Matrix elements of the Boltzmann collision operator for gas mixtures

Abstract The matrix elements of the collision operators that arise in the linearization of the Boltzman equations for gas mixtures are calculated. The matrix representatives of the operators with the Burnett functions (products of Laguerre polynomials and spherical harmonics) are evaluated for power law potentials. The final expressions for the matrix elements involve a small number of summations and for the hard sphere cross section, analytic expressions in terms of the mass ratios are obtained.