Rearrangement in folding potentials with density-dependent nucleon-nucleon interaction

We discuss optical potentials for the nuclear elastic scattering from a variational viewpoint. Density-dependence in the effective $N$-$N$ interaction leads to density rearrangement terms, in addition to the conventional folding term. Effects of the rearrangement on the $N$-$A$ optical potential are illustrated in the nuclear-matter limit. Closely relating to consistency with the saturation, the rearrangement appreciably improves the isoscalar optical potential depth over the previous folding model calculations. The rearrangement gives stronger effects as the density grows. We also present rearrangement terms in the $A$-$A$ double-folding potential. Since the rearrangement terms are relevant to the nuclear structure but should be handled within the reaction model, $N$-$N$ effective interactions applicable both to structure models and to the folding model will be desired for unambiguous description of the nuclear elastic scattering.