q-deformed pairing-vibrations(3)

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

experimentaldatabutthephysicalcontentofthemodel.Assuchseveralcalculationsareavailablefortestnucleiinadditiontothoseforrealnuclei.ItisseenthatastheinteractionbetweenthepairsbecomesstrongeralargenumberofzerocoupledpairsareabletocrosstheFermisurfaceresultinginaphasetransitionofthenucleus.AtthispointtheRPAapproximationbreaksdown.Thecriticalpointbehaviorofanuclearsystemisdeterminedtoalargeextentbyhowtheinteractionbetweenthepairsistakenintoaccount.OurobjectistoanalyzethecharacteristicsofpairingvibrationsinducedbybosonoperatorswithJπ=0+constructedfromdeformedzerocoupledfermionpairsanddeformedzerocoupledquasi-particlepairsinordertohaveabetterinsightintothephysicalcontentofthedeformationparameter.

Wehaveorganisedthepaperasfollows.Insection2,weconstructbosonsfromdeformedzerocoupledfermionpairs,setuptheRPAequationsandobtainthedispersionrelationthesolutionofwhichgivesbosonexcitationenergiesfornon-superconductingnuclei.Theenergiesof0+statesofPbisotopesarediscussedinsection3andthecalculatedratiooftwo

+208nucleontransfercross-sectionsforpopulatingthe0+Pbiscomparedwith2and01statesof

theexperimentaldatatounderstandtheextenttowhichanharmonicitiesaresimulatedbythedeformation.Section4dealswiththeconstructionofdeformedquasi-bosonoperatorsandobtainingdeformedQP-RPA(quasi-particleRadomPhaseapproximation)equations.Theformalismofsections2and4isappliedinsection5tothetestcaseofN=20particlesintwoshellsandtheresultsfortheenergyofthelowest0+statefromdeformedbosonapproximationanddeformedquasi-bosonapproximationcomparedwiththeexactresults.Conclusionsarepresentedinsection6.Thede nitionsofnormalizeddeformedfermionpaircreationoperatorandquasi-particlepaircreationoperatorsaregiveninAppendicesAandBrespectively.

2Deformedpair-RPAequations

InRef.[12]ithasbeenshownthatthecreationoperatorZ0andtheannihilationoperator

Z0=

S (q){ }q(1)