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 $g[\rho ,\beta ]$. 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 $\delta g$-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 $\approx 65$ MeV, at momentum transfers $q$ below $\approx 1{\mathrm{fm}}^{-1}$, 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.

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• Elastic scattering reactions
• Nuclear forces
• Nuclear many-body theory
• Nuclear reactions
• Nucleon-nucleon interactions
• Optical, coupled-channel & distorted wave models