  Two different approximation schemes for the self-consistent solution of the
relativistic Brueckner-Hartree-Fock equation for finite nuclei are discussed
using realistic One-Boson-Exchange potentials. In a first scheme, the effects
of correlations are deduced from a study of nuclear matter and parameterized in
terms of an effective $\sigma$, $\omega$ and $\pi$ exchange. Employing this
effective interaction relativistic Hartree-Fock equations are solved for finite
nuclei \osi , \caf\ and \cafe . In the second approach the effect of
correlations are treated in the Brueckner-Hartree-Fock approximation directly
for the finite nuclei, but the modifications of the Dirac spinors in the medium
are derived from nuclear matter assuming a local-density approximation. Both
approaches yield rather similar results for binding energies and radii in fair
agreement with experimental data. The importance of the density dependent
correlation effects is demonstrated and different ingredients to the spin-orbit
splitting in the shell-model of the nucleus are discussed.
