Towards a Hartree-Fock Mass Formula

We first describe our nuclear mass formula HFBCS-1, the first to be based on the Hartree-Fock-BCS method. The fitted force is a conventional 10-parameter Skyrme force (t₀, t₁, t₂, and t₃ terms), along with a 4-parameter δ-function pairing force and a 2-parameter phenomenological Wigner term. The rms error of our fit to the 1888 measured nuclei with Z, N ≥ 8 is 0.738 MeV. The value of the effective mass M*/M that emerges from these fits is 1.05, which falls within the range of values long known to be necessary for a fit to single-particle (s.p.) level densities in the vicinity of the Fermi surface. On the other hand, realistic nuclear-matter calculations lead to M*/M ≃ 0.8, a result that is confirmed experimentally. By adding to the Skyrme force a term with simultaneous momentum and density dependence, M* becomes a non-monotonic function of density, and we find that it is possible to impose the realistic value of M*/M = 0.8 at nuclear-matter densities, i.e., at the centre of the nucleus, while maintaining an effective mean value over the nucleus of around 1.0, so that heavy-nucleus s.p. level densities are well reproduced in the Fermi surface. In this way we find acceptable mass fits even under the constraint of M*/M = 0.8 at nuclear-matter densities. Such forces should be useful in describing the nuclear processes that occur in stellar collapse and in decompressing nuclear matter.