Pseudo-spin-orbit potential in the relativistic Hartree-Fock formalism

The pseudo-spin symmetry (PSS) is investigated in the framework of the relativistic Hartree-Fock approximation (RHFA). The Dirac equation is reduced to a Schroedinger like equation for the small component of the nucleon spinor. Though this equation reveals that the symmetry appears to be broken even in the ΣSD+Σ0D=0 limit, where ΣSD and Σ0D are the direct (Hartree) scalar and time component of the vector nucleon self-energies, respectively, pseudo-spin symmetry is approximately conserved. The behavior of the single-particle potentials and of the wave functions of both neutron and proton pseudo-spin doublets in the 40Ca and 48Ca nuclei are analyzed. There is no dominance of the term dependent on the pseudo-orbital angular momentum (containing the pseudo-centrifugal barrier) compared to the pseudo-spin-orbit potential (PSOP). The contributions to the energy of each pseudo-spin doublet (PSD) level coming from all terms entering the equation for the small component of the Dirac spinor are calculated. The quasi-degeneracy of the PSD levels in the RHFA can be explained by a compensation of the differences between these contributions. The effect of the self-consistency is comparable to that of the PSOP itself