||An analytical expression is derived for average vibrational energy lost or gained [Delta E-v] per collinear collision of an atom and a diatom. The derivation, based on classical mechanics, uses the perturbative method of the variation of constants and is valid in the weak coupling limit. Second-order results for [Delta E-v] are obtained in terms of power spectra of the uncoupled vibrational and translational degrees of freedom. The classical results are compared to perturbative quantum calculations, and differences between the two are described. (C) 1999 Elsevier Science B.V. All rights reserved.