Stine, J. R. and Marcus, R. A. (1973) Semiclassical transition probabilities by an asymptotic evaluation of the S matrix for elastic and inelastic collisions. Bessel uniform approximation. Journal of Chemical Physics, 59 (9). pp. 5145-5150. ISSN 0021-9606 http://resolver.caltech.edu/CaltechAUTHORS:20120802-162507229
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It has been observed in the past that the usual Airy uniform approximation gives probabilities greater than one, especially for near elastic collisions. By mapping the phase onto −ζ cos y + ky + A rather than (1∕3)y^3 − ζy + A one obtains a uniform approximation involving Bessel functions of the first kind, which approaches unity for the elastic collision. This Bessel uniform approximation is no more complicated than the Airy and also gives good agreement with exact quantum results, even if probabilities are large.
|Additional Information:||© 1973 The American Institute of Physics. Received 29 June 1973. Supported in part by a grant from the National Science Foundation.|
|Official Citation:||Semiclassical transition probabilities by an asymptotic evaluation of the S matrix for elastic and inelastic collisions. Bessel uniform approximation J. R. Stine and R. A. Marcus, J. Chem. Phys. 59, 5145 (1973), DOI:10.1063/1.1680733|
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|Deposited On:||02 Aug 2012 23:55|
|Last Modified:||26 Dec 2012 15:48|
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