q-deformed pairing-vibrations(11)

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

inamuchsimplermodelbyusingdeformedpairs.Wemayinferthatarealdeformationofzerocoupledpairstakesintoaccounttheanharmonicitiesnotbeingaccountedforinbosonapproximationinthesimplemodelathandwiththesamepairingstrengthforallorbits.Wealsonotethatasthedeformationparameterisincreasedthetransitiontosuperconduct-ingphaseoccursforsuccessivelysmallervaluesofpairinginteractionstrengthparameterforτrealandforsccessivelylargervaluesofGforimaginaryvaluesofτ.Thisbehaviourisconsistentwithourearlierconclusion[12]thatthedeformedfermionpairsaremorestronglyboundforrealvaluedτandthedeformationinthiscasesimulatestheresidualattractiveinteraction.SimilarresultshavebeenobtainedbyBonatsoset.al[21]intheframeworkofMoszkowskimodelwhereincreasingq-deformationhasbeenshowntofacilitatethephasetransitionfromthevibrationaltotherotationalbehavior.Forq=eiτ,ontheotherhand,deformingthepairamountstoweakeningthepair.Theroleofcomplexvaluedqisakintoapairbreakingresidualrepulsiveforce.

Inboththecasesthecollectivityofthestateisseentobeafunctionofdeformationparameterasisevidentfromthevariationofcalculatedtwonucleontransfercrosssectionsin gures(3a,3b).WemaypointoutthatdeformingthezerocoupledpairsisnotthesameaschangingthevalueofthepairingstrengthparameterG.Forphononexcitationenergiesclosetotheunperturbedenergiesthecollectivityisalmostindependentofthevalueofparameterτ.Howeverintheregionclosetophasetransitionitisverysensitivetodeformation.ThedeformedpairHamiltonianapparentlyaccountsformany-bodycorrelations,thestrengthofhigherorderforcetermsbeingdeterminedbythedeformationparameter.

Forthetestmodelof20particlesintwoshells,theresultsofq-deformedbosonandquasi-bosonapproxmationshavebeencomparedwithexactresults.Thedeformedbosonapproximationresultsforτ=i0.104anddeformedquasi-bosonenergiesforτ=0.15overlaptheexactcalculationresultsinawideregionawayfromthephasetransitionregion.Ap-parentlythedeformatione ectivelytakesintoaccountthecorrelationsnotbeingaccountedforinapproximatetreatments.Assuch,inarealisticcalculationthedeformationparametermaybetakenasaquantitativemeasureofcorrelationsleftoverinanapproximatetreat-mentascomparedtotheexacttreatment.Thetestmodelresultsthatthedeformedbosonpairsanddeformedquasi-bosonpairsaremore(less)stronglyboundascomparedtotheirundeformedcounterparts,forreal(imaginary)τ,con rmsourearlierconclusions.

Wemayconcludethat,inarealisticcase,areal(imaginary)deformationmaybeusedasameasureofanharmonicitiescausedbyaresidualattractive(repulsive)interactionnot