Spin-orbit splitting in non-relativistic and relativistic self-consistent models

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