Theory of Semiclassical Transition Probabilities for Inelastic and Reactive Collisions. II Asymptotic Evaluation of the S Matrix

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摘要：

The asymptotic evaluation of the integral representation for anSmatrix element in a previously developed semiclassical theory of molecular collisions is considered. The integral representation is evaluated asymptotically by the method of Chester, Friedman, and Ursell to give a uniform approximation for theSmatrix element which is valid for classically accessible and classically inaccessible transitions. The results unify and extend those previously derived, which were restricted to the simple semiclassical and Airy function cases. A comparison is made with the simple, Airy, and uniform semiclassical approximations that occur in Miller's semiclassical theory of molecular collisions. Although the starting point of the two theories is different, it is concluded that their asymptotic results are essentially identical. In addition, a simpler derivation of the integral representation for anSmatrix element from the semiclassical wavefunction is given, one which avoids the use of Green's theorem.

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关键词：

n32240* --physics--atomic & molecular physics--collision phenomena asymptotic solutions chemical reactions inelastic scattering s- matrix collision processes/s matrix for inelastic and reactive, asymptotic evaluation of

DOI：

10.1063/1.1675732

被引量：

364

年份：

1971