Probability distribution transition moment derivation

Induction forces, on the other hand, may be responsible for the enchanced V y intensity. The squared transition moment expected for the dimer with two independent ethylene partners is twice that of the monomer. Inspection of Table 1 shows that the observed probability is somewhat higher than this. Vibration in each molecule induces oscillations in the polarizable charge distribution of the partner, leading to an enhanced dipole moment derivative. Numerical results for bound to a polarizable atom show that this enhancement is of the same magnitude as that observed (17). 

Ao and Rammer [166] obtained the same result (and more) on the basis of a fully quantum mechanical treatment. Frauenfelder and Wolynes [78] derived it from simple physical arguments. Equation (9.98) predicts a quasiadiabatic result, = h k/ v 1 and the Golden Rule result, Pk = k/ v, in the opposite limit, which is qualitatively similar to the Landau-Zener behavior of the transition probability but the implications are different. Equation (9.98) is the result of multiple nonadiabatic crossings of the delta sink although it does not depend on details of the stochastic process Xj- t). This can be understood from the following consideration. For each moment of time, the fast coordinate has a Gaussian distribution, p Xf, t) = (xy — Xj, transition region, the fast coordinate crosses it very frequently and thus forms an effective sink for the slow coordinate. 

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