  A study of the nucleon mean-field potential in nuclear matter (NM) is done
within an extended Hartree-Fock (HF) formalism, using the CDM3Y6 density
dependent version of the M3Y interaction which is associated with the nuclear
incompressibility $K\simeq 252$ MeV. The momentum dependence of nucleon optical
potential (OP) in NM at the saturation density $\rho_0$ is shown to be due
mainly to its exchange term up to $k\approx 2$ fm$^{-1}$, so that the Pauli
nonlocality is expected to be the main origin of the nucleon effective mass at
low momenta. Because nucleons in neutron-rich NM at $\rho\approx \rho_0$ are
either weakly bound or unbound by the in-medium nucleon-nucleon interaction,
the determination of the effective mass of nucleon scattered on targets with
neutron excess at low energies should be of interest for the mean-field studies
of neutron star matter. For this purpose, the folding model is used to
calculate the nonlocal nucleon OP for the optical model analysis of elastic
nucleon scattering on $^{40,48}$Ca, $^{90}$Zr, and $^{208}$Pb targets at
energies $E<50$ MeV, to probe the model reliability and validate the WKB local
approximation to obtain the local folded nucleon OP. The nucleon effective mass
$m^*$ is then carefully deduced from the momentum dependence of the local
folded nucleon OP which is resulted from the Pauli nonlocality of the exchange
term. The neutron-proton effective mass splitting determined at
$\rho\approx\rho_0$ from the central strength of the real folded nucleon OP for
$^{48}$Ca, $^{90}$Zr, and $^{208}$Pb targets has been found to depend linearly
on the neutron-proton asymmetry parameter as $m^*_{n-p}\approx (0.167\pm
0.018)\delta$, in a good agreement with the recent empirical constraints.
