherelativeintrinsicpeakwasdeterminedforCr+WmeasurementasRelpeak;int=PscalPMscal;CalMCalMscalMPscal;CalPCal(4.11)whereMandMCalarethesumofthenumberofcountsinthetwomonitorsrecordedinthedataacquisitionsystemfortheprimaryC+Wmeasurementsandthecalibrationrun,110Table4.5:Thenumberofcountsinthetwomonitors(M),thenumberofpulsereventsintheBackMWPC(P),andthescalersvaluesforthemonitors(Mscal)andpulser(Pscal)fromthemeasurementof50Cr+180Wasanexampleandthecalibrationmeasurementof50Cr+184W.50Cr+180W50Cr+184W(Cal)Pscal7.45103867.9210389P7.24103857.0810384Mscal1.541041.21021.631041.3102M1.521041.21021.561041.3102respectively.Forexample,thevaluesusedineq.4.11for50Cr+180Wandthecalibrationmeasurementof50Cr+184WareprovidedinTable4.5.DetectorvaluesforeachsystemareprovidedinTable4.6.Thesolid,redlineshownwiththeangulardistributionineachpanelofFigure4.15isasinefunctiontothedatatohighlightthegeneralshapeoftheangulardistribution.A˜2minimizationwasperformedtodeterminethenormalizationofthesinefunctionrelativetothedata.Thesharpincreaseintheangulardistributiondataatlargeanglesindicatesthepresenceof.4.2Cr+W:E=52.0MeVTheresultsofthemeasurementsoftheeightCr+WreactionsatECN=52.0MeVarepresentedinthissection.Reactionsatthesameexcitationenergyareparticularlyinterestingforsuperheavyelementproductionreactionsasdiscussedinpreviouschapters(see2.1.1).11150Cr+180W!230Cf=052Cr+180W!232Cf=254Cr+180W!234Cf=450Cr+186W!236Cf=6Figure4.15:Theangulardistribution(d˙(lab;E)=dforalleightCr+WsystemsmeasureinthepresentworkatEc:m:/VB=1.13shownasafunctionofc:m:isrepresentedbytheblackdatapoints.Thesolid,redlineisasinefunctiontotheexperimentaldatapointsusinga˜2minimization.112Figure4.15:(cont'd)52Cr+184W!236Cf=654Cr+182W!236Cf=654Cr+184W!238Cf=854Cr+186W!240Cf=10113Table4.6:RelativepeakintrinsicoftheBackMWPCandtheSimonitordetectorsforallsystemsmeasuredinthepresentworkrelativetothecalibrationrunof50Cr+184W!234CfatElab=186:0MeV.Ec:m:/VB=1.13ECN=52.0MeVReactionRelpeak;int(MWPC0)Relpeak;int(MWPC0)50Cr+180W!230Cf00.9310.0300.9540.02450Cr+186W!236Cf60.9310.0290.9750.02252Cr+180W!232Cf21.0130.0251.0280.02352Cr+184W!236Cf61.0240.0251.0470.02154Cr+180W!234Cf40.9680.0350.9580.03554Cr+182W!236Cf60.9800.0310.9810.03254Cr+184W!238Cf80.9840.0270.9990.02554Cr+186W!240Cf100.9640.0280.9770.0254.2.1Mass-AngleDistributionsSimilartothesystemsmeasuredatEc:m:/VB=1.13,theunsymmetrizedMADsforthesystemsmeasuredatECN=52.0MeVareshowninFigure4.16fortheBackMWPCandinFigure4.17fortheFrontMWPC.ThesymmetrizedMADsforalleightofthesystemsareshowninFigure4.18.AcorrelationbetweenmassandanglecanbeseenineachMAD,indi-catingthepresenceofAgain,themassdistributionswereusedinaquantitativedeterminationofthecontributionfrom4.2.2MassDistributionsThemassdistributionsfortheeightsystemsmeasuredatECN=52:0MeVareshowninFigure4.19.Aimportantfeaturetonoteinthissetofmassdistributionsistheshapeofthelikeregion.Threeofthesystems,50Cr+180W(Figure4.19panelA),50Cr+186W(Figure4.19panelD),and52Cr+184W(Figure4.19panelE)haveaminimumor11450Cr+180W!240Cf=052Cr+180W!232Cf=254Cr+180W!234Cf=450Cr+186W!236Cf=6Figure4.16:UnsymmetrizedMADsobservedintheBackMWPCforalleightsystemspresentedinthisworkatECN=52.0MeV.isthechangeinthenumberofneutronsinthecompoundnucleusrelativeto50Cr+180W,whereN=132.115Figure4.16:(cont'd)52Cr+184W!236Cf=654Cr+182W!236Cf=654Cr+184W!238Cf=Z54Cr+186W!240Cf=1011650Cr+180W!240Cf=052Cr+180W!232Cf=254Cr+180W!234Cf=450Cr+186W!236Cf=6Figure4.17:UnsymmetrizedMADsobservedintheFrontMWPCforalleightsystemspresentedinthisworkatECN=52.0MeV.117Figure4.17:(cont'd)52Cr+184W!236Cf=654Cr+182W!236Cf=654Cr+184W!238Cf=Z54Cr+186W!240Cf=1011850Cr+180W!230Cf=052Cr+180W!232Cf=254Cr+180W!234Cf=450Cr+186W!236Cf=6Figure4.18:SymmetrizedMADsfortheCr+WsystemsmeasuredinthisworkatECN=52.0MeV.119Figure4.18:(cont'd)52Cr+184W!236Cf=654Cr+182W!236Cf=654Cr+184W!238Cf=854Cr+186W!240Cf=1012050Cr+180W!230Cf=052Cr+180W!232Cf=254Cr+180W!234Cf=450Cr+186W!236Cf=6Figure4.19:MassdistributionsforCr+WsystemspresentedinthisworkatECN=52.0MeV.Thesolidgreenlinerepresentstheseconddegreepolynomialtothedata.areatmassratioof0.5ratherthanamaximum.ThisisverytfromthesystemsmeasuredatEc:m:=VB=1:13whereallofthesystemshadamaximumatMR=0:5.ThemassdistributionsobservedforthesesystemsappeartocrosstheboundarybetweenTypeIIandTypeIIIsystemsasdiscussedinSection1.3.3.1[40].Duetothisceintheshapesofthemassdistributions,aGaussianfunctiontothedatawasnotappropriateandatanalysistechniquewasnecessary.121Figure4.19:(cont'd)52Cr+184W!236Cf=654Cr+182W!236Cf=654Cr+184W!238Cf=854Cr+186W!240Cf=101224.2.2.1CurvatureAnalysisTechniquesRatherthanaGaussianfunction,eachmassdistributionwaswithaseconddegreepolynomialfunction.Theresultsofseconddegreepolynomialstothemassdistribu-tionsforthesystemsmeasuredatECN=52:0MeVareshownineachpanelofFigure4.19asthesolid,greenline.Thesecondderivativeofthefunctionresultingfromthewascalculatedastwotimesthecotofthesecond-ordercottocomparetherelativeshapesofthemassdistributionsandisreferredtoasthecurvatureparameter.ThecurvatureparameterwasthenusedasameanstoquantitativelycomparemassdistributionsgeneratedforthesystemsatECN=52:0MeVinasimilarmannertothewidthsfromtheGaussianfunctionusedforthemassdistributionsforthesystemsmeasuredatEc:m:=VB=1:13.Alargercurvatureisequivalenttoasmallermasswidthandindicatesadecreaseintheamountofinthereaction.ThevaluesofthecurvatureparameterdeterminedforthesystemsmeasuredinthepresentworkarelistedinTable4.7.Theuncertaintyassociatedwiththesecond-ordertermofthesecond-degreepolynomialtothedatawasdeter-minedinachi-squaredminimizationandisreportedinTable4.7.ThistechniquewasabletothesystemsthatwerenearlyorhadaminimumatMR=0.5.ApositivecurvatureparametersisdeterminedforthesystemswithaminimumatMR=0.5.Systemsthathavenearlyatmassdistributionswillhavecurvatureparametersneartozero.ThesesystemsfallintotheTypeIcategoryidenbyDuRietzetal.[40]asdescribedinSection1.3.3.1.Shorttimescaleqdominatesinreactionswithpositivecurvatureparameters.4.2.2.2VwithEc:m:=VB=1:13systemsThevalidityofthecurvatureanalysistechniquewastestedagainstthemasswidthtechniquewiththesystemsthatweremeasuredatEc:m:/VB=1.13.Theeightsystemsmeasuredat123Table4.7:Curvatureparametersanderrorsdeterminedforall8systemsmeasuredatcenter-of-massenergiesresultingincompoundnucleiwithECN=52:0MeV.SystemCurvatureParameter(arb.units)error50Cr+180W5.5x1031.9x10350Cr+186W1.1x1031.7x10352Cr+180W-1.50x1042.3x10352Cr+184W-1.15x1042.3x10354Cr+180W-1.73x1041.9x10354Cr+182W-1.99x1041.7x10354Cr+184W-3.57x1042.0x10354Cr+186W-4.34x1041.9x103Ec:m:/VB=1.13wereeachwithaseconddegreepolynomialandthecurvatureparameterwasdetermined.TheresultofthatcomparisonispresentedinFigure4.20.Thestrong,linearcorrelationbetweentheupperlimitsofPCNandthecurvatureparametersindicatesthatoverallthetwomethodsarequalitativelyconsistent.Forexample,50Cr+180WhasthelowestupperlimitofPCN(0.180.3)andthelargestcurvatureparameter(-4.81031.6103)amongthesystems,while50Cr+180WhasathelargestupperlimitofPCN(0.5210.007)andthesmallestcurvatureparameter(-5.791042.0103)amongthesystems.4.2.3AngularDistributionsTheangulardistributionsfortheeightCr+WsystemsmeasuredatECN=52.0MeVareshowninFigure4.21.TheangulardistributionswereobtainedusingthemethoddescribedaboveinSection4.1.3.SimilartotheangulardistributionsforthesystemswithEc:m:/VB=1.13,eachiscomparedtoasinefunctiontothedata,representedbytheredline.Thesharpincreaseintheangulardistributionwithincreasingangleindicatesthepresence124Figure4.20:ComparisonoftheresultsfromthetwomethodsfordeterminingtherelativeshapesexperimentalmassdistributionsappliedtotheCr+WdataatEc:m:/VB=1.13.ofinalloftheCr+WsystemsmeasuredatECN=52:0MeV.12550Cr+180W!230Cf=052Cr+180W!232Cf=254Cr+180W!234Cf=450Cr+186W!236Cf=6Figure4.21:Theangulardistribution(d˙(lab;E)=dforCr+WsystemsmeasuredinthepresentworkatECN=52:0MeVshownasafunctionofc:m:isrepresentedbytheblackdatapoints.Thesolid,redlineisasinefunctiontotheexperimentaldatapointsusinga˜2minimization.126Figure4.21:(cont'd)52Cr+184W!236Cf=654Cr+182W!236Cf=654Cr+184W!238Cf=854Cr+186W!240Cf=10127Chapter5DiscussionTheprimarygoalofthisworkwastoexploretheofvaryingtheneutron-richnessofthereactionsystemonthereactiondynamicsinaseriesofCr+Wreactions.Inparticular,theofvaryingtheneutron-richnessonthecompetitionbetweentheandreactionchannelswasexamined.ThischapterpresentstheinterpretationsoftheresultsinChapter4inthecontextofthisgoal.First,thesubsetofthesystemsformingthesamecompoundnucleusarecomparedwiththepredictionsoftheBohrindependencehypothesistodemonstratethepresenceofnonequilibriumprocesseslikeinthesystemsmeasuredinthepresentwork.Then,theimpactofincreasingneutron-richnessontheisdiscussedforboththesystemsmeasuredatEc:m:=VB=1:13andECN=52:0MeV.Ineachcasetheunderlyingreactiondynamicsarediscussed.Finally,thesystemsmeasuredinthepresentworkareconsideredinabroadercontextthroughcomparisonwithsystemspreviouslymeasuredatANUformingthesamecompoundnuclei.5.1BohrIndependenceHypothesisBohrpostulatedthatthedecaymodeofacompoundnucleusshouldbeindependentofitsmodeofformation[113],whichistermedtheBohrindependencehypothesis.Iftheresultingcompoundnucleusreachesfullequilibrationofalldegreesoffreedom,thentheBohrindepen-dencehypothesisshouldholdtrue.Inthecaseofthepresentwork,itisexpectedthatifthe128systemsweretofusethentheBohrindependencehypothesiswouldholdtrue.Assionisanon-equilibriumprocess,reactionswithtcrosssectioninthisexitchannelwoulddeviatefromtheBohrindependencehypothesis.Inthepresentwork,asubsetofsixCr+Wmeasurementsformthesamecompoundnucleusthroughthreetentrancechannels.Threerentprojectileandtargetcombinations(50Cr+186W,52Cr+184W,and54Cr+182W)formthesamecompoundnucleus236Cf.EachofthesesystemswasmeasuredatEc:m:=VB=1.13andE=52.0MeVtogivesixentrancechannelcombinationsallform-ingthesamecompoundnucleus.IfthesystemsmeasuredinthepresentworkunderwentequilibrationthentheupperlimitsofPCNfromthethreesystemsforming236Cfateachenergyshouldbeconsistent.Themassdistributionsforallsixsystemsforming236CfasthecompoundnucleuswereshowninPanelsD,E,andFofFigures4.7and4.19.Themeasureoftherelativeamountofssioninthesystemswasdeterminedwiththetechniquesdescribedpreviously.TheupperlimitsofPCNdeterminedfortheCr+Wsystemsforming236CfareshowninFigure5.1asafunctionofthemassoftheprojectileatEc:m:=VB=1.13andthecurvatureparameterdeterminedfortheCr+Wsystemsforming236CfisshowninFigure5.2asafunctionofthemassoftheprojectileECN=52.0MeV.TheupperlimitsofPCNdeterminedforthesystemsforming236Cfrangefrom0.41to0.52.Soapproximatelyhalfoftheeventsarelosttothereactionchannelanddonotformafullyequilibratedcompoundnucleus.Thecurvatureparametersdeterminedforthesystemsforming236Cfvarytly.Thus,themassdistributionsfromthesethreereactionshavetlytshapes.The-likeregionofthemassdistributiongeneratedfor52Cr+184Whasaminimumatmassratiosof0.5,whiletheeregionofthemassdistributionmeasuredfor50Cr+186Wisessentiallyandthemassdistribution129measuredfor54Cr+182Whasamaximumatamassratioof0.5.TheBohrindependencehypothesispredictsthatthesesystemsshouldhavesimilarmassdistributions.Therearetwopotentialreasonsforthisdiscrepancy.Ononehand,theindependencehypothesismaynothold.Ontheotherhand,compoundnucleusformationmaynotbetheonlyprominentreactionchannel.IfthesystemdoesnotundergocompoundnucleusformationthentheBohrIndependenceHypothesiswouldnotapplyandthevariationinthecurvatureparametercouldbeattributedtothereactionchannel.5.2Cr+W:Ec:m:/VB=1.13InthissectiontheresultsfromthesystemsmeasuredatEc:m:/VB=1.13arediscussed.TheupperlimitofPCNisshowninFigure5.3asafunctionof(N/Z)CNdeterminedasdescribedinSection4.1.2foreachofthesystemsmeasuredatEc:m:/VB=1.13.NoticethattheupperlimitofPCNincreaseswith(N/Z)CN.Thistrendindicatesthatinthemoreneutron-richsystemslessislosttocomparedtothelossinthetsystems.ForCr+Watenergies13%abovetheinteractionbarrier[9],usingmoreneutron-richprojectilesandtargetsisseentoincreasetheamountoffusion-Thisresultispromisingforfuturesuperheavynucleiproductionmeasurementswiththemostneutron-rich,radioactivebeams.Tounderstandthereactiondynamicsthatmaybebehindthisrelationshipbetweenandthechangeinneutron-richness,theoftheyandmassasymmetryofthesystemareexploredinthenextsection.130Figure5.1:UpperlimitofPCNdeterminedfortheCr+Wsystemsforming236Cfmeasuredinthepresentworkasafunctionofthemassoftheprojectile.ThesesystemsweremeasuredatEc:m:=VB=1.13.Thecolorsoftheupperlimitmarkerscorrespondtotheprojectileusedinthereaction.Figure5.2:CurvatureparameterdeterminedfortheCr+Wsystemsforming236Cfmeasuredinthepresentworkasafunctionofthemassoftheprojectile.ThesesystemsweremeasuredatECN=52.0MeV.Thecolorsoftheupperlimitmarkerscorrespondtotheprojectileusedinthereaction.131Figure5.3:UpperlimitofPCNforeachsystemmeasuredatEc:m:=VB=1:13isshownasafunctionof(N/Z)CN.Thecoloroftheupperlimitmarkerscorrespondtotheprojectileusedinthereaction.5.2.1FissilityandMassAsymmetryBoththecompoundnucleary(˜CN)andthemassasymmetry()arepropertiesofaheavy-ionreactionsystemthathavebeenshowntobedominantencesontheoccurrenceofinheavy-ionreactions[7,74,72].FissilityisascalingparameterthatprovidesameasureoftheratiooftheCoulombandnuclearforcesinadinuclearsystem[38,40,56,71]throughtheratiooftheCoulombandsurfacetermsintheliquiddropmodel.SeethediscussioninSection1.2.2.1.Therearemanyrelatedversionsoftheyparameterintheliterature.Theilityparameterusedhereisthecompoundnucleary,whichhasoftenbeenconnectedwith132achangeinthereactiondynamics.Itiscalculatedas˜CN=(Z2=A)(Z2=A)crit(5.1)where(Z2=A)crit=50:883(11:7826I2)andI=(A2Z)=A[71,30].Themassasymmetryoftheentrancechannelisanothervariableoftenusedintheoreticaldescriptionsofheavy-ionreactionstodeterminethestrengthofthequexitchannel.Themassasymmetryofadinuclearsystemisadimensionlesscomparisonofthesizeoftheprojectiletothatofthetargetandisas=AtargetAprojectileAtarget+Aprojectile:(5.2)Notethatwhentheneutron-richnessofthereactionsystemisincreasedintheCr+Wsystemsboththeyandthemassasymmetrydecrease.Forexample,50Cr+180W!230Cfisthemosttsysteminthisworkandhas˜CNandvaluesof0.854and0.565,respectively.Themostneutron-richsystem54Cr+186W!240Cfhassmaller˜CNof0.837andof0.550.The˜CNandvaluesforthereactionspresentedinthisworkedarelistedinTable5.1.ThemassasymmetryisshowninFigure5.4asafunctionoftheyofthesystemsmeasuredinthepresentwork.Theyandmassasymmetrypredicttoutcomesinthepresentwork,wheretheneutron-richnessisvariedforreactionsbetweenaconstantpairofelements.Ithasbeenpreviouslyshownthatasmassasymmetryincreases,decreases[7],whileotherworkshaveconcludedthatanincreaseinyleadstoanincreasein[80,81,54,46,8].Thisleadstocontradictorypredictionsfortheofincreasingtheneutron-richnessonquIfthemassasymmetryisthevariablewiththemostonthereactionchannel,then133Figure5.4:Themassasymmetryofthesystemsmeasuredinthepresentworkshownasafunctionofthesystemsy.Thecolorsofthemarkerscorrespondtotheprojectileusedinthereaction.theprominenceofthequasssionreactionchannelshouldincreaseinthereactionof54Cr+186W!240Cf(themostneutron-richsystem)relativetotheprominenceofthereactionchannelinthereactionof50Cr+180W!230Cf(themostentsystem).Alternatively,ifcompoundnuclearssilityisthevariablewiththedominanteonthereactionchannel,thenthecontributionshoulddecreaseinthereactionof54Cr+186W!240Cfrelativetothetsystems.Itisnecessarytodisentanglethesetwoconceptsanddeterminewhichdominatestofullyunderstandhowevolveswithincreasingneutron-richness.TheupperlimitofPCNdeterminedforeachofthesystemsinthepresentworkatEc:m:=VB=1.13areshowninFigure5.5asafunctionofthecompoundnucleusy.Similarly,theupperlimitofPCNdeterminedforeachofthesystemsinthepresentworkareshowninFigure5.6atEc:m:=VB=1.13asafunctionoftheentrancechannelmassasym-134Table5.1:Compoundnucleary(˜CN)andmassasymmetry()valuesofeachoftheeightCr+Wsystemspresentedinthiswork.ThedeterminedupperlimitsofPCN,capturecrosssection,andevaporationresiduecrosssectionsarealsoincluded.System˜CN50Cr+180W!230Cf00.8540.56550Cr+186W!236Cf60.8430.57652Cr+180W!232Cf20.8500.55252Cr+184W!236Cf60.8430.55954Cr+180W!234Cf40.8460.53854Cr+182W!236Cf60.8430.54254Cr+184W!238Cf80.8400.54654Cr+186W!240Cf100.8370.550metry.AroughlylinearrelationshipcanbeobservedbetweentheyofthecompoundnucleusandtheupperlimitofPCNdeterminedforeachofthesystemsmeasuredatEc:m:=VB=1.13whilenocleartrendcanbeobservedwiththedeterminedupperlimitsofPCNandthemassasymmetriesofthesystems.Thus,itcanbesuggestedthatyisthedom-inantvariableintheseheavy-ionreactionsastheneutron-richnessincreasesinareactionwithagivenelementalpair.5.2.2MassWidthsComparedtoTheoreticalCalculationsRecentwork[87,114,115,116]hasshownthattimedependentHartree-Fock(TDHF)cal-culationscanprovideinsightintothereactiondynamicsofheavy-ionfusionreactions,inparticularwithregardtothecompetitionbetweenandThissec-tionpresentsacomparisonbetweenthereactionsmeasuredinthepresentworkatEc:m:/VB=1.13andrecentTDHFcalculationsperformedbyVolkerOberackerandSaitUmaratVan-derbiltUniversity[117].TDHFisbasedonameaformalismandusesamicroscopic135Figure5.5:DeducedupperlimitsforPCNshownasafunctionofthecompoundnuclearyforthesystemsmeasuredatEc:m:/VB=1.13.Thecolorsoftheupperlimitmarkerscorrespondtotheprojectileusedinthereaction.Figure5.6:DeducedupperlimitsforPCNshownasafunctionofthemassasymmetryforthesystemsmeasuredatEc:m:/VB=1.13.Thecolorsoftheupperlimitmarkerscorrespondtotheprojectileusedinthereaction.136approachtodescribetheevolutionofamany-bodysystemasafunctionoftime[117].TDHFcalculationswerecompletedforvariousimpactparametersforthemostneutron-t(50Cr+180W!240Cf)andthemostneutron-rich(54Cr+186W!240Cf)systemsinthepresentwork[10].ThecalculatedmassratioMRandthechargeratioZRareshowninPanelAinFigure5.7andthecontacttimeinPanelBasafunctionofimpactparameter.AnexampleoftheevolutionofthedensitydistributionofasystemovertimeisshownintheupperrightcornerofeachpanelinFigure5.7.Theevolutionofthedensitydistributionsatanimpactparameterof3fmwhereseparationoccursisshowninPanelAinFigure5.7.Anexamplecaseatanimpactparameterof0fmwherethesystemwasconsideredtoeventuallyfuseisshowninPanelBinFigure5.7.FortheTDHFcalculationspresentedhere,fusionwasconsideredtooccurifthesystemdidnotseparateduringthe35zsaftercontact,basedonpreviouscalculations.Theresultsofthecalculationsshowthebothsystemsfuseatthesmallestimpactparameters(i.e.belowb˘2fm).Thislimitisindicatedbytheboxeslabel\Fusion".Therewasnomassratio,chargeratio,orcontacttimeinthecalculationsassociatedwiththefusingsystemssotheboxesareplacedatthemassratio,chargeratio,orcontacttimecorrespondingtotheimpactparameteratwhichfusionoccurred.Thischoiceisforvisualclarityonly.Thebetweenthetwosystemsbecomeapparentatimpactparameters2.5andgreater,wheretheseparationofthedinuclearsystemoccurs.Themoreneutron-richsystemhaslargermassandchargeratiosandlongercontacttimesrelativetotheneutrotsystem.ThelongerthedinuclearsystemremainsincontactthelargertheprobabilityitwillnotundergoTheresultsfromtheTDHFcalculationsagreewiththeexperimentalresultsfromtheupperlimitsofPCNwherebyincreasingtheneutron-richnessofsystemincreasesthelikelihoodthatthesystemwillfuse.NotethatTDHFprovidesanaverageresultateachimpactparameter.Atimpactparameters137whereeitherfusionormaydominate,theotherprocessmaystillbepresentbecauseTDHFonlyprovidesthemostlikelyexitchannel.5.2.3ComparisonwithAnalyticalCalculationsofPCNTherehasbeenmuchworkattemptingtocalculatethevalueofPCNempirically.However,thepredictionsvarybyordersofmagnitudeasdiscussedinSection1.2.3.Threeofthecommonly-usedapproachesintheliteraturetocalculatePCNarecomparedwiththeupperlimitsforPCNdeterminedfortheCr+Wreactionsmeasuredinthepresentwork.Thethreeanalyticalcalculationsaredescribedinthefollowingsections.TherearetheoreticalapproachesbeyondanalyticalcalculationswheredynamicalmodelsusepotentialenergysurfacestodetermineofPCN,however,thesemodelsrequireparametersandwerenotexploredinthepresentwork[6,118].5.2.3.1Armbruster'sAnalyticalDescriptionofPCNTheresultsoftheanalyticalcalculationsforPCNandtheupperlimitsofPCNdeterminedinthepresentworkareshowninFigure5.8.TheempiricalpredictionwasbasedonaformdevelopedbyArmbruster,etal.[119]andto63hot-andcold-fusiondatasetsofheavynuclei[29].Inthisapproach,PCNiscalculatedasPCN=12expc(˜analytical˜thr)(5.3)where˜thristhethresholdy.Avalueof˜thr=0:72wasdeterminedin[119]andusedinthepresentwork.Thescalingparametercwassetto-106andwascalculatedfromatoexperimentaldatafortheprobabilityoffusionattheBassbarrier(P(VB))138Figure5.7:TDHFcalculationsformassratioMR,chargeratioZR(a)andcontacttime(b)for50Cr+180W!240Cfand54Cr+186W!240Cfshownasafunctionofimpactparameterb[10].Theinsertinpanel(a)showsanexampleofadensityplotwherethedinuclearsystemseparates.Theinsertinpanelbshowsanexampleofadensityplotwherethesystemfuses,seethetext.Reprintedwithpermissionfrom[10]Copyright(2015)bytheAmericanPhysicalSociety.http://dx.doi.org/10.1103/PhysRevC.91.041602139asafunctionoftheaverageey.Armbrusteretal.[119]thedatawiththefunctionc=lnPCN=˜.Additionalparametersetshavebeenproposedmorerecentlyintheliterature[29].Theeyusedhereisavariationoftheyusedearlierineq.5.1andiswrittenas˜analytical="(Z2=A)(Z2=A)crit#(1+f(k))(5.4)where(Z2=A)critiscalculatedasineq.5.1,is1/3andf(k)isasf(k)=4k2+k+1k+1k2(5.5)wherek=(A1=A2)1=3isaparameterthatcharacterizestheentrancechannelasymmetryandA1andA2aretheprojectileandtargetmassnumbers,respectively[119].TheresultsofthiscalculationofPCNfortheCr+Wsystemsmeasuredinthepresentworkarerepresentedbytheshort-dashed,greenlinesegmentsinFigure5.8.5.2.3.2Zagrebaev'sAnalyticalDescriptionofPCNZagrebaevetal.[36]proposedthatPCNcouldbeanalyticallydescribedbythefunction:PCN(E)=P0CN1+expEBEint;(5.6)whereP0CNisthefusionprobabilityabovetheBassbarrier,EBistheexcitationenergyofacompoundnucleusresultingfromareactionatacenter-of-massbeamenergyequivalenttotheBassbarrierenergy[34],andisequaltothewidthofthebarrierdistribution.This140widthwastakeninthepresentworktobe4.0MeVasin[36].P0CNwascalculatedasP0CN=1(1+exp(Z1Z2˘)˝=0:272(5.7)where˘=45and˝=1760weretakenfromatoexperimentaldata[36]andZ1andZ2arethechargeofthechromiumandtungsten.ThevaluesofPCNdeterminedfortheCr+WsystemsinthepresentworkusingZagrabaev'scalculationarerepresentedinFigure5.8bythedot-dashed,redline.5.2.3.3Siwek-Wilczynskana'sAnalyticalDescriptionofPCNInthethirdanalyticalapproachconsideredhere[120]asetof28reactionswereconsid-eredwheretheevaporation-residuecrosssectiondatawerepreviouslymeasured.PCNwasdeducedfromitsdependenceonaCoulombinteractionparameterandtheexcessen-ergyabovetheinteractionbarrier.TheCoulombinteractionparameter,z,isasz=Z1Z2=(A1=31+A1=32).Siwek-Wilczynskana,etal.[120]proposedthefollowingfunctionofzasthebesttothedata:PCN=exp(za)k(5.8)wherek=3.0,andaisdependentontheexcessenergyabovetheirbarrier(Ec:m:-VB).WhenEc:m:-VB=0MeV,eq.5.8bestthedatawithaˇ135[120].ForEc:m:-B0=10MeVthebestwasfoundwithaˇ155[120].ForthesystemsmeasuredinthepresentworkEc:m:-VBwasonaverage25MeV.ThevaluesofPCNweredeterminedfortheCr+Wsystemsinthepresentworkusingbotha=135(indicatedbythedot-long-dashed,lightbluelinesegments)anda=155(indicatedbythelong-dashed,bluelinesegments).141Assumingalinearincreaseina,atEc:m:-VB=25MeVashouldequalto185(indicatedbythedot-dashed,pinklinesegments).Tothedatainthepresentworkaneedstobeapproximately250.ThesePCNvaluesareincludedinFigure5.8fortavalues.5.2.3.4ComparisonofResultsofAnalyticalCalculationsThevaluesofPCNcalculatedfromthethreeanalyticalequationsareshowninFigure5.8asafunctionof(N/Z)CN.TheupperlimitsofPCNfromthepresentworkarealsoshownforcomparison.ThevaluesofPCNdeducedinthepresentworkareupperlimitssotheymaynotmatchtheabsolutevaluesofPCNcalculatedfromtheanalyticalequations.AsshowninFigure5.8,thecalculatedanddeducedvaluesofPCNvarybyordersofmagnitude.Despitethelackofquantitativeagreement,however,qualitativeinsightcanbegainedbycomparingthegeneraltrendscalculatedfromtheanalyticalequationstothetrendofdeducedPCNforthesystemsinthepresentwork.Infact,alloftheanalyticalcalculationsresultinanincreaseinPCNwithneutron-richness.5.3Cr+W:E=52.0MeVTheresultsfromthesubsetofsystemsmeasuredinthepresentworkatthesamecompoundnuclearexcitationenergyprovideinterestinginsightthatisrelevantforsuperheavyproduc-tionreactions.AsdiscussedinSection2.1.1,excitationenergyisanimportantvariableinsuperheavyproductionreactionsbecausetheexcitationenergyessentiallydeterminesthespevaporationresiduesthatcanbeproduced.TheinterpretationoftheresultsfromtheCr+WreactionsmeasuredatE=52.0MeVarepresentedinSection5.3isdiscussedinthissection.142Figure5.8:PCNcalculatedfromthreeanalyticalfunctions[119,29,120]shownasafunctionof(N/Z)CN.Theupperlimitsdeducedforthesystemsinthepresentworkareincludedasthehorizontallines.143InSection5.3theshapeofthemassdistributionswereshowntobepoorlydescribedbyaGaussianfunction.Inordertoprovideameasureoftherelativeamountofbetweenthesystemsmeasuredinthepresentworkthecurvatureanalysistechnique(dis-cussedinSection4.2.2.2)wasused.ThecurvatureparametersdeterminedforthesystemsmeasuredinthepresentworkatE=52.0MeVareshowninFigure5.9asafunctionofthe(N/Z)CN.RecallthatadecreaseinthecurvatureparameteriscomparabletoadecreaseinPCNandindicatesarelativeincreaseintheprominenceofthequasssionreactionchannel.AnegativecurvatureparameterindicatesthattherewasamaximumatMR=0.5inmassdistribution,whileapositivecurvatureparameterindicatesthattherewasaminimumatMR=0.5inthemassdistribution.Forsystemswithnearlymassdistributions,thecurvatureparameterswillbenearzero.Thetwosystemswhere50Crwastheprojectilehaveapositivecurvatureparameter.Themassdistributionsfromthetwo50CrsystemsaresimilarinshapetothoselabeledbyDuRietzetal.