Classical, diatomic molecule, kinetic theory cross sections. III. Rigid body models

Expressions are developed for the generalized or kinetic theory cross sections of a gas of diatomic molecules, modeled as rigid, cylindrically symmetric bodies. The rigid bodies are described by ’’supporting functions’’ and the expressions reduced to forms involving integrations over the final translational energy, the final rotational energies of each molecule, and five angles. The expression for any particular cross section may then be obtained in the form of a double integral; as an example such a result is obtained for the ’’viscosity’’ cross section. As a more detailed example, an explicit expression for this cross section for the ’’loaded sphere’’ model is then obtained to second order in the displacement of the load from the geometric center; this result is consistent with the earlier result obtained as the classical limit of the quantum expression.