Multiquantum Vibrational-Energy Exchange

Abstract

A theory for exchange of vibrational quanta between molecules is formulated which does not rely on the Born expansion of the $S$ matrix. A transformation is derived which diagonalizes the vibrational operators responsible for exchange. The scattering operator is then expanded in a series of rotational tensor operators which permits evaluation of $S$-matrix elements to all orders. This formulation shows that multiquantum processes, both rotational and vibrational, play an important role when transition moments are large. Numerical calculations for vibrational exchange rates of carbon monoxide are compared with results of the first Born approximation from which they differ significantly. The dependence of the cross section on vibrational-energy defect is much less drastic than that of the Born approximation. The present calculations indicate that cross sections for the exchange of more than one vibrational quantum are substantial, in marked contrast to the Born approximation where they are forbidden. The size of these multiquantum cross sections indicates that they can play an important role in the detailed kinetic modeling of CO lasers.