Transport Properties of a Gas of Diatomic Molecules. IV. Classical Limit

The differential cross sections for rotational excitation in collisions of diatomic molecules may be expressed in terms of the generalized phase shift, $\mathrm{H}\mathrm{(l̄}{\mathrm{S}}_a{\mathrm{S}}_b)$ . As with the usual phase shift, $\mathrm{\eta (l̄)}$ , a semiclassical expansion of ${\mathrm{\hslash \; H(l̄S}}_a{\mathrm{S}}_b)$ begins with a term of zero order in $\hslash$ . Unlike the expansion of $\mathrm{\hslash \; \eta (l̄)}$ , however, the next term in the expansion of ${\mathrm{\hslash \; H(l̄S}}_a{\mathrm{S}}_b)$ is a purely imaginary term of order $\hslash$ . The effect of this term in the expansion on the classical limit of certain sums and integrals of the cross sections related to the transport coefficients is considered.