"Nuclear matter" approach to the energy dependence of the real part of the proton-nucleus optical potential at intermediate incident energies

Abstract

We present and discuss here the results of a calculation of the real part of the potential energy of a proton within nuclear matter, making use of the realistic Reid soft-core nucleon-nucleon interaction, which we justify in the intermediate-energy range. The problem of evaluating the volume of the real part of the proton-nucleus optical-model potential as a function of incident energy is solved with the help of a number of techniques previously developed in the literature of nuclear-matter theory. We find good agreement with results of various phenomenological studies over an energy range of 100 to 1050 MeV incident proton energy for targets $^{40}\mathrm{Ca}$ and $^{208}\mathrm{Pb}$, which we adopt as test cases. Furthermore, we consider a number of higher-order corrections to our initial result; all of these have minimal effect in the energy regime we have considered except for the third-order correction proposed by Rajaraman, as we demonstrate and discuss. Finally, we show that the conventional approach to the nucleon-nucleus potential at medium energy, the so-called Rayleigh-Lax potential, which makes use of a straightforward impulse approximation and an empirical nucleon-nucleon scattering amplitude, is in gross disagreement both with phenomenological findings concerning the energy dependence of the optical potential and with results of the present calculations. We make an effort to shed some light on the physical reasons for the failure of the Rayleigh-Lax approach, as opposed to the success of other approaches relying upon realistic nucleon-nucleon interactions or phase shifts rather than an empirical medium-energy nucleon-nucleon $T$ matrix.[NUCLEAR REACTIONS $^{40}\mathrm{Ca}(p,p)$, $^{208}\mathrm{Pb}(p,p)$, $E=100\ensuremath{-}1050$ MeV; nuclear matter approach used to estimate volume of real part proton-nucleus optical model potential, multiple-scattering formalism, numerical estimates of various higher-order terms.]