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