  The nucleon mean-field potential has been thoroughly investigated in an
extended Hartree-Fock (HF) calculation of nuclear matter (NM) using the CDM3Y3
and CDM3Y6 density dependent versions of the M3Y interaction. The
single-particle (s/p) energies of nucleons in NM are determined according to
the Hugenholtz-van Hove theorem, which gives rise naturally to a rearrangement
term (RT) of the s/p potential at the Fermi momentum. Using the RT obtained
exactly at the different NM densities and neutron-proton asymmetries, a
consistent method is suggested to take into account effectively the momentum
dependence of the RT of the s/p potential within the standard HF scheme. To
obtain a realistic momentum dependence of the nucleon optical potential (OP),
the high-momentum part of the s/p potential was accurately readjusted to
reproduce the observed energy dependence of the nucleon OP over a wide range of
energies. The impact of the RT and momentum dependence of the s/p potential on
the density dependence of the nuclear symmetry energy and nucleon effective
mass has been studied in details. The high-momentum tail of the s/p potential
was found to have a sizable effect on the slope of the symmetry energy and the
neutron-proton effective mass splitting at supranuclear densities of the NM.
Based on a local density approximation, the folding model of the nucleon OP of
finite nuclei has been extended to take into account consistently the RT and
momentum dependence of the nucleon OP in the same mean-field manner, and
successfully applied to study the elastic neutron scattering on the lead target
at the energies around the Fermi energy.
