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By:J. W. Rich,R. G. Rehm
Published on 1967 by


The terms in the master equation for vibrational relaxation of anharmonic oscillators are ordered according to the rates of the relaxation processes (vibrational exchange, vibrational-energy transfer to translation). A perturbation procedure is developed by making use of the fact that the vibration-translation energy exchange transitions are much slower than the vibration-vibration transitions. The population distributions in the master equation are expanded about their values when the vibration-vibration mechanism is the only one present. To zeroth order, the master equation is satisfied by a distribution derived previously by Treanor for anharmonic oscillators. This distribution is maintained by vibration-vibration exchange, and is only Boltzmann during relaxation in the limit of vanishing anharmonicity. The perturbation on this distribution, created by vibration energy transfer to translation, is calculated to first order for a special case. The relaxation of the first moment of the zeroth-order distribution function is also investigated. The population of the lowest vibrational states can be considerably lower than the population predicted by the Landau-Teller model for the relaxation process. Furthermore, since the inversion tends to weight those states having fast vibration-to-translation energy transfer rates, the overall energy relaxation rate can be accelerated. (Author).

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