Realistic density dependent CDM3Yn versions of the M3Y interaction have beenused in an extended Hartree-Fock (HF) calculation of nuclear matter (NM), withthe nucleon single-particle potential determined from the total NM energy basedon the Hugenholtz-van Hove theorem that gives rise naturally to a rearrangementterm (RT). Using the RT of the single-nucleon potential obtained exactly atdifferent NM densities, the density- and energy dependence of the CDM3Yninteractions was modified to account properly for both the RT and observedenergy dependence of the nucleon optical potential. Based on a local densityapproximation, the double-folding model of the nucleus-nucleus opticalpotential has been extended to take into account consistently the rearrangementeffect and energy dependence of the nuclear mean-field potential, using themodified CDM3Yn interactions. The extended double-folding model was applied tostudy the elastic $^{12}$C+$^{12}$C and $^{16}$O+$^{12}$C scattering at therefractive energies, where the Airy structure of the nuclear rainbow has beenwell established. The RT was found to affect significantly the realnucleus-nucleus optical potential at small internuclear distances, giving thepotential strength close to that implied by the realistic optical modeldescription of the Airy oscillation.
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