q-deformed pairing-vibrations(9)

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

Hc= G

22 viujSi (q)Sj (q) ij222u2iujSi+(q)Sj (q) uivjSi+(q)Sj+(q)+22vivjSi (q)Sj+(q) .(31)

Indeformedquasi-bosonapproximation,onevaluatingEq.(29)theamplitudesXν’sandYν’sarefoundtosatisfythefollowingsetofcoupledequations,

(¯hων ν2Em)Xm

ν2Em)Ym= G=G { p}q{ p}q (¯hων+ ν2Xp(u2mup+22vmvp) 2Ypν(u2mvp+22vmup) (32)

(33)2Ypν(u2mup+22vmvp) ν2Xp(u2mvp+22vmup) .

ThesetofEqs.(32,33)canbesolvedbyusingstandardmethodstofurnishtherootsE=h¯ων.

5TwoShellTestModel

Foranalyzingthebehaviourofpairingvibrationstatesinthedeformedbosonapproxi-mationanddeformedquasi-bosonapproximation,weexaminethesestatesforatestmodelinwhichN=2 particlesaredistributedovertwoshellmodelorbits,eachwithadegener-acy2 .TheShellmodelorbitshavesingleparticleenergiesgivenby

tionofG 2respectively.FollowingHogaasen[15],weplotin g.(5)thelowestenergyrootinunitsof2 asafunc-

2 =1.0andterminateatE