Molecular Collisions. III. Symmetric Top Molecules

Abstract

The question of rotational energy transfer in molecular collisions is treated for the case of symmetric top molecules. The Schrödinger equation for this problem, which can be taken as an integral equation over nine variables, is reduced to a set of coupled one dimensional integral equations by means of expansions over the irreducible representations of the three-dimensional rotation group. Various selection rules are found, of which two, in indices (in the matrix elements of the potential) related to the quantum number k, have no counterpart in the previously developed theory for diatomic molecules. The results are exhibited as cross sections for the excitation of rotational states, given the states before the collision. The rotational states for the symmetric top rotors are specified by the usual quantum numbers k, l, m, and the translational states by the velocity and direction of motion. The angular dependence of the cross section is treated by means of an expansion in spherical harmonics which is new in this context and which promises to be extremely useful in the application to transport processes.