Three-Particle Collision Integrals for a Gas of Hard Spheres

Abstract

In order to predict the first density corrections to the transport coefficients of gases, it is necessary to evaluate collision integrals which account for the correlations in the position and velocity variables of three molecules. These correlations are both of a statistical and dynamical nature. For a gas of hard spheres the statistical correlations reduce to excluded volume effects and the dynamical correlations are brought about by sequences of binary collisions among three molecules. It is shown how a systematic analysis of these two types of correlations leads to a decomposition of the three‐particle collision integrals in terms of symmetric collision integrals associated with the dynamics of one, two, three, and four successive collisions among three molecules. These collision integrals are derived explicitly for the coefficients of thermal conductivity, viscosity, and self‐diffusion.