Relativistic Hartree-Fock description of nuclei

A relativistic nuclear Hamiltonian is constructed, from which the relativistic Hartree and Hartree-Fock equations are derived. Then the Hartree equations are applied to ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ nuclei taking as input different relativistic one-boson-exchange potentials as well as the effective interaction of Walecka, introduced in his theory of highly condensed matter. Single-particle energies turn out to be of the correct magnitude. In particular, it is possible to explain the magnitude of the spin-orbit splitting without any free parameter.