q-deformed pairing-vibrations(10)

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

theexactresultforvaluesofGnotveryclosetoGc.Fordeformedbosoncalculationthecrit-icalvalueofpairingstrengthG,forwhichtheenergyofthelowestenergystateapproacheszero,isseentogoupasthedeformationisincreased.Inotherwords,increasingthedefor-mationparametercausesthetransitiontosuperconductingphasetooccuratsuccessivelylowervaluesofG.

In g.(5b)thedeformationparameteristakentobepurelyimaginarywiththecurvesshownforτ=i0.05,i0.1andi0.15.ForagivenvalueofG,animaginarydeformationparam-eterτraisestheexcitationenergyinthebosonaswellasthequasi-bosonapproximation.Itmaybeinterpretedasananti-pairinge ect.AsthebosonapproximationenergieslielowerthantheexactenergyeigenvaluesforthesameGvalue,forasuitablechoiceofτwecanobtainadeformedbosonapproximationcurvehavingagoodoverlapwiththeexactresultsforareasonablylargerangeofGvaluesintheregionawayfromthephasetransitionregion.Deformationinthiscasesimulatesthecorrelationsnotaccountedforinthebosonapproximation.Inarealisticcase,animaginarydeformationmaybeusedasameasureofcorrelationscausedbyaresidualrepulsiveinteractionnotbeingaccountedforinthebosonorquasi-bosonapproximation.

WehaveplottedinFig.(5c)thedeformedbosonapproximationenergiesforτ=i0.104andquasi-bosonenergiesforτ=0.15thedeformationvaluesforwhichagoodagreementwiththeexactcalculationresultsisobtainedinawideregionawayfromthephasetransitionregion.

6Conclusions

Wehaveconstructedq-analoguesofbosonapproximationandquasi-bosonapproxima-tiontounderstandthephysicalmeaningofrealandimaginarydeformationinthecontextofinteractionbetweenzerocoupledpairs.Theformalismfornon-superconductingnucleihasbeenappliedtotheclassicexampleoftheDoublePairingVibrationalstate0+2inthenucleus

R=208Pb.Forarealdeformationvalueofτ=0.405,thecalculationreproducestheob-servedexcitationenergyofthe0+2state,E=4.87MeV,aswellastheratioofcrosssections,σ(0+

2)