  A set of relativistic mean field models is constructed including the Hartree
and Hartree-Fock approximation accounting for the exchange of isoscalar and
isovector mesons as well as the pion. Density dependent coupling functions are
determined to reproduce the components of the nucleon self-energy at the Fermi
surface, obtained within the Dirac-Brueckner-Hartree-Fock (DBHF) approach using
a realistic nucleon-nucleon interaction. It is investigated, to which extend
the various mean field models can reproduce the DBHF results for the momentum
dependence of the self-energies and the total energy of infinite matter. The
mean field models are also used to evaluate the bulk properties of spherical
closed-shell nuclei. We find that the Hartree-Fock model allowing for the
exchange of $\sigma,\,\omega,\,\rho,\,\delta$ mesons and pions, yield the best
reproduction of the DBHF results in infinite matter and also provides a good
description of the properties of finite nuclei without any adjustment of
parameters.
