  The key question in the interaction of antinucleons in the nuclear medium
concerns the deepness of the antinucleon-nucleus optical potential. In this
work we study this task in the framework of the non-linear derivative (NLD)
model which describes consistently bulk properties of nuclear matter and Dirac
phenomenology of nucleon-nucleus interactions. We apply the NLD model to
antinucleon interactions in nuclear matter and find a strong decrease of the
vector and scalar self-energies in energy and density and thus a strong
suppression of the optical potential at zero momentum and, in particular, at
FAIR energies. This is in agreement with available empirical information and,
therefore, resolves the issue concerning the incompatibility of G-parity
arguments in relativistic mean-field (RMF) models. We conclude the relevance of
our results for the future activities at FAIR.

Nuclear Theory