Connor, J. N. L. and Marcus, R. A. (1971) Theory of Semiclassical Transition Probabilities for Inelastic and Reactive Collisions. II Asymptotic Evaluation of the S Matrix. Journal of Chemical Physics, 55 (12). pp. 5636-5643. ISSN 0021-9606. http://resolver.caltech.edu/CaltechAUTHORS:CONjcp71
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The asymptotic evaluation of the integral representation for an S matrix 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 the S matrix 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 an S matrix element from the semiclassical wavefunction is given, one which avoids the use of Green's theorem.
|Additional Information:||©1971 The American Institute of Physics. Received 29 July 1971. We have benefited from discussions with Dr. W.H. Wong. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. This research was also supported by a grant from the National Science Foundation at the University of Illinois.|
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|Deposited On:||29 Sep 2008 17:35|
|Last Modified:||26 Dec 2012 10:19|
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