STUDIES OF NUCLEAR ISOMERS FROM MEDIUM MASS TO HEAVY MASS NUCLEI

Abstract

With recentadvancesinexperimentaltechniques,nuclearisomershavetakenacentre stage innuclearphysicsastheyprovideausefulhandletostudyvariousnuclear structure propertiesinunusualsituations.Largeamountofexperimentaldatais, therefore, nowavailablefornuclearisomers.Wehaverecentlypresentedan\Atlas of NuclearIsomers",whichlistsmorethan2450nuclearisomers.Inthisthesis,we mainly focusonthenuclearisomersinsemi-magicnuclei,particularlytheseniority isomers. Theconceptofseniority,abeautifulsymmetryarisingfromthepairing interactioninnuclei,hasprovedveryusefulinunderstandingthebehaviorofsemi- magic nuclei.Weuseageneralizationofthisconcept,knownasthegeneralized seniority,andshowthatitremainsanearlygoodquantumnumberthroughoutthe varioussemi-magicchains. It hasgenerallybeenbelievedthattheseniorityisomersariseonlydueto E2 tran- sitions, astheodd-tensordecaysconservetheseniorityandshowaparticlenumber independentbehaviorinasingle􀀀j scheme.Byextendingthesenioritypictureto the multi􀀀j degenerate orbitalsi.e.the\generalizedseniority",wecouldestablish that thedecaypropertiesaresimilarforbothevenandoddtensorelectrictransitions. Wehaveusedthisresulttounderstandthedecaytrendsofisomericstatesaswell as otherexcitedstatesinthemulti􀀀j environment.Forexample,wehaveshownfor i ii the rsttimethattheisomersfromtheSn-isotopicchaindisplayasimilarbehavior for E1 decaying13􀀀 isomers, and E2 decaying10+ and 15􀀀 isomers. These ndingshaveopenedupwayto ndnewkindofseniorityisomersdecaying via odd-Electrictransitions.Hence,forthevery rsttime,theseniorityisomers with oddtensorelectrictransitionshavebeenidenti edandinterpretedinterms of generalizedseniority.Wealso ndthatthecon gurationmixingisessentialto fully describetheeventensortransitionsforthe10+ isomers also,whichweresofar interpretedaspure h11=2 isomers. Thishighlightstheimportanceofcon guration mixing, suggestedbygeneralizedseniority,ingeneratingagivensetofstates.These isomers havealsobeencomparedwiththeidenticaltrendsforthe10+ isomers inthe N = 82isotonicchainandthe12+ isomers inthe Z = 82isotopicchain.We nd that theseniorityisomersfromdifferentsemi-magicchainsbehavequitesimilarto eachother,thoughtheyhavedifferentvalencespaces,anddifferentsetoforbitals. The reasonbehindthissimilarityisthegoodnessofgeneralizedseniorityforthese isomeric states,whichgovernstheidenticalbehavioroftheseisomersindifferent semi-magic chains.Thissimpleschemeofcalculatingthe B(EL) valuesmayalsobe used toestimatethehalf-livesinunknowncasesand,hencepredictnewisomers. Tofurtherextendtheresultsforsenioritychangingtransitionsi.e.Δv = 2transi- tions, westudythe rstexcited2+ and 3􀀀 states inSn-isotopes,andfoundthatour schemesuccessfullyexplainstheasymmetricdoubleparabolictrendof B(E2) val- ues andtheinvertedparabolicbehaviorof B(E3) values.Thesesimplecalculations reproducetheexperimentaldataquitewellalongwiththedipinthemiddle.This also worksasaguideto xtheorbitalsinvolvedincon gurationmixing.Thisinfor- mation turnsouttobeveryusefulindecidingthecon gurationsinthelargescale shell model(LSSM)calculations,whichagainreproducetheexperimentaltrendvery well.NotethattheLSSMcalculationscarriedoutbyusmaynotbeperfectinterms of truncations,yettheresultssupporttheimportanceofcon gurationsprovidedby generalized seniority.Hence,thedipinthemiddleofthe B(E2 "; 0+ ! 