Fermi’s golden rule expression

Recently, the electron-transfer kinetics in the DSSC, shown as a schematic diagram in Fig. 10, have been under intensive investigation. Time-resolved laser spectroscopy measurements are used to study one of the most important primary processes—electron injection from dye photosensitizers into the conduction band of semiconductors [30-47]. The electron-transfer rate from the dye photosensitizer into the semiconductor depends on the configuration of the adsorbed dye photosensitizers on the semiconductor surface and the energy gap between the LUMO level of the dye photosensitizers and the conduction-band level of the semiconductor. For example, the rate constant for electron injection, kini, is given by Fermi s golden rule expression ... 

In eq. (5-2), vt, refers to the frequency of the ith chromophore vibration (populated by the IVR transition), and the proportionality to l/v( is purely phenomenological. This proportionality reflects the expectation that low frequency chromophore modes will couple most efficiently to the (low frequency) vdW modes. Fermi s Golden Rule expression has two important consequences. First, it predicts that... 

This expression will, depending on the value of the time t, assume positive and negative values. In order to assure that a monotonically increasing excited-state population is prepared, the simplest choice for the parameter co is co = (E — Eq)/H, which is the resonance condition obtained from Fermi s Golden rule expression... 

Fermi s Golden Rule expresses the rate of transitions between b and a as... 

When chemisorption can be considered as a weak disturbance, the electron densities of adsorbate and surface orbitals will be hardly affected. Then, for an adsorbate with one atomic orbital, the interaction energy, AF, can be calculated using Fermi s golden rule expression [19] ... 

Let us substitute relation (A2.14) into the expression for Fermi s golden rule ... 

This expression was obtained by Forster and reformulated later on as Fermi s Golden Rule (Eq. B4.4.7 in Box 4.4). 

The rate expression described in Sect. 2, Fermi s golden rule, is commonly derived from a minimal model of two interacting quantum states plus environmental (bath) states which serve to provide the localizing fluctuations. As the... 

For a given microwave frequency a , the right hand side of (6.2.47) is constant. Thus, (6.2.47) can be solved immediately with the result Pn(i) = exp(—A t). Therefore, A has the physical meaning of a one-photon decay rate to the continuum. The expression (6.2.48) is a form of Fermi s golden rule. 

This expression is the exact form of Fermi s Golden Rule, familiar in time-dependent perturbation theory where F[, 0)) is approximated by o) (Merzbacher, 1970). p( ,) is the density of final states. 

It can be shown that the calculation of lm[ o] in real space and its subsequent substitution in the expressions for the Auger rate, equations (9) and (10), leads to die standard Fermi s golden rule for the calculation of the Auger rate when the excitations in the medium are obtained in the singleparticle approximation [22] ... 

Thus, to have a proper estimate of photocurrent from expression (75), it is desirable to calculate the transition probability, T E,hv)y using the time-dependent perturbation theory. The general expression of T E, hv) in terms of Fermi s golden rule of time-dependent perturbation theory... 

In the last section, we used the stochastic Liouville equation to find the steady-state rate of transitions between two weakly-coupled quantum states, on the assumption that coherence decayed rapidly relative to the rate of the transitions. The resulting expression (Eq. 10.36) reproduces Fermi s golden rule. We can use the same... 

The following generalized rate expression, derived from Fermi s golden rule (see e.g., [9,11]), is useful for discussing the effects of cofactor structure changes on the electron transfer rate constant (kgj) ... 

This last expression is known as Fermi s golden rule. For transitions from one single-particle state to another single-particle state in which case neither the density of states g(e/) nor the dependence of the transition probability on c/ enter, the transition rate takes the form... 

Under the assumption of long laser pulses and weak light-matter interaction, formally quite simple expressions for the various photodissociation cross sections can be derived (Fermi s Golden Rule). For consistency we will use the same notation as in Ref. 1. 

In a quantum-electrodynamical approach the general expression for the substrate contribution to the rate of the relaxation transition from the excited state a) follows from Fermi s golden rule and has the form (Wylie and Sipe 1985)... 

In the large-molecule (statistical) limit, the 1 manifold is composed of randomly distributed, overlapping levels whose individual properties cannot be determined. It may be thus treated only by statistical methods. As long as the s levels form a discrete set, the system may be described in terms of one s> state coupled to a dissipative continuum the resulting nonradiative width y " of the s> state is given by the Fermi golden rule expression, justified in Section II,E,2... 

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) ... 

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