SHELL-MODEL STUDY FOR NEUTRON-RICH NUCLEI

Abstract

This thesisaimstogainknowledgeofnuclearstructure,collectivity,andisomers in thevastregionofthenuclearchart,inparticularthe 132Sn and 208Pb regions.The relevanceofthemodelspacehasbeendiscussedandanalyzedtolearntheevolu- tion oftheexcitationenergiesandelectromagneticobservablesandpredictedseveral missing piecesofinformation.Further,severalnewlevelassignmentsandisomeric states havebeenproposed,whichcanbehelpfulforexperimentalistsandshell-model practitioners. Theneutron-richnucleihavealsobeendescribedintermsofseniority, core polarization,spectroscopicfactorande ectivesingle-particleenergy. In ordertounderstandthesigni canceofthe g9/2 and d5/2 orbitals, we rstex- plored theCaregionandpresentedshell-modelresultsforthe 47−58Ca isotopesin the fp, fpg9/2 and fpg9/2d5/2 modelspacesusingrealistic NN interaction.Addi- tionally,employinginteractionsfromthein-mediumsimilarityrenormalizationgroup (IM-SRG)aimedforaspeci cnucleuswithchiral NN and 3N forces, wecarried out acompleteshell-modelanalysis.Itisdemonstratedthatwhilethe g9/2 and d5/2 orbitals aremarginalforlighter 47−52Ca isotopes;theyplayasigni cantroleforheav- ier neutron-rich 54−58Ca isotopes.Toseethesigni canceofthe g9/2 orbital andthe decrease inenergyofthe 2+ state after 54Ca, wehavemodi edthesingle-particle energy.Asweproceedtowardsheavier 54−58Ca isotopes,theconsiderableriseinoc- cupancy forthe g9/2 orbital isreachedabove N = 34. Thisworksupportsthe N = 32 and N = 34 sub-shell closuresinthe 52Ca and 54Ca isotopes. The 132Sn regionhasbeenexaminedinthisthesis.Thisstudyusesfull- edged shell modelcalculationsinthe50-82modelspace,whichismadeupofthe 1g7/2, 2d5/2, 1h11/2, 3s1/2, and 2d3/2 orbitals, toexplainexperimentaldatauptohigh-spin states of 119−126Sn isotopeswithdi erentseniority(v). Thesestatesareexplainedin terms ofbrokenneutronpairsoccupyingthe h11/2 orbital. Dueto v = 2,3,4,and 5, Snisotopeshavehigh-spinisomers.Thestudyhasnowbeenexpandedtoinclude the 208Pb region,particularlyfortheseniorityisomers. Systematic large-scaleshell-modelcalculationsarepresentedforRnisotopeswith A = 207 to216.Alongwiththeestimatedenergyspectraandelectromagneticchar- acteristics, wealsorecommendspinsandparitiesforseveraluncon rmedstatesthat haverecentlybeenmeasuredinexperiments.Thecomputedshell-modelcon gura- tions andhalf-livesarepresented,alongwithadetailedanalysisofseveralisomeric states. Itisnecessarytoconsiderenoughorbitalsbelowtheshellclosureforlow-lying states otherthanthecore-excitationforhighermassisotopes 213−216Rn. Weobserved that high-lyingstatesexhibitlesscollectivebehaviour,whereaslow-lyingstatesresult from signi cantcon gurationmixing.Aswemovefurtherawayfromtheshellclo- sure, collectivityandcon gurationmixinggrowrapidlyfortheisotopesclosetothe N = 126 shell closure.Thisdemonstrateshowcrucialitistoincludeenoughmodel space inthe 208Pb regiontoreproducetheenergyspectrumaccurately.Theisomeric states intheRnisotopesarecausedbytheorbitals h9/2 and i13/2, andthehigh-spin isomers arecausedby v = 1,2,3,4,5,6,and7. The spectroscopyof 132Sn and 208Pb, whichareverydi erentlylocatedtothe valleyofstability,exhibitsimilarityinmanyways.Motivatedbythis,weusedthe nuclearshellmodeltoconductanewkindofinvestigationintothesimilaritiesbetween the N = 82 (52 ≤ Z ≤ 60) and N = 126 (84 ≤ Z ≤ 92) isotones.Thestrong resemblancebetweenthehigh-j orbitals hasbeenusedtoreportsimilaritiesbetween these twoisotonicchains.Accordingtoourstudy,severalisomericstatesinthe N = 82 and N = 126 isotones arecausedbythebreakupofhigh-j nucleonpairs and arewellde nedbyseniorityquantumnumber.Theidenticalsenioritystatesin the SnandPbregionsexhibitasimilarevolutionofexcitationenergy.Thehigh- j orbitals abovetheshellgapsexhibitsimilarbehaviourusingtherelationshipbetween the SnandPbregions,ultimatelydeterminingadditionalspectroscopicproperties. In additiontothestudiesalreadydescribed,calculationsusingalarge-scalenuclear shell modelhavebeendoneonthe 204−210Tl isotopesmotivatedbythe ndingsofthe study forRnisotopesmentionedearlierfortherequirementofinclusionofcore- excitation. Thesecalculationsincludecon gurationsthatallowedbothneutronand proton coreexcitationsacrossthe Z = 82and N = 126shellgaps.Thestructureof Tl isotopeshasbeeninvestigatedforasigni cantlylargemodelspaceinresponseto the mostrecenthigh-spinexperimentaldata.TheKHH7BandKHM3Yinteractions havebeenusedtoperformthecalculationwithcoreexcitation.Thelevelspectraof 204−210Tl isotopesaredescribedandexplainedbycoreexcitationsacrossthe 208Pb core andbymulti-nucleoncouplingsofsingle-particle-holeorbitalsinsidethevalence space.