ASYMPTOTIC METHODS IN ASYMMETRIC ROTOR $THEORY^{*}$
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Date
1963
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Ohio State University
Abstract
“Asymptotic methods for the treatment of asymmetric rotor problems in the domain of high J and low $K^{1}$ have been generalized in two ways: (1) A non-linear differential equation with periodic coefficients takes the place of the linear Mathieu type equation, which has first been used by $Golden^{2}$ to calculate approximately asymmetric rotor eigenvalues, and which has served as starting point to derive asymptotic formulas in reference 1. The characteristic matrix of this non-linear equation is infinite, but its elements are exactly identical with the elements of a reduced form of the asymmetric rotor matrix within their domain of definition. (2) A procedure permitting extension of asymptotic expansions for eigenvalues and eigenfunctions of the Mathieu equation into the domain of noticeable symmetry type splitting has recently been developed by Dingle and $Mueller.^{3}$ This procedure is now adapted to the derivation of the corresponding asymptotic formulas in asymmetric rotor theory for energy levels and transitions for which symmetry-type splittings are noticeable but still small. The inclusion of such symmetry type corrections extends appreciably the domain of applicability of the asymptotic methods.”
Description
$^{*}$Supported by the Geophysics Research Directorate, Air Force Cambridge Research Laboratories. $^{1}$E. K. Gora, International Symposium on Molecular Structure and Spectroscopy, Tokyo, 1962. Paper C, 208-1. $^{2}$S. Golden, J. Chem. Phys. 16, 78 (1948). $^{3}$R. B. Dingle and H. W. Mueller, Journal fuer Mathematik, 211, 11 (1962).
Author Institution: Physics Department, Providence College
Author Institution: Physics Department, Providence College