Non-locality function of microscopic optical potentials from Skyrme-based nuclear structure models at low energies

Abstract

The non-locality of the imaginary part of the microscopic optical potential is investigated for neutron elastic scattering on $^{16}$O, $^{40}$Ca, $^{48}$Ca, and $^{208}$Pb at incident energies up to 30~MeV. The potential is derived within the particle-vibration coupling framework using fully self-consistent Skyrme-Hartree-Fock plus RPA calculations with the SLy5 interaction, without \textit{ad hoc} adjustable parameters. By fitting the non-locality coordinate dependence of the absorptive potential $W(R,s) \equiv \mathrm{Im}\,\Delta\Sigma$, where $\Delta\Sigma$ is the dynamical part of the nucleon self-energy, to a Gaussian form at representative volume and surface radial positions, we extract the radius- and energy-dependent non-locality function $\beta(R,E)$, whose values range from $1.01$ to $2.03$~fm, with a clear dependence on radial position, incident energy, and target mass. These results demonstrate that, for the absorptive part of the optical potential, a single universal constant such as the Perey--Buck value $\beta = 0.85$~fm cannot capture the radial, energy, and target-mass dependence of the non-locality, and that nucleus-dependent, energy-dependent, and radially-resolved descriptions of the absorptive potential $W$ are required for precision nuclear reaction calculations.