Optical-model potential in finite nuclei from Reid's hard core interaction

Abstract

Starting from the Brueckner-Hartree-Fock approximation and Reid's hard core nucleon-nucleon interaction, we calculate and parametrize the energy---and the density---dependence of the isoscalar, isovector, and Coulomb components of the complex optical-model potential in infinite nuclear matter, for energies up to 160 MeV. We then construct the optical-model potential in a finite nucleus. In a first step, we adopt a local density approximation which implies that the value of the complex potential at each point of the nucleus is the same as in a uniform medium with the local density. We compute the corresponding volume integrals per nucleon and mean square radii of the real and of the imaginary parts of the optical-model potential, in particular for protons scattered by $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{27}\mathrm{Al}$, $^{40}\mathrm{Ca}$, $^{58}\mathrm{Ni}$, $^{120}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$. We compare these results with a compilation of empirical values and find that the calculated and experimental volume integrals are in good agreement but that the theoretical mean square radii are too small. We ascribe this discrepancy to the fact that our local density approximation does not include accurately the effect in a nonuniform medium of the range of the effective interaction. We include this range in a semiphenomenological way suggested by the Hartree approximation. With a reasonable value for this range parameter, which is the only one occurring in our work, good agreement is obtained between the theoretical and the empirical values of the volume integrals and mean square radii of the real and, to a lesser extent, of the imaginary parts of the optical-model potential, for mass numbers $12\ensuremath{\le}A\ensuremath{\le}208$ and for energies $E$ up to 160 MeV. Our results are given in analytic form and can thus be used in analyses of experimental data. We also discuss the difference between the optical-model potentials for protons and for neutrons.[NUCLEAR REACTIONS Calculation of the complex optical-model potential for finite nuclei from Reid's hard core interaction; comparison with a compilation of empirical potentials.]