q-deformed pairing-vibrations(5)

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

ofmotion,Eq.(7).For

thetwokindsofpossiblevariations,δRν=

weobtainthefollowingsetofequationsforthenucleus(A+2),

(¯hων ν2 n)XnSn (q){ n}qandδRν=Sj (q){ j}q,= G

=G(¯hων

withsolutions2 j)Yjν { m}q G{ m}q+Gν { i}q{ i}q

.(11)(12)νXn= N

Nνde nedas

ν(¯hων 2 n) mνXm Yjν=Nν(¯hων 2 j){ i}q (13)N=G

j(14)evaluatedbyusingthenormalizationcondition, nν2|Xn| |Yjν|2=1

1

(15)isgivenby

N=ν n{ n}q(2 j h¯ων)2

G= n{ n}q(2 j h¯ων)(17)

readilyyieldsagraphicalsolution.Asimilarequationisobtainedfortheeigenstatesofthenucleus(A 2)usingatwo-holebosoncreationoperatoroftheform,

µR+= m

µwiththetwo-holephononstatesgivenby|(A 2),µ =R+|A,0 .µ Xm Sm (q) µ Si (q) Yi{ m}q{ i}qi ;µµ[H,R+]=h¯ωµR+(18)

Theexcited0+statesofthenucleus|A,0 arethetwo-phononstates

µν|ν,µ =R+R+|A,0 (19)

(20)withexcitationenergyE(0+)=h¯ων+h¯ωµ

Theoperatorfortwonucleontransferis

F= mSm+(q)+

iSi+(q)(21)