Franck-Condon factors equivalence

Equation (A 1.6.94) is called the KHD expression for the polarizability, a. Inspection of the denominators indicates that the first temi is the resonant temi and the second temi is tire non-resonant temi. Note the product of Franck-Condon factors in the numerator one corresponding to the amplitude for excitation and the other to the amplitude for emission. The KHD fonnula is sometimes called the siim-over-states fonnula, since fonnally it requires a sum over all intennediate states j, each intennediate state participating according to how far it is from resonance and the size of the matrix elements that coimect it to the states i. and The KHD fonnula is fiilly equivalent to the time domain fonnula, equation (Al.6.92). and can be derived from the latter in a straightforward way. However, the time domain fonnula can be much more convenient, particularly as one detunes from resonance, since one can exploit the fact that the effective dynamic becomes shorter and shorter as the detuning is increased. 

Rn is usually given as a product of Franck-Condon factors corresponding to the so-called accepting modes which receive the energy released by the excited electronic state (Fong 1975). An estimation of Rs at OK can be made by the following analysis (Auzel 1980a). Let p be the probability for one of a set of S equivalent modes to jump to the next state. /A is the probability to have N simultaneous jumps in the same direction for... 

One of the new features of the photon echo phenomenon in the multilevel case is that not all initial pulse delays, t = t2 - t, are equivalent. If t is chosen such that g(t ) has returned to the Franck-Condon region, for instance, the echo will be more intense than otherwise. Furthermore, for other values of t the most complete echo may not be at t" = t , but will depend on choosing t" = t4- t3 such that Z(t" t ) and the extra phase factor are maximized. 

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