Landau-Teller formula

The most simple way to accomplish this objective is to correct the external field operator post factum, as was repeatedly done in magnetic resonance theory, e.g. in [39]. Unfortunately this method is inapplicable to systems with an unrestricted energy spectrum. Neither can one use the method utilizing the Landau-Teller formula for an equidistant energy spectrum of the harmonic oscillator. In this simplest case one need correct... 

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

Landau-Teller Formula for VT-Relaxation Rate Coefficients... 

The formula can be rewritten for the rate coefficient of VT relaxation of a single vibrational quantum (Landau Teller, 1936), which is known as the Landau-Teller formula ... 

The Landau-Teller formula was generalized in SSH theory (Schwartz, Slawsky, Herzfeld, 1952) and, in particular, by Bilhng (1986). A semi-empirical numerical relation... 

The temperature dependence for the probability of VT relaxation for anharmonic oscillators (2-178) is similar to that of harmonic oscillators (2-172), (2-173), and corresponds to the Landau-Teller formula. The exponential parameter 5vx can be expressed for anharmonic oscillators as... 

CO2 molecules to the variation of their translational temperature, which can be found based on the Landau-Teller formula (see Chapter 2). Results of numerical calculations of the function Tq) (5-49) at an initial gas temperature Tq = 300K are shown in... 

After the time interval exceeds the critical one (t > tvt), the translational temperature growth becomes explosive (see Fig. 5-18). The explosion of To is due to the strong exponential dependence of the VT-relaxation rate on temperature (see Chapter 2, Landau-Teller formula). VT-relaxation deterMnes gas heating and increase of translational temperature, which then leads to an exponential acceleration of the VT relaxation and further and faster gas heating. A linear growth of translational temperature is limited by the characteristic time Tvt and, hence, by the maximum linear preheating before the explosion ... 

The most extreme case corresponds to pure VR energy exchange. This approximation was first formulated by Cottrell and Matheson [97] and later on by Moore [315] who replaced the relative velocity of translational motion in the Landau-Teller formula by the relative rotational velocity of partners at the point of their closest approach. The translational motion only helps to bring the colliding molecules into contact. 

At all events, the role of Coulombic forces for VET in solution was first examined in a molecular dynamics simulation for the 680 cm-1 C-Cl vibration of the CH3CI molecule (modeled as a diatomic) in water solvent by Whitnell et al. (19). The (classical) relaxation time Ti was determined both by nonequilibrium simulations and by use of the classical Landau-Teller (LT) formula (1,3,19,20). 

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