Asymptotic evaluation of WKB matrix elements

Abstract

A procedure is given for the analytic asymptotic evaluation of certain integrals which arise in the quantum mechanical theory of inelastic molecular collisions. The integrals are evaluated using WKB wavefunctions and the saddle-point method. The method is equivalent to Landau's but is considerably more transparent and is easily applied to vibrational and rotational transitions for which there is no crossing of potential energy surfaces, as well as to electronic transitions near a crossing point. The special case of resonance collisions is discussed and the method is illustrated with an example.