Three-Particle Collisions in a Gas of Hard Spheres

The triple-collision integrals which determine the first density correction to the transport coefficients are derived for a gas of hard spheres using the binary-collision expansion. This expansion provides a convenient technique for classifying the contributions in terms of sequences of successive binary collisions between three molecules. Such sequences contain both interacting and noninteracting collisions. It is demonstrated that for three hard spheres all sequences terminate after four successive collisions, Independent of the interacting or noninteracting nature of the collisions. As a consequence, the collision integrals are related to a limited number of sequences with three and four collisions only. It is shown that equivalent results are obtained from the surface-integral form of the triple-collision operator, derived earlier by Green and Sengers.