Microscopic calculation of the symmetry and Coulomb components of the complex optical-model potential

Abstract

We first investigate how the mass operator for symmetric and uncharged nuclear matter is modified in the presence of a Coulomb field and of neutron excess. Detailed calculations are performed with Reid's hard-core nucleon-nucleon interaction. They are carried out in the framework of the Brueckner-Hartree-Fock approximation, although some higher-order contributions to the low-density expansion of the mass operator are also considered. We relate the mass operator to the optical-model potential. We then use a local density approximation to construct the optical-model potential in a finite nucleus. We find that the half-depth radius of the isoscalar part of the calculated optical-model potential has the form ${r}_{V}{A}^{\frac{1}{3}}$, where $A$ denotes the mass number. Since this property has always been assumed in the phenomenological analysis of the scattering data, a meaningful comparison is possible between our theoretical results for the symmetry and for the Coulomb components of the optical-model potential on the one hand, and the empirical values of these quantities as determined from the analysis of proton and neutron elastic scattering data or of direct charge exchange reactions on the other hand. The calculated depth of the symmetry potential is 11.5 MeV, but its range is larger than that of the isoscalar potential. The calculated value of the so-called Coulomb correction is larger than the one that is assumed in most empirical analyses. The combined effect of these features yields good overall agreement between the calculated and the empirical dependence on neutron excess of the optical-model potential.NUCLEAR REACTIONS Calculation of the symmetry and Coulomb components of the optical-model potential from Reid's hard-core nucleon-nucleon interaction.