[40]asTypeIsystems(SeeSection1.3.3.1).InTypeIsystemsshorttimescaledominates.ForthesystemsmeasuredinthepresentworkatE=52.0MeVthereisnostrongglobaltrendwith(N/Z)CNsimilartothatobservedforthesystemsmeasuredatEc:m:/VB=1.13.Thereareclearlyotherfactorsinvolvedinthereactiondynamicswhentheexcitationenergyisheldconstantat52.0MeV.Possibleexplanationsforthisareconsideredinthefollowingsection.5.3.1AngularMomentumAsdiscussedinSection1.2.1.1,theangularmomentumofthesystemplaysanimportantroleinthereactiondynamics.InFigure5.10thecurvatureparametersdeducedforCr+W144Figure5.9:CurvatureparameterinarbitraryunitsdeducedfromthemassdistributionforeachsystemmeasuredatECN=52:0MeVasafunction(N/Z)CN.systemsareshownasafunctionoflmax.InFigure5.11thecurvatureparametersdeducedforCr+Wsystemsareshownasafunctionoflcrit.Thereisnosimplecorrelationbetweenthecurvatureparametersandeitherlmaxorlcrit.Generally,thesystemswiththelowestlmaxorlcrithavethehighestcurvatureparameters,thusthestrongestreactionchannel.5.3.2RotationalEnergyInthesetofsystemsmeasuredatEc:m:/VB=1.13theentrancechannelenergyinthecenter-of-massvariedacrossthesystemsbyonly5MeV.However,inthesystemsmeasuredatE=52.0MeVthecenter-of-massenergyvariedby14MeV.Asaresulttheenergyavailableforrotationofthecompoundnucleusvariedsignitlyamongthesystemsmeasuredat145Figure5.10:CurvatureparameterdeducedfortheCr+WsystemsatECN=52:0MeVinthepresentworkasafunctionofthelmax.Thecolorsofthedatapointsindicatetheprojectileusedinthereaction.Figure5.11:CurvatureparameterdeducedfortheCr+WsystemsatECN=52:0MeVinthepresentworkasafunctionofthelcrit.Thecolorsofthedatapointsindicatetheprojectileusedinthereaction.146ECN=52:0MeV.ThemaximumenergyavailableforrotationErotcanbeestimatedasErot=Ec:m:VB(5.9)whereEc:m:istheentrancechannelcenter-of-massenergyandVBistheaverageBassbar-rier[9,35].ForthesystemsmeasuredatEc:m:/VB=1.13,Erotvariesbylessthan1MeV.Bycontrast,forthesystemsmeasuredatECN=52:0MeV,Erotvariesfrom5to22MeV.ThecurvatureparameterdeterminedforeachofthesystemsinthepresentworkareshowninFigure5.12asafunctionofErot.Althoughthereisnosimplepattern,itisshowninFigure5.12thatthesystemswiththelowestavailablerotationalenergyhavethelargestpositivecurvatureparametersandtheleastlikedistributions.Thisindicatesthattheenergyavailableforrotationandthusrotationofthedinuclearcomplexhasanonthelikelihoodthatthesystemwithseparateviathereactionchan-nel.Notethatthelowestcurvatureparameterswerededucedforthetwomostneutron-richsystems(54Cr+184;186W)despitethefactthatthesetwosystemsdonothavethelargestlmax,lcrit,orErot.5.3.3ofNuclearOrientationsThephysicalshapeofthenucleiinvolvedinaheavy-ionfusionreaction,particularlyalargedeformationoftheheavyreactionpartner,hasbeenshowntohaveatonthereactiondynamicsespeciallyatEc:m:nearorbelowtheinteractionbarrier[60,41,59,64,65,39,63,62].Manypreviousworkshaveshownthattheevaporationresiduecrosssectionishinderedatenergiesnearthebarrier[63,62],whenadeformedheavynucleustakespartinthereaction.Similarly,hindranceoftherelatedreactionchannelhasalso147Figure5.12:CurvatureparameterdeterminedfortheCr+WsystemsatECN=52:0MeVmeasuredinthepresentworkasafunctionofthemaximumavailablerotationalenergydeterminedasineq.5.9inMeV.Thecolorsofthedatapointsindicatetheprojectileusedinthereaction.beenattributedtothepresenceofadeformedheavynucleusintheentrancechannelatcenter-of-massenergiesnearthebarrier[60,41,59,64,65,39].Thislossinandevaporationresidueproductionthenincreasesthestrengthofthereactionchannel[60,41].Collisionsbetweenasphericalprojectileandaprolatedeformednucleusoccurwithacontinuousdistributionbetweentwoextremeorientations(ifthesystemisnotabletoreorientitself).Forsimplicity,thepresentdiscussionwillconsidercollisionsatimpactparameterzero.Inreality,therearemanypossibilitiesofimpactparameterforeachorientation.TwocartoonexamplesoftheextremeorientationsthatwillconsideredinthisdiscussionareshowninFigure5.13.Thecaseinwhichthenuclearsymmetryaxes(indicatedbythedashedlines)arealignedisillustratedinPanelAofFigure5.13.Inthisorientation,theprojectilecollides148Figure5.13:Thetwolimitingcaseofcollisionwithadeformedtargetnucleus.PanelAshowsacollisionwherethenuclearsymmetryaxesarealigned.PanelBshowsthecasewheretheaxesareanti-aligned.withthe\tip"oftheprolatenucleus,forminganelongateddinuclearsystem.Intheotherextreme,theprojectilecollideswiththeelongatedsideofthedeformedtargetsuchthatthenuclearsymmetryaxesareperpendicularoranti-alignedasillustratedinPanelBofFigure5.13.NotethattheCoulombenergyishigherforthelatter(PanelB)collision.5.3.3.1ShapeEvolutionandMassAsymmetryInpreviousworkswherehindranceoftheorevaporationresiduesreactionchannelswasobservedinreactionswithdeformednuclei,thehinderancewasattributedtothebroadeningoftheinteractionbarrierduetothevariouspossiblenuclearorientations[121,39].CollisionslikethoseillustratedinPanelAofFigure5.13withanelongateddinuclearsystem,wereshowntopreferentiallyleadto[121,39].CollisionslikethoseillustratedinPanelBofFigure5.13,whereamorecompactdinuclearsystemisformed,wereshownto149preferentiallyleadto[121,39].Thetungstenisotopesconsideredinthepresentworkareallprolatedeformed,whilethechromiumisotopesareallapproximatelyspherical.The2deformationparametervaluesforallnucleidiscussedinthepresentworkarelistedinTable5.2[?].Toexploretheofthedeformationofthetungstenisotopesonthereactiondynamicsofthesystemsmeasuredinthepresentwork,theinteractionbarriersmustbecalculatedasafunctionoforientation.First,theprincipalradiiofthedeformedtungstennucleiweredetermined.AnaxiallydeformednucleuscanbeapproximatedasanellipsoidofrevolutionwherethevariousradiicanbecalculatedfromR(;˚)=Ravg[1+Y20(;˚)](5.10)whereRavgistheaverageradiusofthetwomajoraxes,isthedeformationparameteralongthesemi-majoraxisofinterest,andY20isasphericalharmonicfunction(YLM)whereLis2andMis0[67].Inaprolatedeformednucleus,therearetwoaxesofinterest:(1)theelongatedsemi-majoraxis,alongthenuclearsymmetryaxisindicatedbythedashed,blacklineintheexampleprolatedeformednucleusinFigure5.13,(2)theshortenedsemi-minoraxisindicatedbythesolid,blacklineintheexampleprolatedeformednucleusinFigure5.13.Thelimitingcaseofthesemi-majorandsemi-minoraxescanbecalculatedas:150Y20(;˚)=14r5ˇ(3cos21)(5.11)Y20(0o;˚)=14r5ˇ(3cos2(0)1)=r54ˇ(5.12)Y20(90o;˚)=14r5ˇ(3cos2(90)1)=14r5ˇ(5.13)RsemiMajor(;˚)=Ravg[1+14r5ˇ](5.14)RsemiMinor(;˚)=Ravg[1+r54ˇ](5.15)(5.16)TheradiususedinthepresentworkwastakentobetheBlockihalf-densityradius[9]asRavg=1:16A1=31:39A1=3.Foreachnucleusconsideredinthepresentworktheaverage,semi-major,andsemi-minorradiiarelistedinTable5.2.BecauseofthestrongdeformationoftheWnuclei,thesemi-majorandsemi-minoraxeschangebymorethan1fmrelativetotheaverageradius,orbyabout10%ofthetotal.Thishasalargeontheinteractionbarrierassociatedwitheachlimitingcase.TheBassbarriers[9]weredeterminedwiththesemi-majorandsemi-minorradiitoexaminetheofthischangeintheradiiandarelistedinTable5.3.TheinteractionradiuswasdeterminedasRint(orientation)=RCr(orientation)+RW(orientation).Theorientationofthedeformedtargetreducedthebarrierby8%onaverageforthealignedcollisionsandincreasesthebarrierby5%fortheanti-alignedcollisions.InFigure5.14,thecurvatureparametersdeterminedforthesystemsmeasuredinthepresentworkareshownasafunctionofthealignedbarrierinPanelA,theaveragebarrierinPanelB,andtheanti-alignedbarrierinPanelC.Theenhancedcurvatureparametersofthetwo50Crsystemsandthe52Crcanbeunder-151Table5.2:Averageradii,2values[86],semi-majorradii,andsemi-minorradiideterminedforchromiumandtungstenisotopesconsideredinthepresentwork.NucleusRiB(average)(fm)2[86]RiB(aligned)(fm)RiB(anti-aligned)(fm)50Cr3.890.0{{52Cr3.960.0{{54Cr4.020.0{{180W6.300.2587.335.79182W6.330.2597.365.81184W6.350.247.325.87186W6.380.237.305.92stoodinthecontextoftheextremebarriers.Fortheanti-alignedcollisionsthe50Cr+180Wand50Cr+186WhaveEc:m:=VB=0:98and1.01,respectively.Thus,theanti-alignedration,whichpreferentiallyleadstowassuppressedforthesesystemsbecausetheentrancechannelenergywasbeloworbarelyabovetheinteractionbarrier.Thehin-drancetofusionofreactionsatthisorientationcausestheuxtobehighforthesesystemsrelativetothesystemswheretheanti-alignedorientationisavailable.Thecombinationoffromrotationalenergyandchangeintheinteractionbarrierthereactiondynamicsinthesystemmeasuredinthepresentworkattheexcitationenergy.5.4AngularDistributionsInSections4.1.3and4.2.3theangulardistributionsfortheeregionforallofthesystemsmeasuredinthepresentworkatbothenergieswerepresented.Throughouttheliterature,angulardistributionsareoftenpresentedintermsoftheiranisotropy,whereanisotropyisastheratiooftheobservedcrosssectionsatagivenpairofangles.152Figure5.14:CurvatureparametersdeterminedfortheCr+WreactionsmeasuredinthepresentworkasafunctionofEc:m:=VB(aligned)inPanelA,Ec:m:=VB(average)inPanelB,andEc:m:=VB(anti-aligned)inPanelC.153Figure5.14:(cont'd)Table5.3:Bassinteractionbarriers[9]fortheaverageandlimitingorientationsdeterminedfortheCr+Wreactionsconsideredinthepresentwork.SystemVBass(average)(MeV)VBass(aligned)(MeV)VBass(anit-aligned)(MeV)50Cr+180W196.95179.84207.2150Cr+186W195.59180.31204.7052Cr+180W195.75178.86205.8352Cr+184W194.80179.00204.1754Cr+180W194.56177.89204.5154Cr+182W194.12177.46204.1054Cr+184W193.67178.05202.8654Cr+186W193.22178.35202.10154Figure5.15:Angularanisotropy,determinedastheratioofW(142)toW(102)forthesystemsmeasuredatEc:m:=VB=1.13shownasafunctionof(N/Z)CNinthepresentwork.Thecolorsofthedatapointscorrespondtotheprojectileusedinthereaction.Thesolid,greenlineindicatestheratioofW(142)toW(102)fora1/sin()function.Often,theanisotropyisasaratiooftheangulardistributionsfunctionW(),suchasW(0)(orW(180))toW(90).Inthepresentwork,therewasnotfullcoverageoftheemassratiosat=90and180,thus,theanisotropywastakenastheratioofW(142)toW(102).TheanisotropydeterminedfromtheangulardistributionsfromthepresentworkareshowninFigures5.15and5.16.Clearly,thereislittleintheangularanisotropyamongthepresentsystems.TheonefeatureofnoteinFigure5.16istheceinthethreesystemsthatform236Cf,with(N/Z)CN=1.41atECN=52.0MeV.155Figure5.16:Angularanisotropy,determinedastheratioofW(142)toW(102)forthesystemsmeasuredatECN=52.0MeVshownasafunctionof(N/Z)CNinthepresentwork.Thecolorsofthedatapointscorrespondtotheprojectileusedinthereaction.Thesolid,greenlineindicatestheratioofW(142)toW(102)fora1/sin()function.5.5PreviouslyStudiedReactionsforming238Cfand240CfAdditionalinsightintothereactiondynamicscanbegainedwhentheCr+Wsystemsareconsideredinthelargercontextofotherreactionswithtentrancechannelsthatformthesamecompoundnucleus.PreviousexperimentsatANUdeducedthemassdistributionsfor238Cfand240Cfwithtentrancechannelsatcomparableenergies.Table5.4liststheentrancechannelsandenergiesofthesystemspreviouslymeasuredatANUforming238Cfand240Cf[46,40].ThemassdistributionsfromthereactionsshowninFigure5.17indicatethatthereactiondynamicsforthesesystemsaredtthanthosefortheCr+Wsystemseventhoughtheyformthesamecompoundnucleus,especiallyathighercenter-of-massenergies.Forexample,themostasymmetricentrancechannelshavethenarrowesttdistribution.156TheupperlimitsofPCNdeterminedforthesystemsmeasuredinthepresentworkandpreviouslyatANUatenergieswithEc:m:=VBwasˇ1.13areshowninFigures5.19and5.18asafunctionoftheyandmassasymmetry,respectively.(Obviously,theyisthesameforthesystemsformingthesamecompoundnuclei.)Inthisrepresentation,thebetweenthevaluesofPCNforthemostasymmetricsystem,32S+208Pb,andtheothersystemsisapparent.Additionally,thefusion-ionchannelin32S+208Pbisexpectedtobefavoredduetothedoublymagic208Pb[122,119].ThecurvatureparametersdeterminedforthesystemsinthepresentworkandpreviouslyatANUatenergieswherethecompoundnucleuswasformedwithECNˇ52.0MeVareshowninFigures5.21and5.20asafunctionoftheyandmassasymmetry,respectively.SimilartothesystemsmeasuredatEc:m:=VBˇ1.13,themassasymmetryisthedevariable,asinpreviouswork[7]atchangeinchangeinentrancemassasymmetryhasalargeimpactonthewhenthesystemhasthesamey.157158Table5.4:Entrancechannelsystem,y(˜CN),massasymmetry(),center-of-massenergy,energyrelativetotheinterac-tionbarrier[9](Ec:m:/VB),excitationenergy(E),andupperlimitofPCNfortherelevantsystemsmeasuredinthepresentworkandthesystemspreviouslymeasuredatANUwherethecompoundnucleusformedwas238Cfor240Cf.EntranceChannelCompoundNucleus˜CNEc:m:(MeV)Ec:m:/VBECN(MeV)UpperLimitPCNEc:m:/VBˇ1.1354Cr+184W238Cf0.8400.546218.91.1359.030.4460.00940Ca+198Pt[40]238Cf0.8400.664192.591.1170.640.5530.00254Cr+186W240Cf0.8370.550218.31.1360.850.4680.00948Ti+192Os[46]240Cf0.8370.600207.941.1465.540.4510.00332S+208Pb[40]240Cf0.8370.733166.41.1360.610.4480.003ECNˇ52.0MeVCurvatureParameter(arb.units)54Cr+184W238Cf0.8400.546193.081.0952.0-3.571042.010340Ca+198Pt[40]238Cf0.8400.664188.851.0966.7-3.51041.410354Cr+186W240Cf0.8370.550209.481.0852.00-4.341041.910348Ti+192Os[46]240Cf0.8370.600196.01.0753.06-3.61042.010332S+208Pb[40]240Cf0.8370.733158.171.0752.37-2.71041.810340Ca+198Pt!238Cf=840Ca+198Pt!238Cf=848Ti+192Os!240Cf=10[46]48Ti+192Os!240Cf=10[46]32S+208Pb!240Cf=1032S+208Pb!240Cf=10Figure5.17:Massdistributionsforpreviouslymeasuredsystemsforming238Cfor240CfatcomparableenergiestotheCr+WsystemsmeasuredatEc:m:/VBˇ1.13(panelsA,C,andE)andECNˇ52.0MeV(panelsB,D,andF).159Figure5.18:TheupperlimitofPCNdeterminedforthesystemsinthepresentworkandpreviouslymeasuredatANUforming238Cfor240Cfasthecompoundnucleusareshownasafunctionoftheyofthecompoundnucleus.Thesystemsaredistinguishedininthelegend.160Figure5.19:TheupperlimitofPCNdeterminedforthesystemsinthepresentworkandpreviouslymeasuredatANUforming238Cfor240Cfasthecompoundnucleusareshownasafunctionoftheentrancechannelmassasymmetry.Thesystemsaredistinguishedininthelegend.161Figure5.20:ThecurvatureparametersdeterminedforthesystemsinthepresentworkandpreviouslymeasuredatANUforming238Cfor240Cfasthecompoundnucleusareshownasafunctionoftheyofthecompoundnucleus.Thesystemsforming238Cfareindicatedbythesolidmarkers,whilethesystemsforming240Cfareindicatedbytheopenmarkers.Thesystemsaredistinguishedininthelegend.Theinsetinthelowerrightcorneristhesameplotzoomedinonthesystemsotherthan32S+208Pb.162Figure5.21:ThecurvatureparametersdeterminedforthesystemsinthepresentworkandpreviouslymeasuredatANUforming238Cfor240Cfasthecompoundnucleusareshownasafunctionoftheentrancechannelmassasymmetry.Thesystemsforming238Cfareindicatedbythesolidmarkers,whilethesystemsforming240Cfareindicatedbytheopenmarkers.Thesystemsaredistinguishedininthelegend.Theinsetinthelowerrightcorneristhesameplotzoomedinonthesystemsotherthan32S+208Pb.163Chapter6ConclusionsThemassangledistributionsforeightisotopicallytCr+Wreactionsweresuccess-fullydeducedandprovidedimportantinsightaboutthereactionmechanismwithincreasingneutron-richness.Thegoalofthepresentworkwastogainanunderstandingoftheimpactofincreasingtheneutron-richnessonthereactiondynamicsinheavy-ionfusionreactions.Twostronglycompetingexitchannelsinpreviouslyidenheavy-ionfusionreactionsareandThetworeactiontypescompetewithoneanotherandmakeupthebulkofthereactioncrosssectionfortheformationoftheheaviestnuclei.Whenispresentaantportionofthereactionislostasaresultofafail-uretoproduceacompoundnucleus.Thislossisparticularlydetrimentaltosuperheavyelementformationreactions.Improvedestimatesofthecrosssectionsofheavy-ionfusionreactions,particularlyforsuperheavyelementformation,requireafullunderstandingofthecomponent.Theofneutron-richnesshasbeensuggestedtobeimportantforfuturesuperheavyelementproductionreactionswhenmoreneutron-richbeamsareusedtoproducenucleiinthepredicted\IslandofStability".Inthepresentwork,thereactiondynamicswereexploredwithincreasingneutron-richness.Here,eighttisotopiccombinationsofthereactionofchromiumandtungstenweremeasured.Eachreactionwasmeasuredundertwoenergyconditions,oneatEc:m:=VB=1.13andECNof52.0MeVattheHeavyIonAcceleratorFacilityattheAustraliaNa-tionalUniversity.Thechromiumbeamswereacceleratedbythe14UDtandemvandegraf164acceleratorandthesuperconductingLINAC.ThepositionandtiminginformationforsionfragmentsresultingfromtheCr+WreactionswasmeasuredwiththeCUBEfragmentdetectorsystem.Thekinematiccoincidencemethodwasusedtotransformthepositionandtiminginformationintomassratiosandcenter-of-massangles.Theresultingmassandangulardistributionswereusedtodeducemass-angledistributions.Thepresenceofastrongmass-anglecorrelationindicatedthedominanceoftheexitchannelforallreactionsconsideredhere.Theprojectionofthemassangledistributionontothemassaxiswasanalyzedwithtwotmethods,masswidthsandcurvature,tocomparetherelativedistributionsamongthesystemsmeasuredinthepresentwork.AtEc:m:=VB=1.13thebroadeningofthemassdistributiondecreasedwithincreasingneutron-richness.AtECNof52.0MeVtherelationshipbetweenandneutron-richnesswaslessclear.ThevariationoftheinteractionbarrierduetothedeformationofthetungstennucleusmayhaveatimpactonthereactiondynamicsatlowECN.Fromtheprojectionofthemassangledistributionontotheangleaxis,theangulardistributionwasdeterminedfortheeightsystemsateachenergy.Theangularanisotropywasconsistentlylargerthanthatexpectedforforeachsystemindicatingthedominanceofinthesereactions.Forthesystemsat13%aboveinteractionbarrier,theexperimentalupperlimitsofPCNwerecomparedwiththeility(˜)andmassasymmetry()ofthesystemstodistinguishbetweenthesetwocommonlyusedvariablesforpredicatingthepresenceofFromtheupperlimitsdeterminedforPCNinthepresentwork,itwasconcludedthat,fortheCr+Wsystem,theyistheprimarypredictorofthechangeinForthesystemswheretheexcitationenergyofthecompoundnuclearwasheldconstantat52.0MeV,itwasfoundthatthedeformationoftheheavyreactionpartnerisveryimportant.Thechangeinradiusresultingfromthedeformationcausedthecenter-of-massenergyofthe165reactiontoberightatthebarrierforthemostlikelytoformacompoundnucleus.Thus,theprocessofformingacompoundnucleuswashinderedrelativetothatofseparatingviaThisisanimportantfactortoconsiderforsuperheavyproductionreactions,wheretheexcitationenergyisimportantfortheneutronevaporationlikelihoodleadingtothedesiredevaporationresidue.Overall,thepresentworkhasshownthatplaysatroleinthereactiondynamicsforalloftheCr+Wreactions.Theobserveddecreaseinwithincreasingneutron-richnessforEc:m:=VB=1.13canbeviewedasapositiveresultforfuturesuperheavyproductionreactionsinvolvingmoreneutron-rich,evenradioactive,projectilebeams.Basedontheresultsofthepresentwork,theincreaseinneutron-richnessshouldincreasetheprobabilityofformingacompoundnucleusrelativetoamoreneutron-tisotopiccombination.Thereisstillmuchworktobedonetounderstandthecompetitionbetweenandinheavy-ionfusionreactions.Heavy-ionfusionexperimentswithneutron-richradioactivebeamsprovideanewmeansofexploringthereactionmechanism.Theheavy-ionfusionreactionmeasurementwitharadioactivebeamproducedbytheNSCLReA3facilitywasmeasuredinOctober2015[123].Thefusionexcitationfunctionwasdeducedforthereactionof46K+181TausingthenewCoincidentFissionFragmentDetector[124].ThisdetectorsetupwasbasedontheCUBEdetectorsetupusedinthepresentwork.InfutureexperimentswithreacceleratedradioactivebeamstheCoincidentFissionFragmentDetectorcouldbeusedforstudiescomparabletothepresentworkwherereactiondynamicsareexploredthroughobservedmassandangulardistributions.166BIBLIOGRAPHY167BIBLIOGRAPHY[1]J.Hamilton,S.Hofmann,andY.Oganessian,\SearchforSuperheavyNuclei,"AnnualReviewofNuclearandParticleScience,63,383,(2013).[2]Y.T.Oganessian,F.S.Abdullin,C.Alexander,J.Binder,R.a.Boll,S.N.Dmitriev,J.Ezold,K.Felker,J.M.Gostic,R.K.Grzywacz,J.H.Hamilton,R.A.Henderson,M.G.Itkis,K.Miernik,D.Miller,K.J.Moody,A.N.Polyakov,A.V.Ramayya,J.B.Roberto,M.a.Ryabinin,K.P.Rykaczewski,R.N.Sagaidak,D.a.Shaughnessy,I.V.Shirokovsky,M.V.Shumeiko,M.A.Stoyer,N.J.Stoyer,V.G.Subbotin,A.M.Sukhov,Y.S.Tsyganov,V.K.Utyonkov,A.A.Voinov,andG.K.Vostokin,\Produc-tionandDecayoftheHeaviestNuclei293;294117and294118,"PhysicalReviewLetters,109,162501,(2012).[3]Y.Oganessian,\Heaviestnucleifrom48Ca-inducedreactions,"JournalofPhysicsG:NuclearandParticlePhysics,34,R165,(2007).[4]J.Toke,R.Bock,G.X.Dai,A.Gobbi,S.Gralla,K.D.Hildenbrand,J.Kuzminski,W.F.J.Muller,A.Olmi,H.Stelser,\Quasi-Fission-TheMass-DriftModeinHeavy-IonReactions,"NuclearPhysicsA,440,327,(1985).[5]B.B.Back,\Completefusionandinreactionsbetweenheavyions,"Phys-icalReviewC,31,2104,(1985).[6]V.Zagrebaev,Y.Aritomo,M.Itkis,Y.Oganessian,andM.Ohta,\Synthesisofsu-perheavynuclei:Howaccuratelycanwedescribeitandcalculatethecrosssections?,"PhysicalReviewC,65,014607,(2001).[7]A.C.Berriman,D.J.Hinde,M.Dasgupta,C.R.Morton,R.D.Butt,andJ.O.Newton,\Unexpectedinhibitionoffusioninnucleus-nucleuscollisions.,"Nature,413,144,(2001).[8]R.Yanez,W.Loveland,J.S.Barrett,L.Yao,B.B.Back,S.Zhu,andT.L.Khoo,\Measurementofthefusionprobability,PCN,forhotfusionreactions,"PhysicalRe-viewC,88,014606,(2013).[9]R.Bass,\Nucleus-NucleusPotentialDeducedfromExperimentalFusionCrossSec-tions,"Phys.Rev.Lett.,39,265,(1977).168[10]K.Hammerton,Z.Kohley,D.J.Hinde,M.Dasgupta,A.Wakhle,E.Williams,V.E.Oberacker,A.S.Umar,I.P.Carter,K.J.Cook,J.Greene,D.Y.Jeung,D.H.Luong,S.D.Mcneil,C.S.Palshetkar,D.C.y,C.Simenel,andK.Stiefel,\Reducedquioncompetitioninfusionreactionsformingneutron-richheavyele-ments,"PhysicalReviewC,91,041602(R)(2015).[11]Y.T.Oganessian,F.S.Abdullin,P.D.Bailey,D.E.Benker,M.E.Bennett,S.N.Dmitriev,J.G.Ezold,J.H.Hamilton,R.A.Henderson,M.G.Itkis,Y.V.Lobanov,a.N.Mezentsev,K.J.Moody,S.L.Nelson,A.N.Polyakov,C.E.Porter,A.V.Ra-mayya,F.D.Riley,J.B.Roberto,M.A.Ryabinin,K.P.Rykaczewski,R.N.Sagaidak,D.A.Shaughnessy,I.V.Shirokovsky,M.A.Stoyer,V.G.Subbotin,R.Sudowe,A.M.Sukhov,Y.S.Tsyganov,V.K.Utyonkov,A.A.Voinov,G.K.Vostokin,andP.A.Wilk,\SynthesisofaNewElementwithAtomicNumberZ=117,"PhysicalReviewLetters,104,142502,(2010).[12]K.Morita,K.Morimoto,D.Kaji,T.Akiyama,S.-I.Goto,H.Haba,E.Ideguchi,R.Kanungo,K.Katori,H.Koura,H.Kudo,T.Ohnishi,A.Ozawa,T.Suda,K.Sueki,H.Xu,T.Yamaguchi,A.Yoneda,A.Yoshida,andY.Zhao,\ExperimentontheSynthesisofElement113intheReaction,"JournalofthePhysicalSocietyofJapan,72,2593,(2004).[13]Y.T.Oganessian,\Synthesisoftheheaviestelementsin48Ca-inducedreactions,"RadiochimicaActa,99,429,(2011).[14]Y.T.Oganessian,V.K.Utyonkoy,Y.V.Lobanov,F.S.Abdullin,A.N.Polyakov,I.V.Shirokovsky,Y.S.Tsyganov,G.G.Gulbekian,S.L.Bogomolov,A.N.Mezentsev,S.Iliev,V.G.Subbotin,A.M.Sukhov,A.A.Voinov,G.V.Buklanov,K.Subotic,V.I.Zagrebaev,M.G.Itkis,J.B.Patin,K.J.Moody,J.F.Wild,M.A.Stoyer,N.J.Stoyer,D.A.Shaughnessy,J.M.Kenneally,andR.W.Lougheed,\Experimentsonthesynthesisofelement115inthereaction243Am(48Ca,xn)291x115x,"PhysicalReviewC,69,021601(R),(2004).[15]Y.T.Oganessian,V.K.Utyonkov,Y.V.Lobanov,F.S.Abdullin,A.N.Polyakov,R.N.Sagaidak,I.V.Shirokovsky,Y.S.Tsyganov,A.A.Voinov,G.G.Gulbekian,S.L.Bogomolov,B.N.Gikal,A.N.Mezentsev,S.Iliev,V.G.Subbotin,A.M.Sukhov,K.Subotic,V.I.Zagrebaev,G.K.Vostokin,M.G.Itkis,K.J.Moody,J.B.Patin,D.A.Shaughnessy,M.A.Stoyer,N.J.Stoyer,P.A.Wilk,J.M.Kenneally,J.H.Landrum,J.F.Wild,andR.W.Lougheed,\Synthesisoftheisotopesofelements118and116inthe249Cfand245Cm+28Cafusionreactions,"PhysicalReviewC,74,044602,(2006).[16]Y.T.Oganessian,Y.P.Tret'yakov,A.S.Il'inov,A.G.Demin,A.A.Pleve,S.P.Tret'yakov,V.M.Plotko,M.P.Ivanov,N.A.Danilov,Y.S.Korotkin,andG.N.169Flerov,\Synthesisoftisotopesoffermium,kurchatovium,andelement106,"JournalofExperimentalandTheoriticalPhysicsLetters,20,265,(1974).[17]Y.Oganessian,A.Demin,A.Iljinov,S.Tretyakova,A.Pleve,Y.Penionzhkevich,M.Ivanov,andY.Tretyakov,\Experimentsonthesynthesisoftkur-chatoviumisotopesinreactionsinducedby50TiIons,"NuclearPhysicsA,239,157,(1975).[18]Y.OganessianandV.Utyonkov,\Superheavynucleifrom48Ca-inducedreactions,"NuclearPhysicsA,944,62-98,(2015).[19]V.I.Zagrebaev,A.V.Karpov,andW.Greiner,\Possibilitiesforsynthesisofnewisotopesofsuperheavyelementsinfusionreactions,"PhysicalReviewC,85,014608,(2012).[20]A.J.B.Roberto,C.W.Alexander,R.A.Boll,J.D.Burns,J.G.Ezold,L.K.Felker,S.L.Hogle,andK.P.Rykaczewski,\Actinidetargetsforthesynthesisofsuper-heavyelements,"NuclearPhysicsA,944,99,(2015).[21]A.Sobiczewski,F.A.Gareev,andKalinkinBN,\ClosedShellsforZ>82andN>126inaPotentialWell,"PhysicsLetters,22,500,(1966).[22]M.Bender,K.Rutz,P.-G.Reinhard,J.A.Maruhn,andW.Greiner,\Shellstructureofsuperheavynucleiinself-consistentmeamodels,"PhysicalReviewC,60,034304(1999).