  Spin and pseudospin symmetries in the spectra of nucleons and antinucleons
are studied in a relativistic mean-field theory with scalar and vector
Woods-Saxon potentials, in which the strength of the latter is allowed to
change. We observe that, for nucleons and antinucleons, the spin symmetry is of
perturbative nature and it is almost an exact symmetry in the physical region
for antinucleons. The opposite situation is found in the pseudospin symmetry
case, which is better realized for nucleons than for antinucleons, but is of
dynamical nature and cannot be viewed in a perturbative way both for nucleons
and antinucleons. This is shown by computing the spin-orbit and
pseudospin-orbit couplings for selected spin and pseudospin partners in both
spectra.
