Equation Landau-Teller

As long as repulsive interaction is dominant, there is no ftmdamental difference in the theoretical description between the quenching of ions and the quenching of neutral molecules. This problem was solved first by Landau and Teller (1936), leading to the famous Landau-Teller equation for the vibrational quenching rate constant. 

We can thus summarize the necessary conditions for an efficient energy transfer (i.e., a resonance function near unity). At a given energy gap, the resonance function 7 ( ) will be exponentially small at low velocities, and will increase with increasing velocities. This version is the form most useful for colhsion theory. An indirect illustration of this exponential gap principle is the strong positive temperature dependence of the V—T relaxation rate. For most diatomic molecules the temperature dependence is best fitted 1 a so-called Landau-Teller equation... 

Laguerre polynomials 3-D. /-space 264 eigenfunctions 119, 262-3 Raman and CARS spectra 120 Landau-Teller formula 159 Langevin model equation 32... 

Here is a fascinating result if the harmonic scheme of Equation (18) is applied to Equation (14), using Equation (12) for Ti recovers exactly the classical Landau-Teller result, as recently shown by Bader and Berne (16). Thus, if the oscillator and bath are both harmonic and are bilinearly coupled, the exact quantum result and the exact classical result are identical This provides some justification for using the purely classical result of Equation (13) even in situations where one clearly is not in the classical limit. 

Note that for /3fiLandau-Teller result of Equation (13). 

This is the famous result of Landau and Teller. In many of the more detailed theories, to be discussed below, this result appears explicitly as the principal contribution to the dependence of transition probability on temperature. In practical units, equation (6) is frequently written in the form ... 

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