Schwartz-Slawsky-Herzfeld model

Quantitative calculations of the rate constants ky y for vibrational transitions are relatively easy if the diatomic molecules are simulated by a harmonic oscillator interacting isotropically with the impinging atom (the so-called breathing sphere or the SSH (Schwartz-Slawsky-Herzfeld) model [3, 192, 339, 395] based on the one-dimensional Landau-Teller model [261]). Then the mean transition probability Py y per one gas-kinetic collision calculated to the first order of the semiclassical perturbation treatment is... 

To date, the theoretical results most useful for the discussion of collision induced intramolecular energy exchange have come from grossly oversimplified models of the collision. The most widely used of these models was proposed by Schwartz, Slawsky, and Herzfeld (SSH) and later modified by Tanczos and Stretton. ... 

A simple well-known extension of a collinear Landau-Teller model is provided by the breathing sphere (BSP) model of Schwartz, Slawsky and Herzfeld [13] which fully retains the Landau-Teller exponential factor. More consistent treatment, which approximately takes into account the anisotropic character of the atom-molecule interaction, is based on the so-called infinite order sudden approximation (lOSA) [14] with respect to rotational transitions that accompany the vibrational transition. Within this approximation the rotation of the relaxing molecule plays the role of a spectator, which insignificantly modifies the exponent in Eq. (8) through quite unimportant redefinition of a. If, in addition, the quasiclassical correction to the semiclassical Landau-Teller exponent is small and the effect of the attractive part of the potential is weak, one can write the following simple expression for the deactivation rate constant within BSP or lOSA approximation ... 

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