  Calculations for infinite nuclear matter with realistic nucleon-nucleon
interactions suggest that the isoscalar effective mass (IEM) of a nucleon at
the saturation density equals $m^*/m\sim 0.8\pm 0.1$, at variance with
empirical data on the nuclear level density in finite nuclei which are
consistent with $m^*/m\approx 1$. This contradicting results might be
reconciled by enriching the radial dependence of IEM. In this work four new
terms are introduced into the Skyrme-force inspired local energy-density
functional: $\tau(\nabla\rho)^2$, $\tau\frac{d\rho}{dr}$, $\tau^2$ and
$\tau\Delta\rho$. The aim is to investigate how they influence the radial
dependence of IEM and, in turn, the single-particle spectra.
