Nonlocality parameters of microscopic optical potentials from Skyrme-based nuclear structure models at low energies

We investigate the non-locality parameters $\beta$ in nucleon-nucleus interactions for $^{16}\mathrm{O}$, $^{40}\mathrm{Ca}$, $^{48}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$ using a microscopic optical potential (MOP) derived from nuclear structure models based on Skyrme self-consistent mean-field calculations at low incident energies. No ad hoc adjusted parameters were employed in the present calculations. The analysis reveals that the non-locality parameter exhibits a clear dependence on the radial position within the nucleus, the incident nucleon energy, and the choice of target nucleus. At incident energies below $30$ MeV, the $\beta$ lies between $0.8$ fm and $1.2$ fm for all considered targets. For the light nucleus $^{16}\mathrm{O}$, the non-locality parameter in the interior is smaller than that on the surface, whereas for medium and heavy nuclei $( ^{40}\mathrm{Ca}$, $^{48}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$ ), the values are comparable in both regions.