NUCLEAR INCOMPRESSIBILITY AND DENSITY-DEPENDENT NN INTERACTIONS IN THE FOLDING MODEL FOR NUCLEUS-NUCLEUS POTENTIALS

A generalized version of density dependence has been introduced into t he M3Y effective nucleon-nucleon (NN) interaction that was based on th e G-matrix elements of the Paris NN potential. The density dependent p arameters have been chosen to reproduce the saturation binding energy and density of normal nuclear matter within a Hartree-Fock scheme, but with various values for the corresponding nuclear incompressibility K ranging from 176 to 270 MeV. We use these new density dependent inter actions in the folding model to calculate the real parts of alpha-nucl eus and nucleus-nucleus optical potentials for those systems where str ongly refractive scattering patterns have been observed. These provide some information on the potentials at short distances, where there is a strong overlap of the projectile and target density distributions, and hence where the density dependence of the interaction plays an imp ortant role. We try to infer, from careful optical model (OM) analyses , the sensitivity of the scattering data to different K values. Result s obtained for elastic alpha scattering on targets ranging from C-12 t o Pb-208 allow us to determine unambiguously that the K value favored in this approach is within the range of 240 to 270 MeV. Similar OM ana lyses have also been done an measurements of the elastic scattering of C-12+C-12, O-16+C-12, and O-16+O-16 at incident energies up to 94 MeV /nucleon. These data were found to be much less sensitive over such a narrow range of K values. This lack of sensitivity is due mainly to th e smaller maximum overlap density which occurs for these systems, comp ared to that which is formed in an alpha-nucleus collision. This makes the effects of density dependence less substantial. Another reason is that a small difference between two folded heavy ion potentials can o ften be compensated for, in part, by a small overall renormalization o f one of them. This renormalization is often allowed in optical model analyses, and interpreted, for example, as accounting for a contributi on from a higher-order dynamic polarization potential. In an attempt t o avoid this ambiguity, some OM analyses of the extensive and accurate data for O-16+O-16 scattering were done using the unrenormalized fold ed potentials, together with the explicit addition of a correction ter m, expressed in terms of cubic splines. This correction term can be in terpreted as representing a contribution to the real potential from th e dynamic polarization potential. The results of such a ''folding + sp line'' analysis suggest a tendency to favor the same K value range tha t was found in the OM analyses of alpha-nucleus scattering.