Lipkin-Nogami pairing scheme in self-consistent nuclear structure calculations

We investigate the pairing treatment with approximate particle number projection, known as the Lipkin-Nogami scheme, in connection with nuclear Hartree-Fock models. A prescription for the pairing strength is developed. It is based on the average gap method and employs a Thomas-Fermi model to estimate the average level density at the Fermi surface. The second-order variation of the Skyrme energy functional gives feedback to the self-consistent density and thus to the mean field. This effect turns out to be small but non-negligible. The Lipkin-Nogami scheme is compared with the conventional treatment of pairing based on the BCS approximation. The bulk observables, especially those which are related to surface properties, depend on the pairing scheme employed, with the differences most noticeable for light nuclei. Pronounced effects on deformation energy surfaces were found, leading to sizable differences in the deformation energies.