Single Particle Energies in Skyrme Hartree-Fock and Woods-Saxon Potentials

Atomic nuclei exhibit the interesting phenomenon of single-particle motion that can be described within the mean field approximation for the many-body system. We have carried out Hartree-Fock calculations for a wide range of nuclei, using the Skyrme-type interactions. We have examined the resulting mean field potentials U$_{HF}$ by fitting r$^{2}$ U$_{HF}$ to r$^{2}$U$_{WS}$, where U$_{WS}$ is the commonly used Woods-Saxon potential. We consider, in particular, the asymmetry (x=(N-Z)/A) dependence in U$_{WS}$ and the spin-orbit splitting in the spectra of of $^{17}$F$_{8}$ and the recently measured spectra of $^{23}$F$_{14}$. Using U$_{WS}$, we obtained good agreement with experimental data.