Surface-peaked effective mass in the nuclear energy density functional and its influence on single-particle spectra

Calculations for infinite nuclear matter with realistic nucleon-nucleon interactions suggest that the isoscalar effective mass of a nucleon at the saturation density m*/m equals 0.8 +/- 0.1. This result is at variance with empirical data on the level density in finite nuclei, which are consistent with m*/m approximate to 1. Ma and Wambach suggested that these two contradicting results may be reconciled within a single theoretical framework by assuming a radial-dependent effective mass, peaked at the nuclear surface. The aim of this exploratory work is to investigate this idea within the density functional theory by using a Skyrme-type local functional enriched with new terms, tau(Delta rho)(2) and tau(d rho/dr), where tau and rho denote the kinetic and particle densities, respectively. We show that each of these terms can give rise to a surface peak in the effective mass, but of a limited height. We investigate the influence of the radial profile of the effective mass on the spin-orbit splittings and centroids. In particular, we demonstrate that the tau(d rho/dr) term quenches the 1f(5/2)-1f(7/2) splitting in Ca-40, which is strongly overestimated within conventional Skyrme parametrizations.