ASYMPTOTIC EVALUATION OF WKB MATRIX ELEMENTS

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.