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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 ~ 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, $τ(\mathbf{\nabla}ρ)^2$ and $τ\frac{dρ}{dr}$, where $τ$ and $ρ$ 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 $τ\frac{dρ}{dr}$ term quenches the 1f5/2-1f7/2 splitting in 40Ca, which is strongly overestimated within conventional Skyrme parametrizations.