On the Collisional Transfer of Rovibronic and Translational Energy between Differently Excited Like Molecules

Abstract

In line with the principle of the first Born approximation, we give a simple treatment of the comprehensive transfer of rotation, vibration, and electronic and translational (rovibronic-translational) energy in the collisions between (electronically) differently excited like molecules. It is shown that the electronic exchange degeneracy between the collision partners gives rise to first-order (long-range) dispersion forces which may result in large energy transfer cross sections. The formalism is for diatomic or linear molecules, with or without electronic angular momentum, and may be easily adapted to symmetric-top molecules. A first-order, general (electronic) multipole-multipole interaction is used as the scattering potential, which is written as a contraction of tensors. The transition matrix elements are evaluated by Racah's method, showing the explicit dependence on the conserved total angular momentum as well as on the angular momenta of the individual molecules and the angular momentum of the relative orbital motion. The relative motion is treated as a plane wave. Coupled representations with definite total angular momentum and alternatively uncoupled representations of the wavefunction (in the Appendix) are used to derive the matrix elements and cross-sections. The general case of small vibronic energy discrepancies is considered. Differential cross sections as well as total cross sections are given explicitly. Under the assumption of long-range electronic interaction and fast electronic transition, the cross sections are shown to be proportional to Franck-Condon overlap integrals, multipole rotational transition line strengths, and Bessel function integrals for the relative motion. The necessary reduced matrix elements for the multipole transition and for the relative motion are computed and discussed. Assuming the validity of the Born-Oppenheimer approximation, i.e., no vibronic interaction and no rotation-electronic interaction, etc., the effect of permuting the nuclei of like molecules of the same nuclear spin is shown to be unimportant if the permanent dipoles of the states are small. This treatment of energy transfer should be applicable to differently excited states (of like molecules) between which there are large multipole transition moments, which interact in the first order because of the exchange degeneracy.