  Using an energy density functional (EDF) based on the thermodynamic
Gibbs-Duhem relation, found equivalent to the standard Skyrme EDF for infinite
nuclear matter, it is demonstrated that the parameters of this EDF are not
uniquely determined from the fit of the empirical and theoretical data related
to nuclear matter. This prevents an unambiguous determination of the nucleon
effective mass ($\frac{m_0^*}{m}$) and its isovector splitting ($\Delta
m_0^*$). Complementary information from dipole polarizability of atomic nuclei
helps in removing this ambiguity and plausible values of $\frac{m_0^*}{m}$ and
$\Delta m_0^*$ can be arrived at. Presently considered fit data on infinite
nuclear matter and dipole polarizability of finite nuclei yield
$\frac{m_0^*}{m} =0.68 \pm 0.04 $ and $\Delta m_0^* =(-0.20 \pm 0.09)\delta $.
This EDF is consistent with the constraint on the maximum mass of the neutron
star.
