Second golden rule, Fermi

This is an application of Fermi s golden rule. The first term is the square of the matrix element of the perturbation, which appears in all versions of perturbation theory. In the second term 8(x) denotes the Dirac delta function. For a full treatment of this function we refer to the literature [2]. Here we note that S(x) is defined such that S(x) = 0 for x 7 0 at the origin S(x) is singular such that / ( r) dx — 1. The term 8 (Ef — Ei) ensures energy conservation since it vanishes unless... 

According to Section IV.A.3, for each wave vector K such that gcTK > A , there is an imaginary solution of (4.25). Thus, since localized states have a projection on every K> state, a very fast photon emission occurs (coherent emission) in the direction determined by K. In second-order perturbation theory124 126 (Fermi s golden rule"), / K takes values between 0 and x for... 

In the non-adiabatic limit, the rate constant for ET is determined in the lowest (i.e., the second) order in /. Therefore, the rate constant is given by Fermi s Golden Rule,... 

Finally, it may be useful to note that the Fermi golden rule and time correlation function expressions often used (see ref. 12, for example) to express the rates of electron transfer have been shown [13], for other classes of dynamical processes, to be equivalent to LZ estimates of these same rates. So, it should not be surprising that our approach, in which we focus on events with no reorganization energy requirement and we use LZ theory to evaluate the intrinsic rates, is closely related to the more common approach used to treat electron transfer in condensed media where the reorganization energy plays a central role in determining the rates but the z factor plays a second central role. 

The second theoretical approach is quantum mechanical in nature and is based on the Fermi Golden Rule expression for nonradiative decay processes [45,46]... 

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