  With applications in astroparticle physics in mind, we generalize a method
for the solution of the nonlinear, space homogeneous Boltzmann equation with
isotropic distribution function to arbitrary matrix elements. The method is
based on the expansion of the matrix element in terms of two cosines of the
"scattering angles". The scattering functions used by previous authors in
particle physics for matrix elements in Fermi-approximation are retrieved as
lowest order results in this expansion. The method is designed for the unified
treatment of reactive mixtures of particles obeying different scattering laws,
including the quantum statistical terms for blocking or stimulated emission, in
possibly large networks of Boltzmann equations. Although our notation is the
relativistic one, as it is used in astroparticle physics, the results can also
be applied in the classical case.
