Effects of Long-Lived Collisions in the Boltzmann Equation

Abstract

The general formulation of transport theory in gases does not take into account long-lived collisions or other properties of collision duration and molecular size that become especially important at higher densities. All these properties can be included in the theory in a uniform way by introducing the concept of the collision lifetime in addition to the collision cross section in the derivation of the equations of transport theory. A formulation of the classical Boltzmann equation is given in which the two-body collision term containing the collision lifetime explictly appears. In addition, two-body correction terms reflecting the spatial extension of the collision are derived.