  The Lagrangian density of relativistic mean-field (RMF) theory with
non-linear derivative (NLD) interactions is applied to isospin asymmetric
nuclear matter. We study the symmetry energy and the density and energy
dependences of nucleon selfenergies. At high baryon densities a soft symmetry
energy is obtained. The energy dependence of the isovector selfenergy
suppresses the Lane-type optical potential with increasing energy and predicts
a $\rho$-meson induced mass splitting between protons and neutrons in isospin
asymmetric matter.
