Hartree-Fock calculations of the semi-infinite superfluid nuclear matter by using Gogny D1 interaction

The Hartree-Fock calculations with Skyrme-type effective interactions give quite good results in describing the average basic properties of nuclei and nuclear matter. When one tries to extend this description to superfluid matter then the gap equation becomes divergent and usually one resorts to an angular momentum cut-off procedure. However, for finite range of interactions as the case of Gogny D1 is, that problem does not arise. On the other hand, it is known that the D1 force gives acceptable results for the pairing properties in finite nuclei. In their D1 calculations of infinite superfluid nuclear matter at the saturation point (kf 1.35 fm-1), Kucharek et al. have obtained a 7 MeV gap and a maximum value of 2.76 MeV for kf 0.82 fm-1. These results are in disagreement with the nuclear matter microscopic calculations which led to vanishing values for the energy gap. In addition, Kucharek et al. have shown that the correlation energies are in agreement with the Hartree-Fock-Bogolyubov calculations. In this work we proposed to make use of the semi-infinite nuclear matter model to evaluate the effect of the surface on the gap and correlation energies