Exact pairing calculations in a large Nilsson-model basis: comparison with BCS and Lipkin-Nogami methods

Abstract

Abstract Full many-body calculations of the spectra of heavy deformed nuclei become prohibitively large and one is forced to employ approximate mean-field methods. The deformation is accounted for by a deformed single-particle potential (e.g. Nilsson model), the rotation by a one-body cranking term and the pairing forces by the introduction of non-interacting quasiparticles. Some properties, however, [e.g. the moments of inertia of multi-quasiparticle (MQP) bands] are rather sensitive to details of the pairing correlations. In this case it would be preferable to account for the pairing exactly and evaluate the moments of inertia in a configuration-mixing calculation or a Harris-type perturbation theory. We show that by exploiting the symmetries of the general state-dependent pairing force of the form ∑G μν a μ † a μ † a ν a ν , the pairing correlations in the band heads of these states, and any states with which they will strongly mix, can be calculated exactly in a large Nilsson-model basis. For 176Hf, where many MQP bands are known and where the neutron and proton level densities are relatively low, a detailed comparison is made with the results of the BCS and Lipkin-Nogami approximations. While a reasonably good representation of the spectra can be obtained with a renormalisation of the pairing strength, there remain significant discrepancies in the single-particle occupations produced by these methods.