Photon excitation, equation

S( at) and G oS) are the sine and cosine Fourier transforms of the luminescence response to r5-function excitation, respectively. N yields the total number of photons of the response to the (5-function excitation. Equation (9.59) can be rewritten in the following form... 

The photochemical stabihty of the molecules is characterized by the quantum yield of photodecomposition, (P = N/Q [69], where N and Q are the numbers of decomposed molecifles and absorbed photons, respectively. The photochemical properties of the fluorene derivatives were investigated in different organic solvents (hexane, CH2CI2, ACN, and polyTHF) at room temperature by the absorption and fluorescence methods and comprehensively described [70-72]. These methods are based on measurements of the temporal changes in the steady-state absorption and fluorescence spectra during irradiation. For the absorption method, the quantum yield of the photodecomposition under one-photon excitation, c >ipa, can be obtained by the equation [73] ... 

In our discussion above, it was pointed out that a molecule in the excited state can return to lower energy levels by collisional transfer or by light emission. Since these two processes are competitive, the fluorescence intensity of a fluorescing system depends on the relative importance of each process. The fluorescence intensity is often defined in terms of quantum yield, represented by (X This describes the efficiency or probability of the fluorescence process. By definition, XL is the ratio of the number of photons emitted to the number of photons absorbed (Equation 5.6). 

A typical problem of interest at Los Alamos is the solution of the infrared multiple photon excitation dynamics of sulfur hexafluoride. This very problem has been quite popular in the literature in the past few years. (7) The solution of this problem is modeled by a molecular Hamiltonian which explicitly treats the asymmetric stretch ladder of the molecule coupled implicitly to the other molecular degrees of freedom. (See Fig. 12.) We consider the the first seven vibrational states of the mode of SF (6v ) the octahedral symmetry of the SF molecule makes these vibrational levels degenerate, and coupling between vibrational and rotational motion splits these degeneracies slightly. Furthermore, there is a rotational manifold of states associated with each vibrational level. Even to describe the zeroth-order level states of this molecule is itself a fairly complicated problem. Now if we were to include collisions in our model of multiple photon excitation of SF, e wou d have to solve a matrix Bloch equation with a minimum of 84 x 84 elements. Clearly such a problem is beyond our current abilities, so in fact we neglect collisional effects in order to stay with a Schrodinger picture of the excitation dynamics. 

The incoming X-ray photons excite electrons into the valence band creating an electron-hole pair. A negative charge is applied to the p-type part of the crystal and a positive charge to the n-type side. This creates a charge pulse of electrons. The number of electron-hole pairs is given by equation (7)... 

Figure 1. Fluorescence intensity versus incident laser light intensity at 320 nm. The straight line was fit to the low-intensity data and is drawn with the assumption that the fluorescence intensity is proportional to the intensity of the incident laser light. The curved solid line is the result predicted by the phenomenological equation for single-photon excitation with y = 4.2 X 10 cm ls. The area of the exciting laser beam was about 0.1 cm. ...

The photoelectrochemical process can be divided into the four reactions (Equations 1-4) involving photon excitation and charge separation in the Pc film (Equation 1) recombination events (Equation 2), charge transfer at the electrode substrate-Pc. interface (Equation 3) and charge transfer at the Pc-solution interface (Equation 4). The net process is the oxidation of hydroquinone with 0 to form quinone and R. If this is normally a thermodynamically uphill process where the dye is superimposed on a semiconductor substrate, then true photosensitized energy conversion has occurred. 

Our conclusions based on estimation (51) need support from strict simulations, which, however, are not easily obtained because we cannot select one-photon or three-photon pumping using strict equations. This means that we can use only some fingerprints of one- or three-photon excitations. One of these fingerprints is tire transmission of the pump field... 

In this case, the second-order hyperpolarizability y can be considered as a unidimensional parameter defined along the axis x of the molecule following the single component Yxxxx- Equation 3 can be simpUfied into the relationship Eq. 5, when applying the three-level model in which the lowest excited state 11) and the two-photon excited state 2) are considered to be the most significant... 

Equations 2.56 and 2.56a describe oxidation via holes from the valence band that originate either from photon excitation of minority carriers in n-Si or from the formation of an accumulation layer by anodic polarization (VJ of p-Si, respectively. Equation 2.57 is the etching reaction for HF that generates hydronium ions (for simplicity, only the solvated protons HI, are written) and Equation 2.57a describes the etching by the hydrogen bridge complex HR" which only takes place at moderately acidic pH. 

The dynamics of populations of the electronic states in a 4,4 -bis(dimethylamino) stilbene molecule (two-photon absorption) was studied against the frequency, intensity, and shape of the laser pulse [52]. Complete breakdown of the standard rotating wave for a two-photon absorption process was observed. An analytical solution for the interaction of a pulse with a three-level system beyond the rotating wave approximation was obtained in close agreement with the strict numerical solution of the amplitude equations. Calculations showed the strong role of the anisotropy of photoexcitation in the coherent control of populations that can affect the anisotropy of photobleaching. The two-photon absorption cross section of an ethanol solution of a trans-stilbene and its derivatives exposed to radiation of the second harmonic of a Nd YAG laser (532 nm) of nanosecond duration has been detected [53]. In experiments, the method based on the measurement of the photochemical decomposition of examined molecules was used. The quantum yield of the photoreaction (y266) of dyes under one-photon excitation (fourth harmonic Nd YAG laser 266 nm) was detected by absorption method. 

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