q-deformed pairing-vibrations(8)

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

4Superconductingnuclei

Forsuperconductingnuclei,theoperatorsforcreatinganddestroyingazerocoupledquasi-particlepairandthecommutationrelationssatis edbythese(inquasi-bosonapprox-imation)aregiveninEq.(52)ofappendixB.

Inanalogywiththecaseofnonsuperconductingnucleiweexpectthatthee ectofresid-ualinteractionbetweenquasi-particlesmaybesimulatedbydeformationofquasi-particlepairs.Assuch,wede nethegeneratorsofSUq(2)forquasi-particlepairssatisfyingtheq-commutationrelationsby

[Si (q),Sj+(q)]={ i Ni}qδi,j

NiSi+(q)=2Si+(q);

by

Z (q)|0 =S+(q)|0 .(26)NiSi (q)= 2Si (q).(24)(25)Thecreationoperatorfornormalizedquasi-particlepairstateforagivenj-shellisde ned

Nextweconstructthequasi-bosoncreationoperatoras

Q ν= pν XpZp(q){ }q YpνZp(q) (27)

Thegroundstateofthenucleus|A,0 andtheeigenstateνofthenucleus|A+2,ν arerelatedby

|A+2,ν =Q ν|A,0 ;Qν|A,0 =0(28)

νToderivetheequationssatis edbyamplitudesXp’sandYpν’swecomputethecommutators

[δQν,[H11+Hc,Q ν]]forthevariationsδQν=Zm(q)andδQν=Zm(q)andtaketheir

expectationvalueswithrespecttothegroundstate|A,0 i.e.evaluate,

A,0|[δQν,[Hc,Q ¯ων A,0|[δQν,Q ν]]|A,0 =hν]|A,0 .(29)

HeretheHamiltonianH11+Hcisobtainedbyreplacingthenormalquasi-particlepaircreationanddestructionoperatorsinH11+HcofappendixBbydeformedquasi-particlepaircreationanddestructionoperatorsthatis

H11= iEiNi

(30)