Abstract

An expression for vibrational energy transfer cross sections has been derived, assuming an electromagnetic interaction, using the quantum first Born approximation. An exact solution has been obtained for the total cross section, which must then be averaged numerically over velocity and rotational state distributions. The formula is valid even when the energy defect becomes of the order of or larger than kT. The theory has been applied to energy transfer between two linear molecules, which occurs via long-range near-resonant processes involving the infrared transition moments of each molecule. The resulting thermally averaged cross sections agree with experiment to within a factor of 2. This represents an improvement of several orders of magnitude when ΔE ≥ kTover previous calculations based on the approximate solution to a semi-classical first Born approximation first obtained by Van Kranendonk¹ and extended by Sharma and Brau and Cross and Gordon.² This expression is applied to previous and new experimental measurements of energy flow in CO₂ and N₂O and their isotopically substituted analogs, providing an effective probe of rate processes of importance to molecular infrared lasers.

© 1986 Optical Society of America