Real part of the neutron and proton optical potentials at 11 MeV for mass numbers 40

Abstract

The real part of the optical-model potentials for neutrons and protons with energy E=11 MeV and for targets with mass numbers 40\ensuremath{\le}A\ensuremath{\le}76 are calculated from two versions of a nuclear matter approach. The theoretical results are compared with compilations of empirical properties associated with phenomenological optical-model potentials for protons with energy 9\ensuremath{\le}E\ensuremath{\le}12 MeV and for neutrons with energy 8\ensuremath{\le}E\ensuremath{\le}15 MeV. Particular attention is paid to the difference between the neutron and proton optical potentials, to the dependence of the theoretical results on the density distributions of the protons and of the neutrons in the target nucleus, and to the role played by the density dependence of the effective interaction. Good agreement between calculated and empirical properties is obtained when one uses the neutron and proton density distributions of the self-consistent extended Thomas-Fermi model, and a recent version of the nuclear matter approach. The root mean square radius of the proton optical potential is larger than that of the neutron potential; it is shown that this has a twofold origin, namely the existence of a neutron excess in the surface tail on the one hand, and the difference between the density dependence of the isoscalar and isovector components of the effective interaction on the other hand.