  The mean free paths and in-medium scattering cross sections of energetic
nucleons in neutron-rich nucleonic matter are investigated using the nucleon
optical potential obtained within the relativistic impulse approximation with
the empirical nucleon-nucleon scattering amplitudes and the nuclear densities
obtained in the relativistic mean field model. It is found that the
isospin-splitting of nucleon mean free paths, sensitive to the imaginary part
of the symmetry potential, changes its sign at certain high kinetic energy. The
in-medium nucleon-nucleon cross sections are analytically and numerically
demonstrated to be essentially independent of the isospin asymmetry of the
medium and increase linearly with density in the high energy region where the
relativistic impulse approximation is applicable.
