Energy dependence of theNNtmatrix in the optical potential for elastic nucleon-nucleus scattering

Abstract

The influence of the energy dependence of the free $\mathrm{NN}$ $t$ matrix on the optical potential of nucleon-nucleus elastic scattering is investigated within the context of a full-folding model based on the impulse approximation. The treatment of the pole structure of the $\mathrm{NN}$ $t$ matrix, which has to be taken into account when integrating to negative energies, is described in detail. We calculate proton-nucleus elastic scattering observables for ${}^{16}$O, ${}^{40}$Ca, and ${}^{208}$Pb between 65 and 200 MeV laboratory energy and study the effect of the energy dependence of the $\mathrm{NN}$ $t$ matrix. We compare this result with experiment and with calculations where the center-of-mass energy of the $\mathrm{NN}$ $t$ matrix is fixed at half the projectile energy. It is found that around 200 MeV the fixed energy approximation is a very good representation of the full calculation; however, deviations occur when going to lower energies (65 MeV).