Etude du spectre d’énergie des noyaux déformes du platine à l’aide du Hamiltonien de Bohr avec la combinaison des potentiels de Morse et Kratzer crible

Abstract

In thisthesis,weproposeanewnuclearmodelcapableofstudyingadeformedsys- tem, thatofatriaxialnucleus.Thismodel,basedonthecombinationoftwopotentials, namely theMorsepotentialandthescreenedKratzerpotential(CPMK)describesremar- kably thenuclearinteractionsandconsequentlythedeformationsundergonebytheato- mic nucleus.UsingBohr’sHamiltonianequation,wemodelthemotionsofthestudied nucleus. Tosolvethisequation,amethodofseparationofvariableswasusedgenerating two equations:onefunctionofthevariable , describingthevibrationalmovementand while theotherfunctionofthevariable , describingthemovementofrotationinthe nucleus. The -part isobtainedfromthepotentialoftheharmonicoscillatorwhilethe -part isresolvedinthepresenceofthe(CPMK).Also,theExtendedNikiforov-Uvarov (ENU) methodwasappliedon to obtaintheenergyspectrumandtheassociatedei- genfunctions usingtheHeunConfluent(HeunC).Theresultsdemonstratedthatapara- meter ofthispotential”c” isaconstraintwhichisafunctionofenergy.Thisworkwill be appliedtothe 192;194;196Pt isotopes ofplatinumbecauseoftheirsimilarpropertiesof conductivity,malleabilityandthefacttheyallbelongtothefamilyoftransitionmetals. After havingcalculatedtheenergyspectrumforeachplatinumisotope,wethencom- parethemwiththeexperimentalenergyvaluestakenfromtheliterature.Inaddition, electric quadrupoletransitionmomentprobabilityratioshavebeencalculatedforthese isotopes. Itemergesfromthiscomparisonthatourresultswithourmodelconverge with thoseobtainedbyexperimentandmakethebetterpredictionthanthatofMorse and KillingbeckplusMorse.