On the sufficient conditions for the pseudospin symmetry in relativistic models

The reliability of the sufficient conditions for the pseudospin symmetry proposed for atomic nuclei has been analyzed, at a quantitative level, in the framework of the relativistic Hartree approximation (some effects of the exchange terms are also investigated). The contribution to the single-particle energy of the different terms appearing in the equation for the small component F of the Dirac spinor is calculated for the neutron pseudospin doublet states in the 40Ca and 208Pb nuclei. The F wave function is numerically calculated for the hypothetical case in which the symmetry is supposed to be exact.