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Journal of Physics B Atomic and Molecular Physics

Excitation transfer, broadening and shift of the lines in nearly resonant collisions between two isotopes

J. C. Gay

Published May 11, 1977• 3 citations
Publisher

Abstract

The cross sections for the excitation transfer between H and D atoms deduced from two previous publications are compared to those given by Kohmoto and Watanabe (1976). They are found to be in good agreement. The evidence for other effects such as the modification of the broadening and shift of the lines which are characteristic of these quasi-resonant processes is also emphasized and discussed.

DOI
10.1088/0022-3700/10/7/016

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The cross sections for the excitation transfer between H and D atoms deduced from two previous publications are compared to those given by Kohmoto and Watanabe (1976). They are found to be in good agreement. The evidence for other effects such as the modification of the broadening and shift of the lines which are characteristic of these quasi-resonant processes is also emphasized and discussed.
The cross sections for the excitation transfer between unlike atoms are calculated by the impact parameter method. Approximate formulas for discrete-continuum and discrete-discrete transition probabilities are obtained. The cross section can be obtained by integrating this probability over the impact parameter. The approximate formula is applied to the case of Deuterium-Hydrogen excitation transfer as one of practical examples. Comparisons are made with two other formulas, i. e. Rosen-Zener (R-Z) and Vanishtein-Presnyakov-Sobelman (V-P-S) formulas. The dependence of the cross section on the resonance defect in the discrete-discrete case is also investigated. The agreements among these three formulas are found not very good.
The cross sections for rubidium $5^{2}P_{\frac{1}{2}}\ensuremath{\rightleftarrows}5^{2}P_{\frac{3}{2}}$ and cesium $6^{2}P_{\frac{1}{2}}\ensuremath{\rightleftarrows}6^{2}P_{\frac{3}{2}}$ excitation transfer due to inert-gas collisions have been measured. The temperature of the collision vessel has been varied from 300\ifmmode^\circ\else\textdegree\fi{}K to 900\ifmmode^\circ\else\textdegree\fi{}K in order to partially establish the velocity dependence of these cross sections (the alkali resonance-line optical depths were always much less than 1). The various cross sections exhibit a systematic behavior that can be combined to find the general shape of a "universal" cross section that ranges across six orders of magnitude, starting just below the threshold for "sudden" collisions. The surprisingly large influence of optical line broadening on these excitation-transfer measurements has been removed as a source of error.
The experimental results for the self-broadening of pure Tl of the previous paper are shown to be in good agreement with the theory of resonant collisions, taking into account the effects of the hyperfine structure. Wall collisions are nearly negligible in that case. The decrease of the self-broadening observed with the addition of a foreign gas is explained in terms of three-body collisions (Tl-He collisions occurring during a Tl*-Tl collision) which broaden the optical transitions of Tl and decrease the resonance effect in the transfer of excitation between Tl atoms. The quantitative agreement obtained with the experimental results shows that these three-body collisions must be responsible for the major part of the observed reduction in self-broadening.
A general theory of line broadening is used to study the effects of collisions on absorption line shapes when self-broadening is important. Special attention is focused on the role of processes in which an excited atom transfers its electronic excitation to an unexcited atom; it is this process which distinguishes self-broadening from foreign-gas broadening. Several forms for the absorption rate are presented corresponding to particular assumptions about the amplitudes associated with this phenomenon. For example, one approximation leads to a generalized Lorentz-Lorenz law in which the one-atom polarizability is replaced by one that accounts for line broadening. Finally, the importance of many-body effects in the calculation of the linewidth is briefly discussed to determine when simple impact theories are applicable.