[23]M.Bender,W.Nazarewicz,andP.-G.Reinhard,\Shellstabilizationofsuper-andhyperheavynucleiwithoutmagicgaps,"PhysicsLettersB,515,42,(2001).[24]W.Nazarewicz,M.Bender,S.Cwiok,P.H.Heenen,A.T.Kruppa,P.-G.Reinhard,andT.Vertse,\Theoreticaldescriptionofsuperheavynuclei,"NuclearPhysicsA,701,165,(2002).[25]S.Hofmann,\ParticleandSynthesisofSuperheavyElementsUsingRadioactiveBeamsand'TargetsDecaypropertiesofSHE's,"ProgressinParticleandNuclearPhysics,46,293,(2001).[26]NationalResearchCouncil,\ScienOpportunitieswithaRare-IsotopesFacilityintheUnitedStates,"NationalAcademicPress,Washington,DC,(2007).[27]NationalResearchCouncil,\NuclearPhysics:ExploringtheHeartofMatter,"DecadalSurveyofNuclearPhysicsbytheNationalResearchCouncil,(2013).170[28]NuclearScienceAdvisoryCommittee,\TheFrontiersofNuclearScience:ALongRangePlan,"(2007).[29]W.Loveland,\Synthesisoftransactinidenucleiusingradioactivebeams,"PhysicalReviewC,76,014612,(2007).[30]S.Bj˝rnholmandW.J.Swiatecki,\Dynamicslaspectsofnucleus-nucleuscollisions,"NuclearPhysicsA,391,471,(1982).[31]R.K.Puri,M.K.Sharma,R.K.Gupta,andP.Schuck,\Isotopicdependenceoffusioncross-sections{linearrelationships,"EuropeanPhysicsJournalA,3,277,(1998).[32]W.U.SchroederandJ.R.Huizenga,TreatiseonHeavyIonScience.NewYork:Plenum,vol.2ed.,(1984).[33]R.Bass,NuclearReactionswithHeavyIons.Berlin:Springer,(1980).[34]R.Bass,\ThresholdandAngularMomentumLimitinCompleteFusionofHeavyIons,"PhysicsLettersB,47,139,(1973Z).[35]R.Bass,\FusionofHeavyNucleiinaClassicalModel,"NuclearPhysicsA,231,45,(1974).[36]V.ZagrebaevandW.Greiner,\Synthesisofsuperheavynuclei:Asearchfornewproductionreactions,"PhysicalReviewC,78,034610,(2008).[37]C.F.Weizsacker,\ZurTheoriederKernmassen,"ZeitschriftfurPhysik,96,431,(1935).[38]J.P.Blocki,H.Feldmeier,andW.J.Swiatecki,\Dynamicalhinderancetocompound-nucleusformationinheavy-ionreactions,"NuclearPhysicsA,459,145,(1986).[39]D.J.Hinde,R.duRietz,M.Dasgupta,R.Thomas,andL.Gasques,\TwoDistinctModesinthe32S+232ThReaction,"PhysicalReviewLetters,101,092701,(2008).[40]R.duRietz,E.Williams,D.J.Hinde,M.Dasgupta,M.Evers,C.J.Lin,D.H.Luong,C.Simenel,andA.Wakhle,\Mappingcharacteristicsandtimescalesinheavyelementformationreactions,"PhysicalReviewC,88,054618,(2013).171[41]D.J.Hinde,M.Dasgupta,J.Leigh,J.Mein,C.Morton,J.Newton,andH.Timmers,\ConclusiveevidencefortheofnuclearorientationonPhysicalreviewC:Nuclearphysics,53,1290,(1996).[42]E.Prokhorova,A.A.Bogachev,M.Itkis,I.Itkis,G.Knyazheva,N.Kondratiev,E.Kozulin,L.Krupa,Y.Oganessian,I.Pokrovsky,V.Pashkevich,andA.Rusanov,\Thefuandprocessesinthereaction48Ca+208PbatenergiesneartheCoulombbarrier,"NuclearPhysicsA,802,45,(2008).[43]E.Williams,D.J.Hinde,M.Dasgupta,R.duRietz,I.P.Carter,M.Evers,D.H.Luong,S.D.McNeil,D.C.y,K.Ramachandran,andA.Wakhle,\Evolutionofsignaturesofinreactionsformingcurium,"PhysicalReviewC,88,034611,(2013).[44]I.M.Itkis,E.M.Kozulin,M.G.Itkis,G.N.Knyazheva,A.A.Bogachev,E.V.Chernysheva,L.Krupa,Y.T.Oganessian,V.I.Zagrebaev,a.Y.Rusanov,F.Goen-nenwein,O.Dorvaux,L.Stuttge,F.Hanappe,E.Vardaci,andE.deGoesBrennand,\Fissionandmodesinheavy-ion-inducedreactionsleadingtotheforma-tionofHs,"PhysicalReviewC,83,064613,(2011).[45]M.G.Itki,J.Aystob,S.Beghini,A.A.Bogache,L.Corradid,M.G.Itkis,J.Aystob,S.Beghini,A.A.Bogachev,L.Corradi,O.Dorvaux,A.Gadea,G.Giardina,F.Hanappe,I.M.Itkis,M.Jandel,J.Kliman,S.V.Khlebnikov,G.N.Kniajeva,N.A.Kondratiev,E.M.Kozulin,L.Krupa,A.Latina,T.Materna,G.Montagnoli,Y.T.Oganessian,Pokrovsky.I.V.,E.V.Prokhorova,N.Rowley,V.A.Rubchenya,A.Y.Rusanov,R.N.Sagaidak,F.Scarlassara,A.M.Stefanini,L.Stuttge,S.Szilner,M.Trotta,W.H.Trzaska,D.N.Vakhtin,A.M.Vinodkumar,V.M.Voskressenski,andV.I.Zagrebaev,\Shellinandofheavyandsuperheavynuclei,"NuclearPhysics,734,136{147,(2004).[46]C.J.Lin,R.duRietz,D.J.Hinde,M.Dasgupta,R.G.Thomas,M.L.Brown,M.Ev-ers,L.R.Gasques,andM.D.Rodriguez,\Systematicbehaviorofmassdistributionsin48Ti-inducedatnear-barrierenergies,"PhysicalReviewC,85,014611,(2012).[47]A.Wakhle,\ExperimentalandTheoreticalStudiesofPhDthesis,TheAustraliaNationalUniversity,(2013).[48]L.J.Colby,Jr.,M.L.Shoaf,andJ.W.Cobble,\Helium-InducedFissionCrossSectionsofU233andU238andNuclearRadiiofHeavyElements",PhysicalReview,121,1415,(1961).172[49]K.F.FlynnandL.E.Glendenin,`Rep.ANL-7749ArgonneNationalLaboratory,Argonne,Illinois(1970).[50]I.V.Ryzhov,S.G.Yavshits,G.A.Tutin,N.V.Kovalev,A.V.Saulski,N.A.Kudrya-shev,M.S.Onegin,L.A.Vaishnene,Yu.A.Gavrikov,O.T.Grudzevich,V.D.Simutkin,S.Pomp,J.Blomgren,M.Osterlund,P.Andersson,R.Bevilacqua,J.P.Meulders,andR.Prieels,\Fragment-massdistributionsinneutron-inducedof232Thand238Uat33,45,and60MeV",PhysicalReviewC,83,054603,(2011).[51]R.VandenboschandJ.R.Huizenga,\NuclearFission,"pp.111{112,(1973).[52]J.A.Wheeler,\ChannelAnalysisofFission,"inFastNeutronPhysics(J.B.MarionandJ.L.Fowler,eds.),NewYork:Wiley,(1963).[53]G.E.Gordon,A.E.Larsh,T.Sikkeland,andG.T.Searorg,\FissionofGoldbyCarbonIons*,"PhysicalReview,120,1341,(1960).[54]B.B.Back,R.R.Betts,J.E.Gindler,B.D.Wilkins,S.Saini,M.B.Tsang,C.K.Gelbke,L.W.G,M.A.McMahan,andP.A.Baisden,\Angulardistributionsinheavy-ion-inducedPhysicalReviewC,32,195,(1985).[55]M.B.Tsang,H.Utsunomiya,C.K.Gelbke,W.G.Lynch,B.B.Back,S.Saini,P.A.Baisden,andM.A.McMahan,\EnergyDependenceofFissionFragmentAngularDistributionsfor19F,24Mg,and28SiInducedReactionson208Pb,"PhysicsLetters,129,18,(1983).[56]R.Bock,Y.T.Chu,A.Gobbi,E.Grosse,A.Olmi,H.Sann,D.Schwalm,U.Lynen,H.Esbensen,W.WandE.Morenzoni,\Dynamicsofthefusionprocess,"NuclearPhysicsA,388,334,(1982).[57]A.Heinz,K.-H.Schmidt,A.R.Junghans,P.Armbruster,J.Benlliure,C.ockstiegel,H.-G.Clerc,A.Grewe,M.DeJong,J.Muller,M.Pfutzner,S.auser,andB.Voss,\Electromagnetic-inducedof238Uprojectilefragments,atestcasefortheproductionofsphericalsuper-heavynuclei,"NuclearPhysicsA,713,3,(2003).[58]M.Dasgupta,D.J.Hinde,N.Rowley,andA.M.Stefanini,\MeasuringBarrierstoFusion,"AnnualReviewofNuclearandParticleScience,48,401,(1998).[59]D.J.Hinde,M.Dasgupta,B.Fulton,C.Morton,R.Wooliscroft,A.Berriman,andK.Hagino,\FusionSuppressionandSub-BarrierBreakupofWeaklyBoundNuclei,"PhysicalReviewLetters,89,272701,(2002).173[60]D.J.Hinde,M.Dasgupta,J.Leigh,J.P.Lestone,J.Mein,C.R.Morton,J.O.Newton,andH.Timmers,\Fusion-Fissionversus:ofNuclearOrientation,"PhysicalReviewLetters,4,1295,(1995).[61]J.Leigh,M.Dasgupta,D.J.Hinde,J.Mein,C.R.Morton,R.C.Lemmon,J.P.Lestone,J.O.Newton,H.Timmers,J.X.Wei,andN.Rowley,\Barrierdistributionsfromthefusionofoxygenionswith144;148;154Smand186W,"PhysicalReviewC,52,3151,(1995).[62]S.Mitsuoka,H.Ikezoe,K.Nishio,K.Satou,andJ.Lu,ofneutronnumberandnucleardeformationoncompletefusionof60;64Ni+154SmneartheCoulombbarrier,"PhysicalReviewC,65,054608,(2002).[63]K.Nishio,H.Ikezoe,S.Mitsuoka,K.Satou,andS.C.Jeong,ofnucleardeformationonfusionprobabilityinthereactionsof82Se+natCeand76Ge+150NdneartheCoulombbarrier,"PhysicalReviewC,63,044610,(2001).[64]R.R.G.Thomas,D.J.Hinde,M.Dasgupta,C.R.Morton,L.R.Gasques,M.L.Brown,andM.D.Rodriguez,\Strongevidenceforinasymmetricreactionsforming202Po,"PhysicalReviewC,77,024606,(2008).[65]R.Thomas,D.J.Hinde,D.Duniec,F.Zenke,M.Dasgupta,M.Brown,M.Ev-ers,L.Gasques,M.Rodriguez,andA.Diaz-Torres,\Entrancechanneldependenceofinreactionsforming220Th,"PhysicalReviewC,77,034610,(2008).[66]Y.X.Watanabe,A.Yoshida,T.Fukuda,T.Sekine,Y.Watanabe,H.Ikezoe,Y.Nagame,andT.Ikuta,\Measurementoffusionexcitationfuncrtionsof(27;29;31)Al+197Au,"TheEuropeanPhysicalJouralA,379,373,(2001).[67]W.Loveland,D.Peterson,A.Vinodkumar,P.Sprunger,D.Shapira,J.Liang,G.Souli-otis,D.Morrissey,andP.Lofy,\Fusionenhancementinthe38S+208Pbreaction,"PhysicalReviewC,74,044607,(2006).[68]K.Zyromski,W.Loveland,G.Souliotis,D.Morrissey,C.Powell,O.Batenkov,K.Alek-lett,R.Yanez,andI.Forsberg,\Fusionenhancementinthe32;38S+181Tareaction,"PhysicalReviewC,63,024615,(2001).[69]Y.TsOganessian,V.K.Utyonkov,Y.V.Lobanov,F.ShAbdullin,A.N.Polyakov,I.V.Shirokovsky,Y.S.Tsyganov,A.N.Mezentsev,S.Iliev,V.G.Subbotin,A.M.Sukhov,K.Subotic,O.V.Ivanov,A.N.Voinov,V.I.Zagrebaev,K.J.Moody,J.F.Wild,N.J.Stoyer,M.A.Stoyer,andR.W.Lougheed,\Measurementsofcrosssectionsforthefusion-evaporationreactions204;206;207;208Pb+48Caand207Pb+34S:Decay174propertiesoftheeven-evennuclides238Cfand250No,"PhysicalReviewC,64,054606,(2001).