Nuclear Surface Properties with a Simple Effective Interaction

Abstract

A simple three-part density-dependent effective interaction is used to calculate several general properties of the semiinfinite nuclear surface. This interaction, which is referred to here as the modified $\ensuremath{\delta}$ interaction (MDI), is quite similar to one introduced by Skyrme. The three parameters of the MDI are fixed by fitting the binding energy and density of infinite nuclear matter with $N=Z$ and also the ground-state energy of $^{16}\mathrm{O}$, all in first-order perturbation theory.The nuclear surface properties are calculated in several different ways. First, they are extracted directly from the single-particle wave functions of a one-dimensional static Woods-Saxon potential. The diffuseness and depth of the potential are obtained by minimizing the surface energy. This procedure is called the independent particle model (IPM). The resulting surface thickness of 2.2 fm and surface energy of 19.3 MeV and the approximately Fermi shape of the density distribution are in good agreement with empirical results.The calculations were then repeated using the Thomas-Fermi approximation to obtain the density. The resultant surface thickness and surface energy, 2.0 fm and 16.0 MeV, are considerably smaller than the IPM results. Furthermore, the calculated density distribution has a longer "shoulder" inside the nucleus and a shorter "tail" outside than the IPM distribution.