Fermi golden rule formula

The first type of interaction, associated with the overlap of wavefunctions localized at different centers in the initial and final states, determines the electron-transfer rate constant. The other two are crucial for vibronic relaxation of excited electronic states. The rate constant in the first order of the perturbation theory in the unaccounted interaction is described by the statistically averaged Fermi golden-rule formula... 

The expression for the rate R (sec ) of photon absorption due to coupling V beriveen a molecule s electronic and nuclear charges and an electromagnetic field is given through first order in perturbation theory by the well known Wentzel Fermi golden rule formula (7,8) ... 

Within the framework of first-order perturbation theory, the rate constant is given by the statistically averaged Fermi golden rule formula ... 

Note that the results derived from this definition are equivalent to those derived from Fermi s golden rule [23]. Hence we refer to them as a Fermi s golden rule formula. 

As the bright state mixes with more and more dark states, the resultant lineshape evolves toward a smooth Lorentzian shape (Bixon and Jortner, 1968). The width of this composite line approaches that predicted by Fermi s Golden rule formula... 

A very similar formula is systematically derived in several important cases. Probably this is why the probability per unit time is called, poetically, the Fermi golden rule ... 

This formula, first obtained by Dirac, is commonly known as Fermi s Golden Rule (FGR). 

The interpretation of Eq. (4-3) is direct and the formula could almost be written down immediately in terms of Fermi s familiar Golden Rule of quantum theory (see, for example, Schiff, 1968, p. 314). The absorption of light arises from the coupling, caused by the electric field, of occupied states with unoccupied states, However the absorption can only occur if the two states differ in energy by hco, so that energy can be conserved if the transition is made and one photon is absorbed. It should also be noted that in a perfect crystal the matrix elements will vanish unless the wave numbers of the coupled states in the Brillouin Zone are the same. That is, the transitions must be between states that are on the same vertical line in a diagram such as Fig. 4-7. We shall return to a more complete description of absorption later. 

This formula of the time-dependent perturbation theory was originally derived by Dirac, but it is often referred to as Fermi s golden rule No. 2. ... 

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