Q-deformed pairing vibrations.

Abstract

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 random phase approximation equations. The solutions of these equations are the pairing vibrations in (A\ifmmode\pm\else\textpm\fi{}2) nuclei. For the ${0}_{1}^{+}$ and ${0}_{2}^{+}$ states of the nucleus $^{208}\mathrm{Pb}$, the variations of relative energies and transfer cross sections for populating these states via (t,p) reaction, with deformation parameter \ensuremath{\tau} have been analyzed. For \ensuremath{\tau}=0.405 the experimental excitation energy of 4.87 MeV and the ratio \ensuremath{\sigma}(${0}_{2}^{+}$)/\ensuremath{\sigma}(${0}_{1}^{+}$)=0.45 are well reproduced. The critical value of pairing interaction strength, for which phase transition takes place, is seen to be lower for deformed zero-coupled nucleon pair condensate with \ensuremath{\tau} real, supporting our earlier conclusion that the real deformation simulates the two-body residual interaction. For \ensuremath{\tau} purely imaginary a stronger pairing interaction is required to bring about the phase transition. The effect of imaginary deformation is akin to that of an antipairing type repulsive interaction. Using deformed zero-coupled quasiparticle pairs, a deformed version of quasiboson approximation for ${0}^{+}$ states in superconducting nuclei is developed. For the test model of 20 particles in two shells, the results of q-deformed boson and quasiboson approximations have been compared with exact results. It is found that the deformation effectively takes into account the anharmonicities and may be taken as a quantitative measure of the correlations not being accounted for in a certain approximate treatment.