  The density dependent relativistic hadron field (DDRH) theory is applied to
strongly asymmetric nuclear matter and finite nuclei far off stability. A new
set of in-medium meson-nucleon vertices is derived from Dirac-Brueckner
Hartree-Fock (DBHF) calculations in asymmetric matter, now accounting also for
the density dependence of isovector coupling constants. The scalar-isovector
$\delta$ meson is included. Nuclear matter calculations show that it is
necessary to introduce a momentum correction in the extraction of coupling
constants from the DBHF self-energies in order to reproduce the DBHF equation
of state by DDRH mean-field calculations. The properties of DDRH vertices
derived from the Groningen and the Bonn A nucleon-nucleon (NN) potentials are
compared in nuclear matter calculations and for finite nuclei. Relativistic
Hartree results for binding energies, charge radii, separation energies and
shell gaps for the Ni and Sn isotopic chains are presented. Using the momentum
corrected vertices an overall agreement to data on a level of a few percent is
obtained. In the accessible range of asymmetries the $\delta$ meson
contributions to the self-energies are found to be of minor importance but
asymmetry dependent fluctuations may occur.