2+) values correspondstothelocationwheretheroleofthe g7=2 orbital istakenoverbythe iii h11=2 orbital. Ontheotherhand,the3􀀀 states havebeenunderstoodintermsof octupolevibrationalcharacter,astheymainlyarisedueto d and h orbitals differing in l valuesby3unitssuggestedbygeneralizedsenioritycalculations. Wealsoextendthesecalculationstothe6+ isomers in 134􀀀138Sn isotopes,and nd thattheanomalyat 136Sn inseniorityschemecannaturallybeexplainedinthe generalized senioritycalculations.Theshellmodelcalculationssupportourclaim. We,however,con rmthatasmallmodi cationintheinteractionbeyondtheN=82 magic numberisindeedrequiredassuggestedearlier.Wemayalsoconcludethat the \RCDB"interactionseemsbettersuitedtoexplainthedataoftheneutronrich systems inthe N = 82 􀀀 126 region.Itwouldbeveryusefultomeasuretheremain- ing B(E2) valuesforthetransitionsin 134􀀀138Sn-isotopesinordertogainfurther understanding oftheeffectiveinteractionsintheneutron-richregion.Thesuccess of thisschemeinexplainingtheavailableexperimentaldatasuggeststhatthestates in thesen-richisotopesareactuallygeneralizedsenioritystatesratherthanpure seniorityones,andsuggestsanenhancedgapbetween i13=2 and theremainingor- bitals ofthevalencespace.Wealsopresenttheresultsofthegeneralizedseniority guided LSSMcalculationstovalidatetheneutron-singleparticleenergiesofthisre- gion. TheseLSSMresultssuggestahigherpositionofthe i13=2 orbital at1:2 MeV, whichreproducestheexperimentaldata,boththelevelenergiesandthetransition probabilities consistently.Ourshellmodelcalculationssuggestanewsub-shellgap at N = 112duetothehigherlocationof i13=2 orbital, alsoinlinewiththegeneralized seniorityresults.Theexistenceofthisgap,however,needsacon rmationfromother calculations andexperimentalmeasurements.However,amarginalreductionof25 keVisfoundtobeessentialtoexplaintheobservedlevelenergiesand B(E2) values consistently. Wealsoapplythegeneralizedseniorityschemetotheodd-Asemi-magicnuclei, particularly theSn-isotopesandPb-isotopes.Wehavestudiedthe27=2 􀀀 , 19=2+ and 23=2+ isomers inn-richSn-isotopesandexplainedtheir B(E2)s usingthisformalism. These calculationssuggestthatthemixingof h11=2, d3=2 and s1=2 orbitals isessential. iv Wealsopresentthe B(E2) valuesforthehigh-seniority v = 5,35=2+ isomer inSn- isotopes.Wethencomparethe33=2+ isomers inPb-isotopeswiththe27=2 􀀀 isomers in Sn-isotopesand ndthatthesimilar B(E2) trendsinboththechainsareduetothe similar generalizedseniorityofthesestates,thoughtheybelongtototallydifferent valencespaces. Tosummarize,weareabletodescribethedecaypropertiesofboththeisomeric states andotherexcitedstatesinsemi-magicnucleiusingasimplemicroscopicgen- eralized seniorityscheme.Theresultsoftheshellmodelcalculationshavealsobeen used tosupportthe ndingsofthegeneralizedseniorityscheme.Somepredictions can alsobemadefortheunknownspectroscopicnumbersatnuclearlimits.The presentschemeislimitedbythefactthatalltheactiveorbitalshavebeentakento bedegenerate.Hence,theextensionoftheschemeintermsofnon-degenerateorbitals is possibleandmayleadtomoreprecisecalculations.Also,thepresentschemetreats only identicalnucleonsofonekind;onemayextendthesestudiesforbothtypeof nucleonswhichwillextendthescopeofapplicabilityoftheseniorityformalism.