Q-DEFORMED PAIRING VIBRATIONS

Boson creation operators constructed from linear combinations of q-def ormed zero-coupled nucleon pair operators acting on the nucleus (A,0) are used to derive pp-random phase approximation equations. The soluti ons of these equations are the pairing vibrations in (A+/-2) nuclei. F or the 0(1)(+) and 0(2)(+) states of the nucleus Pb-208, the variation s of relative energies and transfer cross sections for populating thes e states via (t,p) reaction, with the deformation parameter tau, have been analyzed. For tau = 0.405 the experimental excitation energy of 4 .87 MeV and the ratio sigma(0(2)(+))/sigma(0(1)(+)) = 0.45 are well re produced. The critical value of the pairing interaction strength, for which a phase transition takes place, is seen to be lower for the defo rmed zero-coupled nucleon pair condensate with tau real, supporting ou r earlier conclusion that the real deformation simulates the two-body residual interaction. For tau purely imaginary a stronger pairing inte raction is required to bring about the phase transition. The effect of imaginary deformation is akin to that of an antipairing type repulsiv e interaction. Using deformed zero-coupled quasiparticle pairs, a defo rmed version of the quasi-boson approximation for 0(+) states in super conducting nuclei is developed. For the test model of 20 particles in two shells, the results of q-deformed boson and quasiboson approximati ons have been compared with exact results. It is found that the deform ation effectively takes into account the anharmonicities and may be ta ken as a quantitative measure of the correlations not being accounted for in a certain approximate treatment.