Laguerre polynomial solutions to master equation for vibrational energy relaxation in gases

Abstract

Collisional energy transfer between highly vibrationally excited molecules and a bath gas is considered as a stochastic process occurring in energy space. An exact solution to master equation for the conditional probability is given in terms of simple analytical formulas for weak and strong collisions. The strong collisions are shown to manifest themselves in the distribution pattern composed of maxima and minima in the energy dependence of conditional probability. This effect is explained in detail on physical grounds.