  Using various relativistic mean-field models, including the nonlinear ones
with meson field self-interactions, those with density-dependent meson-nucleon
couplings, and the point-coupling models without meson fields, we have studied
the isospin-dependent bulk and single-particle properties of asymmetric nuclear
matter. In particular, we have determined the density dependence of nuclear
symmetry energy from these different relativistic mean-field models and compare
the results with the constraints recently extracted from analyses of
experimental data on isospin diffusion and isotopic scaling in
intermediate-energy heavy ion collisions as well as from measured isotopic
dependence of the giant monopole resonances in even-A Sn isotopes. Among the 23
parameter sets in the relativistic mean-filed model that are commonly used for
nuclear structure studies, only a few are found to give symmetry energies that
are consistent with the empirical constraints. We have also studied the nuclear
symmetry potential and the isospin-splitting of the nucleon effective mass in
isospin asymmetric nuclear matter. We find that both the momentum dependence of
the nuclear symmetry potential at fixed baryon density and the
isospin-splitting of the nucleon effective mass in neutron-rich nuclear matter
depend not only on the nuclear interactions but also on the definition of the
nucleon optical potential.
