Photon-induced transition rate

Within the electric dipole approximation (Loudon 1983 ch.2) the perturbation is given by 

Equation (2.16) is exact independent of the strength or the shape of the light pulse. 

Under the assumption that the coupling elements daa are very small, Equation (2.16) may be solved by first-order perturbation theory the coefficients aa/ (t) on the right-hand side are replaced by their initial values at t = 0. The evolution of each final state (/ i) is then governed by the (uncoupled) equation 

Within this approximation we explicitly assume that the probabilities aa 2 do not significantly change while the light beam is switched on, i.e., ai(t) 2 1 and af(t) 2 1- Under these restrictions each final 

For uifi 0 (absorption) the first term is usually much smaller than the second one and therefore it is neglected (rotating wave approximation). The reverse holds for 0 (stimulated emission). Within this approximation the time-dependent probability for making a transition from initial state Fj) to final state Ff) under the influence of the photon beam 

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The first-order El "golden-rule" expression for the rates of photon-induced transitions can be recast into a form in which certain specific physical models are easily introduced and insights are easily gained. Moreover, by using so-called equilibrium averaged time correlation functions, it is possible to obtain rate expressions appropriate to a... 

But now, if there is a ample evidence of nonzero photon mass, the question of absorption or emission amplitudes for longitudinal photon has to be answered in a consistent manner. Goldhaber and Nieto [49] showed that these are suppressed in comparison with their transverse counterparts by a factor The corresponding rates and cross sections are suppressed by the square of this factor. The quantum mechanical matrix element for ordinary transverse photon is given by Tf(x,y) = (f JX)y i) for a photon-induced transition to an arbitrary state/, where i is the initial target state. The corresponding matrix for a longitudinal photon is... 

Let us now consider how similar the expression for rates of radiationless transitions induced by non Bom-Oppenheimer couplings can be made to the expressions given above for photon absorption rates. We begin with the corresponding (6,4g) Wentzel-Fermi golden rule expression given in Eq. (10) for the transition rate between electronic states Ti,f and corresponding vibration-rotation states Xi,f appropriate to the non BO case ... 

Therefore, the simplest classical treatment in which the propagator exp(it (T+V) ) is approximated in the product form exp(it (T) ) exp(it (V)/fc) and die nuclear kinetic energy T is conserved during the transition produces a nonsensical approximation to the non BO rate. This should not be surprising because (a) In the photon absorption case, the photon induces a transition in the electronic degrees of freedom which subsequently cause changes in the vibration-rotation energy, while (b) in the non BO case, the electronic and vibration-... 

Spontaneous transitions are not the only possible transitions. Electronic transitions may be also induced by, for example, an external radiation field. According to the detailed equilibrium principle, the rate of transitions from all states of the lower level ct J into all states of the upper level aJ, caused by the absorption of photons from the radiation field, must be equal to the rates of spontaneous and induced transitions from the level a J into a J, i.e. 

As a special application of the two-step model the non-coincident observation of photon-induced Auger electron emission will be considered further. In this case one has to integrate the transition rate P of equ. (8.66a) over dKa, because the photoelectron is not observed, i.e.,... 

A different perspective of the vibrational structure of the Sj electronic state is illustrated in Figure 2.13b. This is an OODR that was obtained by sequentially exciting CI2CS with two photons of different colors. In this experiment, a photon from the first laser (the pump photon) induces a Si <— So vibronic transition that is followed after a short time delay by a second S2 Si, probe photon that carries the excitation to the S2 state. The pump laser is advanced to the blue and interrogates the bands of the S2 <— So system while the probe laser is scanned at the same rate to the red such that the total energy matches a selected vibrational level of the S2 state. In this way, an excitation spectrum of the vibrational band structure of the S2 state is constructed by monitoring the fluorescence that originates from the S2 state. 

Larmor frequency. Syn. precession frequency, nuclear precession frequency, NMR frequency, rotating frame frequency. The rate at which thexy component of a spin precesses about the axis of the applied magnetic field. The frequency of the photons capable of inducing transitions between allowed spin states for a given NMR-active nucleus. 

Sect. 2.8) to all levels with Em < Ek. The quantum efficiency of the excited state T]k = Ak/(Ak Rk) gives the ratio of the spontaneous transition rate to the total deactivation rate, which may also include the radiationless transition rate Rk (e.g., collision-induced transitions). For = 1, the number wpi of fluorescence photons emitted per second equals the number of photons absorbed per second under stationary conditions. 

Physically, 2/T2 represents the absorption rate of a blue photon from [g> to eg>. It can be interpreted as the transition rate given by the Fermi golden rule, with a matrix element f2g/2 and a density of final states 2/irrg and corresponds to the width of the ground state induced by the blue laser. 

The Time Dependent Processes Section uses time-dependent perturbation theory, combined with the classical electric and magnetic fields that arise due to the interaction of photons with the nuclei and electrons of a molecule, to derive expressions for the rates of transitions among atomic or molecular electronic, vibrational, and rotational states induced by photon absorption or emission. Sources of line broadening and time correlation function treatments of absorption lineshapes are briefly introduced. Finally, transitions induced by collisions rather than by electromagnetic fields are briefly treated to provide an introduction to the subject of theoretical chemical dynamics. 

There have been many investigations of photoinduced effects in -Si H films linked to material parameters. Changes have been observed in the carrier diffusion length, unpaired spin density, density of states in the gap, and infrared transmission. The transition from state A to B seems to be induced by any process that creates free carriers, including x-ray radiation and injection (double) from the electrodes. Because degradation in a solar cell is accentuated at the open-circuit voltage conditions, the A to B transition occurs upon recombination of excess free carriers in which the eneigy involved is less than the band gap. It has been pointed out that this transition is a relatively inefficient one and the increase in spin density takes place at a rate of 10-8 spins per absorbed photon. 

Various primary processes induced upon photon absorption by this molecule are also shown in Fig. 2-1. The photon absorption processes associated with the vibrational-electronic transitions from So to Si and S2 are represented by So ->Si Abs. and So —>82 Abs., respectively. By internal conversion (IC) we mean a radiationless process between two different electronic states of the same spin multiplicity. In Fig. 2-1, IC from S2 to S and IC from Si to So are shown. Usually, the rate constants of S2 Si IC and Si —>So IC are more than lO s and 10 -10 s , respectively. By intersystem crossing (ISC) we mean a radiationless process between two different electronic states of two different spin multiplicities. In Fig. 2-1, Si Ti ISC and Ti—>So ISC are shown. The rate constants of the... 

The excitation of the surface plasmon effect also induces strongly enhanced fluorescence properties of gold nanoparticles due to the enhanconent in the radiative rate of the inter-band electronic transitions relative to that in bulk metals. Metal nanoparticles, especially gold nanorods exhibit enhanced two-photon luminescence (TPL) and multi-photon luminescoice (MPL) [7, 8]. Strongly-enhanced TPL has been observed from individual particles [9, 10] and particle solutions [11] under femtosecond NIR laser excitation. This observation raises the possibility of nonlinear optical imaging in the NIR region, where water and biomolecules have... 

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