Kreek, H. and Ellis, R. L. and Marcus, R. A. (1975) Semiclassical collision theory. Application of multidimensional uniform approximations to the atom-rigid-rotor system. Journal of Chemical Physics, 62 (3). pp. 913-926. ISSN 0021-9606 http://resolver.caltech.edu/CaltechAUTHORS:20120809-141336648
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The multidimensional Bessel and Airy uniform approximations developed earlier in this series for the semiclassical S matrix are applied to the atom rigid−rotor system. The need is shown for (a) using a geoemetrical criterion for determining whether a stationary phase point (s.p.pt) is a maximum, minimum, or saddle point; (b) choosing a proper quadrilateral configuration of the s.p.pts. with the phases as nearly equal as possible; and (c) choosing a unit cell to favor near−separation of variables. (a) and (b) apply both to the Airy and to the Bessel uniform approximations, and (c) to the Bessel. The use of a contour plot both to understand and to facilitate the search in new cases is noted. The case of real and complex−valued stationary phase points is also considered, and the Bessel uniform−in−pairs approximation is applied. Comparison is made with exact quantum results. As in the one−dimensional case, the Bessel is an improvement over the Airy for ’’k = 0’’ transitions, while for other transitions they give similar results. Comparison in accuracy with the results of the integral method is also given. As a whole, the agreement can be considered to be reasonable. The improvement of the present over various more approximate results is shown.
|Additional Information:||© 1975 American Institute of Physics. Received 26 September 1974. Supported by a grant from the National Science Foundation.|
|Subject Keywords:||atom−molecule collisions; semiclassical approximation; s matrix; bessel functions; airy functions; rotational states|
|Classification Code:||PACS: 34.50.Ez; 03.65.Sq|
|Official Citation:||Semiclassical collision theory. Application of multidimensional uniform approximations to the atom--rigid-rotor system H. Kreek, R. L. Ellis, and R. A. Marcus, J. Chem. Phys. 62, 913 (1975), DOI:10.1063/1.430543|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Aucoeur Ngo|
|Deposited On:||09 Aug 2012 21:46|
|Last Modified:||26 Dec 2012 15:55|
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