Inelastic Molecular Collisions: Exponential Solution of Coupled Equations for Vibration–Translation Energy Transfer

Abstract

A new numerical method is used to solve the quantum‐mechanical problem of energy transfer between vibrational and translational degrees of freedom in collisions between an oscillator and an atom. The dependence of the probability of vibrational excitation on the energy of the collision and the size of the truncated basis set is examined. The oscillatory dependence of this transition probability on the energy is is shown to be an artifact due to the truncation of the basis set. The new numerical method is the stepwise solution of the coupled first‐order differential equations by exponentiation of the integrated coupling matrices, an application of the general method investigated by Magnus. It is shown to be fast and accurate.