Absorption Probability

Rapid dermal absorption of trichloroethylene is evident from a study in which peak blood and exhaled air concentrations occurred within 5 minutes after a human subject immersed one hand in a solution of unspecified trichloroethylene concentration for 30 minutes (Sato and Nakajima 1978). Studies on dermal absorption of trichloroethylene in humans, as well as animals, are complicated by the fact that exposure in these studies is usually by direct contact of the skin with the undiluted chemical. Trichloroethylene is a lipophilic solvent that defats the skin and disrupts the stratum comeum, thereby enhancing its own absorption. Thus, the rate of absorption probably increases in a nonlinear fashion with greater epidermal disruption. Although the extent of absorption through the skin may be relatively modest with normal industrial use (Sato and Nakajima 1978 Stewart and Dodd 1964), there is insufficient information to evaluate the effects of chronic, low-level exposure in hiunans, especially when multiple routes may be involved. 

Data Analysis Using Absorption Probability Density (Example Guanidinium Nitroprusside)... 

The strongest contribution to the projected mean square displacement (ku)) and therefore to the absorption probability S(E) originates from C-Fe-C and N-Fe-C bending modes (8Ai, 22E, 23E, and 24E in Table 9.2). However, the energy range of these modes (8-15 meV) strongly overlaps with that of the acoustic modes (with composition factor = 0.17, = 337, wtpe = 57) and therefore... 

From the individual contributions of the modes to the msd along the c-axis ( 6 pm ) and along the a-axis ( 8 pm ), the corresponding calculated molecular Lamb-Mossbauer factors for the c-cut crystal (/Lm,c = 0.90) and for the a-cut crystal = 0.87) were derived. Comparison with the experimental /-factor, i.e., / P = 0.20(1) and/ N> = 0.12(1) [45], indicates that by far the largest part of the iron msd must be due to intermolecular vibrations (acoustic modes) of the nitroprusside anions and its counter ions. This behavior is reflected in the NIS spectrum of GNP by the considerable onset of absorption probability density below 30 meV in Fig. 9.36a. 

In a celebrated paper, Einstein (1917) analyzed the nature of atomic transitions in a radiation field and pointed out that, in order to satisfy the conditions of thermal equilibrium, one has to have not only a spontaneous transition probability per unit time A2i from an excited state 2 to a lower state 1 and an absorption probability BUJV from 1 to 2 , but also a stimulated emission probability B2iJv from state 2 to 1 . The latter can be more usefully thought of as negative absorption, which becomes dominant in masers and lasers.1 Relations between the coefficients are found by considering detailed balancing in thermal equilibrium... 

In animal studies [9], up to 8% of isotopically labelled mercuric chloride applied to the skin was absorbed within 5 h. The state of the skin is one factor which determines the rate of absorption [10]. Passive diffusion cannot be the only process involved, since the absolute absorption rate of mercury increases with increasing concentration up to a plateau value. In addition, skin absorption probably occurs transepidermally rather than via the follicular pathway [11]. 

Given randomly oriented dipoles, the absorption probability rate is proportional to the intensity 7, = E,tJ 2. At z = 0, the evanescent intensities are... 

By a careful inspection of Figure 4.17, we see how further transitions between bands below and above the Fermi level can also occur at energies higher than 1.5 eV. However, as these bands are not parallel, the density of states at these energies is lower than at 1.5 eV. In any case, the absorption probability is still significant, and it acconnts for the experimentally observed redaction in the reflectivity of Al in respect to the predictions from the Drude model (see Figure 4.5). 

Expression (5.14) shows that the absorption probability depends on both the incoming light intensity and the matrix element It is easy to see that /Lt,j = l/Lt = /x and so we can conclude that the absorption probability between two defined energy levels i and / is equal to the stimulated emission probability between levels / and i ... 

In the spirit of the adiabatic approximation, the transitions between two vibrational states (belonging to initial and final electronic states) must occur so rapidly that there is no change in the configurational coordinate Q. This is known as the Frank Condon principle and it implies that the transitions between i and / states can be represented by vertical arrows, as shown in Figure 5.12. Let us now assume our system to be at absolute zero temperature (0 K), so that only the phonon level = 0 is populated and all the absorption transitions depart from this phonon ground level to different phonon levels m = 0, 1, 2,... of the excited state. Taking into account Equation (5.25), the absorption probability from the = 0 state to an m state varies as follows ... 

