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

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 Sigma G(mu nu)a(mu)(dagger)a((u) over bar)(dagger)a(<(nu)over bar>)a(nu), 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 Hf-176, 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.