[70]Y.TS.Oganessian,V.K.Utyonkov,F.S.Abdullin,S.N.Dmitriev,R.Graeger,R.a.Henderson,M.G.Itkis,Y.V.Lobanov,a.N.Mezentsev,K.J.Moody,S.L.Nelson,A.N.Polyakov,M.A.Ryabinin,R.N.Sagaidak,D.A.Shaughnessy,I.V.Shirokovsky,M.A.Stoyer,N.J.Stoyer,V.G.Subbotin,K.Subotic,A.M.Sukhov,Y.S.Tsyganov,A.Turler,A.A.Voinov,G.K.Vostokin,P.A.Wilk,andA.Yakushev,\Synthesisandstudyofdecaypropertiesofthedoublymagicnucleus270Hsinthe226Ra+48Careaction,"PhysicalReviewC,87,034605,(2013).[71]W.J.Swiatecki,\TheDynamicsoftheFusionoftwoNuclei,"NuclearPhysicsA,376,275,(1982).[72]J.F.Liang,C.J.Gross,Z.Kohley,D.Shapira,R.L.Varner,J.M.Allmond,A.L.Car-aley,K.Lagergren,andP.E.Mueller,\Fusionprobabilityforneutron-richradioactive-Sn-inducedreactions,"PhysicalReviewC,85,031601,(2012).[73]C.C.Sahm,H.G.Clerc,K.H.Schmidt,W.Reisdorf,P.Armbruster,F.P.Hessberger,J.G.Keller,G.Munzenberg,andD.Vermeulen,\Fusionprobabilityofsymmetricheavy,nuclearsystemsdeterminedfromevaporation-residuecrosssections*,"NuclearPhysicsA,441,316,(1985).[74]K.T.Lesko,W.Henning,K.E.Rehm,G.Rosner,J.P.ScG.S.F.Stephans,B.Zeidman,andS.Freeman,\FissionfollowingfusionofNi+Sn,"PhysicalReviewC,34,2155,(1986).[75]A.Vinodkumar,W.Loveland,J.Neeway,L.Prisbrey,P.Sprunger,D.Peterson,J.Liang,D.Shapira,C.Gross,R.Varner,J.Kolata,A.Roberts,andA.Caraley,\132Sn+96Zrreaction:Astudyoffusionenhancement/hindrance,"PhysicalReviewC,78,054608,(2008).[76]C.Wang,J.Zhang,Z.Z.Ren,andC.W.Shen,\Howtheprojectileneutronnumbertheevaporationcrosssectionincompletefusionreactionswithheavyions,"PhysicalReviewC,82,054605,(2010).[77]G.G.Adamian,N.V.Antonenko,andW.Scheid,\Characteristicsofproductswithinthedinuclearsystemmodel,"PhysicalReviewC,68,034601,(2003).[78]N.Antonenko,E.Cherepanov,A.K.Nasirov,V.Permjakov,andV.Volkov,\Compe-titionbetweencompletefusionandinreactionsbetweenmassivenuclei.Thefusionbarrier,"PhysicsLettersB,319,425,(1993).175[79]N.V.Antonenko,E.A.Cherepanov,A.K.Nasirov,V.P.Permjakov,andV.V.Volkov,\Carnpaundnucleusforxnatianinreactionsbetweenmassivenuclei:Fusionbarrier,"PhysicalReviewC,51,2635,(1995).[80]D.J.Hinde,M.Dasgupta,andA.Mukherjee,\SevereInhibitionofFusionbyQuasi-inReactionsForming220Th,"PhysicsReviewLetters,89,282701,(2002).[81]A.Y.Chizhov,M.G.Itkis,I.M.Itkis,G.N.Kniajeva,E.M.Kozulin,N.A.Kon-dratiev,I.V.Pokrovsky,R.N.Sagaidak,V.M.Voskressensky,A.V.Yeremin,L.Cor-radi,A.Gadea,A.Latina,A.M.Stefanini,S.Szilner,M.Trotta,A.M.Vinodku-mar,S.Beghini,G.Montagnoli,F.Scarlassara,A.YaRusanov,F.Hanappe,O.Dor-vaux,N.Rowley,andL.Stuttge,\Unexpectedentrance-channelintheof216Ra*,"PhysicalReviewC,67,011603(R),(2003).[82]M.Itkis,A.A.Bogachev,I.Itkis,J.Kliman,G.Knyazheva,N.Kondratiev,E.Kozulin,L.Krupa,Y.Oganessian,I.Pokrovsky,E.Prokhorova,andA.Rusanov,\Theprocessesofandofsuperheavynuclei,"NuclearPhysicsA,787,150,(2007).[83]C.Simenel,D.J.Hinde,R.duRietz,M.Dasgupta,M.Evers,C.Lin,D.Luong,andA.Wakhle,ofentrance-channelmagicityandisospinonPhysicsLettersB,710,607,(2012).[84]J.P.GreeneandZ.Kohley,\IsotopicTungstenTargets,"JournalofRadioanalyticalandNuclearChemistry,305,743,(2015).[85]J.K.Tuli,\NuclearWalletCards,"(2011).[86]P.oller,J.R.Nix,W.D.Myers,andW.J.Swiatecki,\NuclearGround-StateMassesandDeformations,"AtomicDataandNuclearDataTables,59,185,(1995).[87]A.Wakhle,C.Simenel,D.J.Hinde,M.Dasgupta,M.Evers,D.H.Luong,R.duRietz,andE.Williams,\InterplaybetweenQuantumShellsandOrientationinPhysicalReviewLetters,113,182502,(2014).[88]O.B.TarasovandD.Bazin,\DevelopmentoftheprogramLISE:applicationtofusion-evaporation,"NuclearInstrumentsandMethodsinPhysicsResearch,B,204,174,(2003).[89]R.MiddletonandC.T.Adams,\Aclosetouniversalnegativeionsource,"NuclearInstrumentsandMethods,118,329,(1974).176[90]R.Middleton,\ANegative-IonCookbook,"UniversityofPennsylvania,Philadelphia,(1990).[91]D.A.Bromley,\Thedevelopmentofelectrostaticaccelerators,"NuclearInstrumentsandMethods,122,1,(1974).[92]R.G.Herb,\Pelletronacceleratorsforveryhighvoltage,"NuclearInstrumentsandMethods,122,267,(1974).[93]T.R.Ophel,J.S.Harrison,J.O.Newton,R.H.Spear,E.W.Titterton,andD.C.Weisser,\The14UDpelletronacceleratorattheAustralianNationalUniversity,"Nu-clearInstrumentsandMethods,122,227,(1974).[94]R.Middleton,\Asurveyofnegativeionsourcesfortandemaccelerators,"NuclearInstrumentsandMethods,122,35,(1974).[95]R.Middleton,\AVersitileHighIntensityNegativeIonSource,"NuclearInstrumentsandMethods,214,139,(1983).[96]A.B.WittkowerandH.D.Betz,\Equilibrium-charge-statedistributionsofenergeticions(Z>2)iongaseousandsolidmedia*,"AtomicDataandNuclearDataTables,5,113,(1973).[97]V.S.NikolaevandI.S.Dmitriev,\OntheEquilibriumChargeDistributionsinHeavyElementBeams,"PhysicsLettersA,28,277,(1968).[98]J.L.Yntema,\HeavyIonStrippinginTandemAcceleratorTerminals,"NuclearIn-strumentsandMethods,122,45,(1974).[99]G.Charpak,R.Bouclier,T.Bressani,J.Favier,andC.Zupancic,\Theuseofmultiwireproportionalcounterstoselectandlocalizechargedparticles,"NuclearInstrumentsandMethods,62,262,(1968).[100]G.Charpak,F.SauliCern,andG.Switzerland,\Multiwireproportionalchambersanddriftchambers,"NuclearInstrumentsandMethods,162,405,(1979).[101]R.Fourme,\Position-sensitivegasdetectors:MWPCsandtheirgifteddescendants,"NuclearInstrumentsandMethodsinPhysicsResearchA,392,1,(1997).[102]G.F.Knoll,RadiationDetectionandMeasurement.Hoboken,NJ:Wiley,4thed.,(2010).177[103]D.J.Hinde,PrivateCommunication.(2016).[104]R.BrunandF.Rademakers,\ROOT{Anobjectorienteddataanalysisframework,"NuclearInstrumentsandMethodsinPhysicsResearchSectionA:Accelerators,Spec-trometers,DetectorsandAssociatedEquipment,389,81,(1997).[105]R.duRietz,D.J.Hinde,M.Dasgupta,R.G.Thomas,L.R.Gasques,M.Evers,N.Lobanov,andA.Wakhle,\PredominantTimeScalesinFissionProcessesinRe-actionsofS,TiandNiwithW:ZeptosecondversusAttosecond,"PhysicalReviewLetters,106,052701,(2011).[106]D.Y.Jeung,E.Williams,D.J.Hinde,M.Dasgupta,R.DuRietz,M.Evers,C.J.Lin,D.H.Luong,C.Simenel,andA.Wakhle,\Dynamicalapproachtoheavyion-inducedEuropeanPhysicsJournalWebofConferences,91,5,(2015).[107]V.E.Viola,\Correlationoffragmentkineticenergydata,"NuclearDataTablesA,1,391,(1966).[108]V.E.Viola,M.Walker,andK.Kwiatkowski,\SystematicsofFissionFragmentTotalKineticEnergyRelease,"PhysicalReviewC31,1550,(1985).[109]M.G.ItkisandA.Y.Rustamov,\Thessionofheatednucleiinreactionsinvolvingheavyions:staticanddynamicalaspects,"Physicsofparticlesandnuclei,29,160,(1998).[110]I.V.Pokrovsky,L.Calabretta,M.G.Itkis,N.A.Kondratiev,E.M.Kozulin,C.Maiolino,E.V.Prokhorova,A.Y.Rusanov,andS.P.Tretyakova,\Threemodesof220Ra,"PhysicalReviewC,60,041304(R),(1999).[111]K.Hagino,N.Rowley,anda.T.Kruppa,\Aprogramforcoupled-channelcalculationswithallordercouplingsforheavy-ionfusionreactions,"ComputerPhysicsCommuni-cations,123,143,(1999).[112]K.HaginoandN.Takigawa,\SubbarrierFusionReactionsandMany-ParticleQuan-tumTunneling,"ProgressofTheoreticalPhysics,128,1001,(2012).[113]N.Bohr,\NeutronCaptureandNuclearConstitution,"Nature,137,344,(1936).[114]C.SimenelandA.S.Umar,\Formationanddynamicsoffragments,"PhysicalReviewC,89,031601,(2014).178[115]V.E.Oberacker,A.S.Umar,andC.Simenel,\DissipativedynamicsinPhysicalReviewC,90,054605,(2014).[116]A.S.UmarandV.Oberacker,\Time-dependentHFapproachtoSHEdynamics,"NuclearPhysicsA,944,238,(2015).[117]A.S.UmarandV.Oberacker,\Three-dimensionalunrestrictedtime-dependentHartree-FockfusioncalculationsusingthefullSkyrmeinteraction,"PhysicalReviewC,73,054607,(2006).[118]V.ZagrebaevandW.Greiner,\Unconsiderationofdeepinelastic,andphenomena,"JournalofPhysicsG:NuclearandParticlePhysics,31,825,(2005).[119]P.Armbruster,\Nuclearstructureincoldrearrangementprocessesinandfu-sion,"ReportsonProgressinPhysics,62,465,(1999).[120]K.Siwek-Wilczynska,A.Borowiec,I.Skwira-Chalot,andJ.Wilczynski,\Entrancechannelinsuppressionoffusionofheavynuclei,"InternationalJournalofMod-ernPhysicsE,17,12,(2008).[121]D.J.Hinde,M.Dasgupta,N.Herrald,R.G.Neilson,J.O.Newton,andM.A.Lane,\Isotopicdependenceoffusionbarrierenergiesinreactionsformingheavyelements,"PhysicalReviewC,75,1,(2007).[122]D.J.HindeandM.Dasgupta,\Anewframeworktoinvestigatethesystematicsoffusionprobabilitiesinheavyelementformation:ApplicationtoThisotopes."PhysicsLettersB,622,23(2005).[123]A.Wakhle,W.Loveland,D.Morrissey,K.Hammerton,K.Stiefel,andR.Yanez,InPreparation,2017.[124]A.Wakhle,K.Hammerton,Z.Kohley,andJ.Yurkon,InPreparation,2017.179