  Nuclear matter and neutron stars are studied in the framework of an extended
relativistic mean-field (RMF) model with higher-order derivative and density
dependent couplings of nucleons to the meson fields. The derivative couplings
lead to an energy dependence of the scalar and vector self-energies of the
nucleons. It can be adjusted to be consistent with experimental results for the
optical potential in nuclear matter. Several parametrisations, which give
identical predictions for the saturation properties of nuclear matter, are
presented for different forms of the derivative coupling functions. The stellar
structure of spherical, non-rotating stars is calculated for these new
equations of state (EoS). A substantial softening of the EoS and a reduction of
the maximum mass of neutron stars is found if the optical potential constraint
is satisfied.
