Spin-Orbit Splitting in Non-Relativistic and Relativistic Self-Consistent Models

The splitting of single-particle energies between spin-orbit partners in nuclei is examined in the framework of different self-consistent approachs, non-relativistic as well as relativistic. Analytical expressions of spin-orbit potentials are given for various cases. Proton spin-orbit splittings are calculated along some isotopic chains (O, Ca, Sn) and they are compared with existing data. It is found that the isotopic dependence of the relativistic mean field predictions is similar to that of some Skyrme forces while the relativistic Hartree-Fock approach leads to a very different dependence due to the strong non-locality.