q-deformed pairing-vibrations(6)

Boson creation operators constructed from linear combinations of q- deformed zero coupled nucleon pair operators acting on the nucleus (A,0), are used to derive pp-RPA equations. The solutions of these equations are the pairing vibrations in (A${\underline

Theamplitudesforpopulatingthegroundstateandtheexcitedstatesofthenucleus|A,0 ,viatwonucleontransferreactionsare

µ A,0|FR+|A,0 =Nµ

G

respectively.Hereµreferstothelowestenergyboson.(23)

30+statesofPbIsotopes

Pbisotopesareawellknownandmuchstudiedexampleofpairingvibrationsinnon-superconductingnuclei.Presentlyweconcentrateonthe0+statesofthenucleus208Pb.Themaininterestistocalculatetheenergyofthedoublepairingvibration(DPV)statefortheneutronpairvibrationsin208Pbwhichisexperimentallyknowntolieat4.87MeVwithrespecttogroundstateandhasbeensubjectofinvestigationinvarioustheoreticalworksonpairingvibrations.BesandBroglia[16]usingasimpli edmodelconsistingoflikeparticlesinteractingviaapairingforcewithconstantmatrixelementpredictedanexcited0+stateat

4.9MeV.Thecalculatedratiobetweenthematrixelmentspopulatingthe rstexcitedstateandthegroundstateviaa(t,p)reactioninthismodelis1.3.BrogliaandRiedel[20]fur-theranlysedthe206Pb(t,p)208Pbdata[19]andshowedthatthelinearpairingmodelproducesonlyaqualitativeagreementwiththeexperimentaldata.Sorensenalso[18]investigatedtheneutronpairingvibrationsin208Pbusingapairingforcehamiltonianwithconstantmatrixelements.Hismodelhoweverusestheideathatthecollectiveexcitationsofthesystemcanbeunderstoodintermsoftheinteractionbetweenafewcolectivebosons,eachofwhichcanbeexpandedintermsoftwo-fermionstates.Thehamiltonianisexpressedintermsofthecollectivebosonsanddiagonalizedinappropriatecollectivebosonvectorspacetoobtainthepropertiesofthe0+states.Inthecaseof0+statesof

slightly,theratioσ(0+

2)208Pb,thee ectofincludinganharmonicitiesinthiswayisthatthoughtheexcitationenergyof02+stateisa ectedonly