Nuclear Physics A 727 (2003) 269–298 www.elsevier.com/locate/npe Pseudo-spin–orbit potential in the relativistic Hartree–Fock formalism M. López-Quelle a,∗ , L.N. Savushkin b , S. Marcos c , P. Bernardos d , R. Niembro c a Departamento de Física Aplicada, Universidad de Cantabria, E-39005 Santander, Spain b Department of Physics, St. Petersburg University for Telecommunications, 191065 St. Petersburg, Russia c Departamento de Física Moderna, Universidad de Cantabria, E-39005 Santander, Spain d Departamento de Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, E-39005 Santander, Spain Received 22 July 2002; received in revised form 13 June 2003; accepted 22 July 2003 Abstract The pseudo-spin symmetry (PSS) is investigated in the framework of the relativistic Hartree–Fock approximation (RHFA). The Dirac equation is reduced to a Schrödinger like equation for the small component of the nucleon spinor. Though this equation reveals that the symmetry appears to be broken even in the Σ D S + Σ D 0 = 0 limit, where Σ D S and Σ D 0 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 40 Ca and 48 Ca 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.  2003 Elsevier B.V. All rights reserved. PACS: 24.10.Jv; 21.60.Jz; 24.80.+y Keywords: Pseudo-spin symmetry; Relativistic Hartree–Fock approach * Corresponding author. E-mail address: lopezqm@unican.es (M. López-Quelle). 0375-9474/$ – see front matter  2003 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2003.07.012