  We present Dirac-Brueckner-Hartree-Fock calculations for isospin asymmetric
nuclear matter which are based on improved approximations schemes. The
potential matrix elements have been adapted for isospin asymmetric nuclear
matter in order to account for the proton-neutron mass splitting in a more
consistent way. The proton properties are particularly sensitive to this
adaption and its consequences, whereas the neutron properties remains almost
unaffected in neutron rich matter. Although at present full Brueckner
calculations are still too complex to apply to finite nuclei, these
relativistic Brueckner results can be used as a guidance to construct a density
dependent relativistic mean field theory, which can be applied to finite
nuclei. It is found that an accurate reproduction of the
Dirac-Brueckner-Hartree-Fock equation of state requires a renormalization of
these coupling functions.
