Proton \textit{s}-resonance states of $^{12}$C and $^{14,15}$O within the Skyrme Hartree-Fock mean-field framework

Abstract

The excitation functions of proton elastic scattering on $^{12}$C and $^{14,15}$O nuclei at the energies near the proton-emission threshold are calculated using the Skyrme Hartree-Fock (SHF) in continuum approach. For each excitation function, the first resonance is identified as the $s$-state resonance of the mean-field theory. For $^{15}$O, whose ground-state spin is nonzero, the $s$-state resonance splits into two resonances via the spin-spin component of the optical potential. With a slight adjustment of the strength of central potential, which is obtained from the SHF in continuum approach, the excitation functions of proton elastic scattering for the three nuclei can be explained with high accuracy. The proposed framework can provide a practical method to explain nuclear scattering at the energies near the proton-emission threshold with minimal experimental input.