Isotropic matrix elements of the collision integral for the Boltzmann equation

Abstract

We have proposed an algorithm for constructing matrix elements of the collision integral for the nonlinear Boltzmann equation isotropic in velocities. These matrix elements have been used to start the recurrent procedure for calculating matrix elements of the velocity-nonisotropic collision integral described in our previous publication. In addition, isotropic matrix elements are of independent interest for calculating isotropic relaxation in a number of physical kinetics problems. It has been shown that the coefficients of expansion of isotropic matrix elements in Ω integrals are connected by the recurrent relations that make it possible to construct the procedure of their sequential determination.