  The properties of nucleon-nucleon scattering inside dense nuclear matter are
investigated. We use the relativistic Brueckner-Hartree-Fock model to determine
on-shell and half off-shell in-medium transition amplitudes and cross sections.
At finite densities the on-shell cross sections are generally suppressed. This
reduction is, however, less pronounced than found in previous works. In the
case that the outgoing momenta are allowed to be off energy shell the
amplitudes show a strong variation with momentum. This description allows to
determine in-medium cross sections beyond the quasi-particle approximation
accounting thereby for the finite width which nucleons acquire in the dense
nuclear medium. For reasonable choices of the in-medium nuclear spectral width,
i.e. $\Gamma\leq 40$ MeV, the resulting total cross sections are, however,
reduced by not more than about 25% compared to the on-shell values. Off-shell
effect are generally more pronounced at large nuclear matter densities.
