Collision kernels for the Waldmann-Snider equation: generalization to gas mixtures

In this paper we generalize the collision kernel method, which had only been worked out for the test particle limit of the linearized Waldmann-Snider equations, to the general linearized Waldmann-Snider equations for non-equilibrium gas mixtures of finite concentration. By using the total angular momentum representation for the transition matrix and a suitable coordinate transformation, which takes advantage of the rotational symmetries of the kernel, the ten-dimensional collision integrals are reduced to sets of two-dimensional integrals. The transformation by Hilbert of the classical Boltzmann equation for rigid spheres to a Fredholm integral equation with symmetric kernel has thus been extended to the Waldmann-Snider equation for diatomic molecules. This transformation enables the extension of collocation methods, which have been profitably used with model Boltzmann equations, to quantum Boltzmann equations that describe the kinetic theory of gases with real molecules.