Correlations in microscopic optical model for nucleon elastic scattering off doubly closed-shell nuclei

Abstract

The random phase approximation (RPA) long-range correlations are known to play a significant role in understanding the depletion of single particle-hole states observed in ($e,{e}^{'}$) and ($e,{e}^{'}p$) measurements. Here the RPA theory, implemented using the D1S force is considered for the specific purpose of building correlated ground states and related one-body density matrix elements. These may be implemented and tested in a fully microscopic optical model for NA scattering off doubly closed-shell nuclei. A method is presented to correct for the correlations overcounting inherent to the RPA formalism. One-body density matrix elements in the uncorrelated (i.e., Hartree-Fock) and correlated (i.e., RPA) ground states are then challenged in proton scattering studies based on the Melbourne microscopic optical model to highlight the role played by the RPA correlations. Agreement between the parameter free scattering predictions and measurements is good for incident proton energies ranging from 200 MeV down to approximately 60 MeV and becomes gradually worse in the lower energy range. Those features point unambiguously to the relevance of the g-matrix method to build microscopic optical model potentials at medium energies, and emphasize the need to include nucleon-phonon coupling, that is, a second-order component of the Feshbach type in the potential at lower energies. Illustrations are given for proton scattering observables measured up to 201 MeV for the $^{16}\mathrm{O}$, $^{40}\mathrm{Ca}$, $^{48}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$ target nuclei.