  Relativistic self-consistent mean-field (SCMF) models naturally account for
the coupling of the nucleon spin to its orbital motion, whereas
non-relativistic SCMF methods necessitate a phenomenological ansatz for the
effective spin-orbit potential. Recent experimental studies aim to explore the
isospin properties of the effective spin-orbit interaction in nuclei. SCMF
models are very useful in the interpretation of the corresponding data, however
standard relativistic mean-field and non-relativistic Hartree-Fock models use
effective spin-orbit potentials with different isovector properties, mainly
because exchange contributions are not treated explicitly in the former. The
impact of exchange terms on the effective spin-orbit potential in relativistic
mean-field models is analysed, and it is shown that it leads to an isovector
structure similar to the one used in standard non-relativistic Hartree-Fock.
Data on the isospin dependence of spin-orbit splittings in spherical nuclei
could be used to constrain the isovector-scalar channel of relativistic
mean-field models. The reproduction of the empirical kink in the isotope shifts
of even Pb nuclei by relativistic effective interactions points to the
occurrence of pseudospin symmetry in the single-neutron spectra in these
nuclei.
