q-deformed pairing-vibrations(2)

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

PACSNumber:21.60.Fw,21.60.Jz,21.10.Re

1Introduction

Thenotionofquantumgroupshasattractedalotofattentionoverthelastfewyears.ThequantizationbydeformationwasstudiedearlierbyBayenet.al[1].Drinfeld[2]gener-alizedthisideatoquantizeclassicalLiealgebrassoastoconstructnon-commutativeHopfalgebrastructure.InparticularthequantumgroupSUq(2),theq-analogofSU(2),hasbeenextensivelystudiedbyJimbo[3],Woronowicz[4]andPasquier[5].Byconstructingaq-analogueofthequantumharmonicoscillator,Biedenharn[6]andMacfarlane[7]havegen-eralizedtoSUq(2),theSchwingerapproachtothequantumtheoryofangularmomentum.Theq-deformedalgebrashavefoundvariousapplicationstophysicalsituationsinnuclearandmolecularphysics[8][9][10].Raychevetal.[8]suggestthatquantumalgebraisappropri-ateforthedescriptionofstretchinge ectsinrotationalnucleiandhavefoundgood tsofrotationalspectraofeven-evenrareearthsandactinidesbyusingahamiltonianproportionaltothesecondorderCasimiroperatorofthequantumalgebraSUq(2).TheSOq(4)quantumalgebrahasalsobeenusedforthedescriptionofq-analogueofthehydrogenatom[11].Inourearlierwork[12]weconstructedaq-deformedanalogueofzerocouplednucleonpairstatesandfoundthesetobemorestronglyboundthanthepairswithzerodeformation,whenarealvaluedq-parameterisused.Aninterestingextensiontothemulti-shellcase,withdeformedzerocoupledpairsdistributedoverseveralsingleparticleorbitsshowedthatthedeformationessentiallysimulatesthee ectiveresidualinteraction.Bonatsos[13]hasalsoshownthatthecommutationrelationsofoperatorsforzerocoupledcorrelatedfermionpairsinasingle-jorbitcanbesatis edupto rstordercorrectionbysuitablyde nedq-bosons,ontowhichthefermionpairoperatorsaremapped.Presently,weconstructtheexcitationoperatorsforpairingvibrationsfromdeformedzerocouplednucleonpairsaswellasdeformedzerocou-pledquasi-particlepairsandanalyzethecriticalpointbehaviourofnucleiasthedeformationparametertakesrealandimaginaryvalues.

Pairingvibrations[14,15,16]arethecollectivevibrationsofzerocoupledfermionpairsaroundtheFermisurface.ThenaturalframeworkforstudyingthepairingvibrationsisRPAfornonsuperconductingnucleiandQuasi-particle-RPAforsuperconductingnuclei.Inwellknownworksonpairingvibrationsthemainconcernhasnotbeenthereproductionof