Nonlocal in-medium 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[ρ,β]. We use the Argonne v₁₈ 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 δg-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 ≈65 MeV, at momentum transfers q below ≈10.28em0exfm^-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.