  After reviewing our microscopic approach to nuclear and neutron-rich matter,
we focus on how nucleon-nucleon scattering is impacted by the presence of a
dense hadronic medium, with special emphasis on the case where neutron and
proton densities are different. We discuss in detail medium and isospin
asymmetry effects on the total elastic cross section and the mean free path of
a neutron or a proton in isospin-asymmetric nuclear matter. We point out that
in-medium cross sections play an important role in heavy-ion simulations aimed
at extracting constraints on the symmetry potential. We argue that medium and
isospin dependence of microscopic cross sections are the results of a complex
balance among various effects, and cannot be simulated with a simple
phenomenological model.
