CaltechAUTHORS
  A Caltech Library Service

Semiclassical transition probabilities by an asymptotic evaluation of the S matrix for elastic and inelastic collisions. Bessel uniform approximation

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

[img]
Preview
PDF - Published Version
See Usage Policy.

336Kb

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20120802-162507229

Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.1680733DOIUNSPECIFIED
http://jcp.aip.org/resource/1/jcpsa6/v59/i9/p5145_s1PublisherUNSPECIFIED
Additional Information:© 1973 The American Institute of Physics. Received 29 June 1973. Supported in part by a grant from the National Science Foundation.
Funders:
Funding AgencyGrant Number
NSFUNSPECIFIED
Record Number:CaltechAUTHORS:20120802-162507229
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120802-162507229
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
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32898
Collection:CaltechAUTHORS
Deposited By: Aucoeur Ngo
Deposited On:02 Aug 2012 23:55
Last Modified:26 Dec 2012 15:48

Repository Staff Only: item control page