Collision kernels and transport coefficients

Abstract

A connection is made between classical transport theory and the usual description of collisional processes in laser spectroscopy. In classical transport theory, collisional processes are described in terms of either transport coefficients or collision integrals. In analyzing the influence of collisions on laser spectroscopic line shapes, collisions are often described in terms of collision kernels. Two sets of equations are obtained relating the collision integrals to the collision kernels. While these two sets of equations are equivalent for any physically realistic kernel, they need not be equivalent if one carries out calculations using phenomenological kernels. If the two methods give similar collision integrals for a phenomenological collision kernel, it may serve as a justification for the use of that kernel. We show that the two methods do give very similar results for the Keilson-Storer kernel but give dramatically different results for a ``difference'' kernel (a kernel that is a function of the difference between the initial and final velocity). The calculations, carried out for a low-density binary gas mixture, provide a link between classical transport theory and the collision kernels commonly used in analyzing experiments in laser spectroscopy. Implications of the results to experimental situations of current interest, such as light-induced drift, are explored.