  Realistic density dependent CDM3Yn versions of the M3Y interaction have been
used in an extended Hartree-Fock (HF) calculation of nuclear matter (NM), with
the nucleon single-particle potential determined from the total NM energy based
on the Hugenholtz-van Hove theorem that gives rise naturally to a rearrangement
term (RT). Using the RT of the single-nucleon potential obtained exactly at
different NM densities, the density- and energy dependence of the CDM3Yn
interactions was modified to account properly for both the RT and observed
energy dependence of the nucleon optical potential. Based on a local density
approximation, the double-folding model of the nucleus-nucleus optical
potential has been extended to take into account consistently the rearrangement
effect and energy dependence of the nuclear mean-field potential, using the
modified CDM3Yn interactions. The extended double-folding model was applied to
study the elastic $^{12}$C+$^{12}$C and $^{16}$O+$^{12}$C scattering at the
refractive energies, where the Airy structure of the nuclear rainbow has been
well established. The RT was found to affect significantly the real
nucleus-nucleus optical potential at small internuclear distances, giving the
potential strength close to that implied by the realistic optical model
description of the Airy oscillation.
