Self-Consistent Treatment of the Pairing Plus Quadrupole Force in the Nilsson Plus BCS Model and in the Interacting Boson Model

Abstract

Variational calculations within the pairing plus quadrupole model are carried out for a set of particles moving in a single j-shell and for values of the coupling constants giving rise to the main features of strongly deformed nuclei. Two calculations are carried out and the corresponding results compared. In the first, particles are allowed to align in the mean field (particle aligned model). In the second, pairs of particles coupled to angular momentum λ = 0 and λ = 2 align themselves in the average field (pair aligned model).Although many features of the results are qualitatively similar, even for well deformed systems, there are important quantitative differences. In particular, the single-particle occupancies predicted by the pair aligned model display a diffusivity around the Fermi surface (effective pairing gap) which is ∼ 1.7 times larger than that predicted by the particle aligned model. The quadrupole moment predicted by the pair aligned model at maximum deformation is ∼ 1.4 smaller than that predicted by the particle aligned model. The pair aligned model and the particle aligned model thus describe two many-body systems which are rather different. In the first pairing correlations are as important as quadrupole correlations while in the second the quadrupole deformation plays the dominant role. The effect of allowing pairs of particles to couple to angular momenta λ > 2 is found to be essential to achieve quantitative agreement between the two models.