A procedure is given for the analytic asymptotic evaluation of certain integrals which arise in the quantumhyphen;mechanical theory of inelastic molecular collisions. The integrals are evaluated using WKB wavefunctions and the saddlehyphen;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 potentialhyphen;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.
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