Test of the validity of the SD truncation for deformed systems

Abstract

We have tested the basic assumption of the interacting boson model stating that only pairs of particles coupled to angular momentum 0 and 2 are important to the description of low-lying nuclear spectra, even for deformed systems. Variational solutions of the pairing plus quadrupole hamiltonian are obtained for a system of particles moving in a realistic set of single-particle orbitais. Two calculations are carried out based on the field approximation. The first corresponds to the quasiparticle Nilsson model, in which pairs of particles can couple to all values of Λ allowed by the angular momentum selection rule. In the second, pairs of particles are restricted to couple to angular momentum Λ = 0 and Λ = 2. Although most of the predicted values of the different observables are qualitatively similar in the two models, the underlying many-body pictures are very different. Restricting pairs of particles to couple to angular momentum Λ = 0 and Λ = 2 leads to a system in which pairing correlations are as strong as quadrupole correlations. On the other hand, quadrupole correlations are dominant in the Nilsson plus BCS model. Pairs of particles coupled to angular momentum Λ > 2 thus seem to play a decisive role in obtaining the many-body correlations appropriate to strongly deformed systems.