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Spin and pseudospin symmetries in the spectra of nucleons and antinucleonsare studied in a relativistic mean-field theory with scalar and vectorWoods-Saxon potentials, in which the strength of the latter is allowed tochange. We observe that, for nucleons and antinucleons, the spin symmetry is ofperturbative nature and it is almost an exact symmetry in the physical regionfor antinucleons. The opposite situation is found in the pseudospin symmetrycase, which is better realized for nucleons than for antinucleons, but is ofdynamical nature and cannot be viewed in a perturbative way both for nucleonsand antinucleons. This is shown by computing the spin-orbit andpseudospin-orbit couplings for selected spin and pseudospin partners in bothspectra.

Spin and pseudospin symmetries in the antinucleon spectrum of nuclei