We provide a microscopic calculation of neutron-proton and neutron-neu
tron cross sections in symmetric nuclear matter at various densities,
using the Brueckner-Hartree-Fock approximation scheme with the Paris p
otential. We investigate separately the medium effects on the effectiv
e mass and on the scattering amplitude. We determine avenge cross sect
ions suitable for application in the dynamical simulation of heavy ion
collisions, including a parametrization of their energy and density d
ependence.