The concentration of liberated iodine, as measured by its absorbance at 5000 A, is proportionalato the two-photon absorption probability, since no reactants have absorption bands at the single... 

Saturation as described above can be observed either when all the molecules in the initial state have the same absorption probability, or when some of the state population is preferentially absorbed, depending on the spatial orientation of the molecules or on their transition frequency, selected from a certain frequency interval. The first case is called homogeneous line saturation, the second is due to inhomogeneous saturation or hole-burning. This different cases will be explained in more detail by discussing some relevant experiments. 

The absorption probability is proportional to the scalar product p = IM I 1 I cos ip, where p is the transition dipole moment, C the electric vector of the exciting light wave and

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Two-photon absorption occurs when the energy of a molecular transition matches the combined energy of two photons. Quantum mechanically, the absorption probability is proportional to the two-photon transition moment from the ground state, g, to the excited state, n, via intermediate state, m, and can be expressed as follows (Boyd 1992 Abe 2001) ... 

If the equilibrium position of the excited state C is located outside the configurational coordinate curve of the ground state, the excited state intersects the ground state in relaxing from B to C, leading to a nonradiative process. As described above, the shape of an optical absorption or emission spectrum is decided by the Franck-Condon factor and also by the electronic population in the vibrational levels at thermal equilibrium. For the special case where both ground and excited states have the same angular frequency, the absorption probability can by calculated with harmonic oscillator wavefunctions in a relatively simple form ... 

Spontaneous emission and absorption probability is enhanced by the factor... 

It is the last term diat accounts for differences in absorption probabilities. This term is the expectation value of the dipole moment operator (see Section 9.1.1) evaluated over different determinants. Its expectation value is referred to as the transition dipole moment. 

Let the coordinate system be such as that given in Figure 4. IS. The electric vectors of a plane polarized radiation vibrate along OZ in the ZX plane and OX is the direction of propagation of the plane polarized wave. When a solution of anisotropic molecules is exposed to this plane polarized radiation, the electric vector will find the solute molecules in random orientation. Only those molecules absorb with maximum probability which have their transition moment oriented parallel to OZ (photoselection). Those molecules which are oriented by an angle 6 to this direction will have their absorption probability reduced by a factor cos 6, and the intensity of absorption by cos2 6. Finally, the molecules oriented perpendicular to the electric vector will not absorb at all. These statements are direct consequences of directional nature of light absorption... 

With vertically polarized exciting light, p0 — when p = 0. But when P = n/2, p0 becomes negative and is equal to —1/3. The values are +1/3 and—1/7 for unpolarized radiation. Thus negative polarization appears when 6 is small, i.e. absorption probability is high and the transition moment in emission is perpendicular to that in absorption. These observations provide a suitable method for assigning the polarization directions of transition moments in different absorption bands of a given molecule from polarization of the fluorescence excitation spectra. 

In the projection operator formalism, which leads to a rigorous basis for the optical potential, the absorptive imaginary part is associated with transitions out of the elastic channel from which no return occurs. Whereas Pgl transitions are in this category, excitation transfer (ET) transitions are not, since return ( virtual excitation ) can occur during the ET collision. In the event that a localized avoided curve crossing with one other state dominates the inelastic process (expected for many endoergic transfers), the total absorption probability (opacity) can still be defined ... 

Additionally, Kharasch and Joshi (15) observed that during the absorption of oxygen, the reaction mixture acquired a dark purple color which was discharged upon neutralization, forming a yellow color. They showed that the dark purple color was caused by the anion of A and suggested that the intensity of absorption probably was associated with resonance stabilization. 

If, in centrosymmetric molecules, states to which a transition is forbidden in the normal absorption spectrum can make important contributions to x(3)> this suggests a strategy for enhancing the figure of merit, x(3)/a> of such a nonlinear material. Chemically introducing low lying states with gerade symmetry and thus small or zero absorption cross sections has the potential to enhance the x(3) but not increase the absorption probability, a. 

Symmetry considerations show that chemical substitution to introduce low lying, one photon forbidden states into the molecule has the potential to enhance the x(3) without increasing the absorption probability, a. 

The spectra of aza-derivatives of benzene contain three regions of diffuse absorption probably related to the 2600, 2000, and 1860 A band systems of the parent hydrocarbon (El-Sayed, 1962). Transitions of the 7T type fall on the long wavelength side of the first system... 

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