  With a view towards implementation in microscopic transport simulations of
heavy-ion collisions, the properties of spin-isospin modes are studied in
nuclear matter consisting of nucleons and Delta isobars that interact by the
exchange of pi and rho mesons. For a standard p-wave interaction and an
effective g' short-range interaction, the dispersion relations for the spin-
isospin modes, and the associated amplitudes, are calculated at various nuclear
densities and temperatures, within the random-phase approximation. Quantities
of physical interest are then extracted, including the total and partial Delta
decay widths and the Delta cross sections in the nuclear medium. The
self-consistent inclusion of the Delta width has a strong effect on the Delta
cross sections at twice normal nuclear density, as compared with the result of
ignoring the width. Generally, the obtained quantities exhibit a strong density
dependence, but are fairly insensitive to the temperature, at least up to T=25
MeV. Finally, it is described how these in-medium effects may be consistently
included into microscopic transport simulations of nuclear collisions, and the
improvements over previous approaches are discussed.
