Nonlocal <i>in-medium</i> effective interaction for nucleon scattering off isospin-asymmetric targets

We have investigated the role of isospin asymmetry of the NN effective interaction in the context of NA elastic scattering. To this purpose we represent the in-medium $g$ matrix as an admixture of isospin-symmetric nuclear matter and pure neutron matter solutions of Brueckner-Hartree-Fock equations for infinite nuclear matter, denoted as $g[\ensuremath{\rho},\ensuremath{\beta}]$. We use the Argonne ${v}_{18}$ bare potential to represent the NN interaction in free space, due to its ability to describe the NN scattering amplitudes up to 350 MeV. The density-dependent isospin-asymmetric $g$ matrices are then used to calculate optical model potentials for elastic nucleon scattering off closed-shell nuclei. For this aim, we make use of the Arellano-Bauge $\ensuremath{\delta}g$-folding approach suited for an explicit treatment of nonlocal density matrices. This approach allows one to account for the local isospin-asymmetry and density dependence of the in-medium NN interaction. The resulting optical potentials are nonlocal since the entire nonlocal structure of the $g$ matrix is retained. We observe that including the isospin asymmetry in the $g$ matrix allows for a reasonable description of differential cross sections at nucleon beam energies between 40 and 200 MeV. In the case of proton scattering at energies below $\ensuremath{\approx}65$ MeV, at momentum transfers $q$ below $\ensuremath{\approx}1\phantom{\rule{0.28em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1}$, the inclusion of neutronic-matter $g$ matrices yields better agreement with the data as compared to the case when symmetric nuclear matter $g$ matrices are used. These results provide evidence that the isospin-asymmetry in the NN effective interaction yield non-negligible effects in nucleon scattering off isospin-asymmetric targets at beam energies below 65 MeV.