Vibrational Relaxation of Anharmonic Oscillators with Exchange-Dominated Collisions

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). The population distributions in the master equation are expanded about their values when the vibration-vibration mechanism is the only one present. An analytic expression is given for the distribution maintained by the vibration-vibration mechanism. In the limiting case of the simple harmonic oscillator, this distribution reduces to the usual Boltzmann-like distribution defined by a single vibrational temperature. The general solution also applies to a mixture of simple-harmonic-oscillator gases of different fundamental frequencies. For such a mixture, each gas relaxes in a Boltzmann-like distribution, but the different gases have different (but related) vibrational temperatures at any given time. The relaxation of the first moment of the distribution function also has been investigated. Anharmonicity causes a marked departure from the Landau-Teller model of vibrational relaxation under conditions of high vibrational energy, coupled with low translational temperature. For such conditions, the populations of the lower vibrational states can be considerably lower than those predicted by the Landau-Teller model. Furthermore, the over-all energy relaxation rate can be accelerated.