A-term scattering

The relative contributions of A-and 6-term scattering under resonance conditions is a subject of considerable interest and different conclusions have been found for different systems. For example the A-term predominates for n-electron systems, e. g. polyenes, especially for their main intense absorption band (Warshel 1977). Vibrational wavefunc-tions of non-totally symmetric modes are more nearly orthogonal. Thus, vibrations may only derive their intensities from the 6-teim. A-term and 6-term enhancement can be distinguished experimentally by their excitation profiles. For A-term scattering a peak in the excitation profile is expected at the origin of the resonant electronic transition and subsidiary peaks at successive excited state vibrational levels. The amplitudes of the peaks depend on the successive Frank-Condon factors. For 6-term scattering excitation profile maxima are expected at the 0 0 and 1 0 positions for each of the mixing... 

A characteristic feature of scattering for totally symmetric modes is that contributions arise generally from all the vibrational levels of the resonant electronic state. The A-term scattering intensity depends on the square modulus of the scattering tensor, which is given by (resonant part only)... 

The temperature dependence of the thermal conductivity of CBCF has been examined by several workers [10,13,14]. Typically, models for the thermal conductivity behavior include a density term and two temperaUrre (7) terms, i.e., a T term representing conduction within the fibers, and a term to account for the radiation contribution due to conduction. The thermal conductivity of CBCF (measured perpendicular to the fibers) over the temperature range 600 to 2200 K for four samples is shown in Fig. 6 [14]. The specimen to specimen variability in the insulation, and typical experimental scatter observed in the thermal conductivity data is evident in Fig. 6. The thermal conductivity of CBCF increases with temperature due to the contribution from radiation and thermally induced improvements in fiber structure and conductivity above 1873 K. 

In principle, the formal preexponential factor kd can be a function of 6 and T. However, often it is more or less correctly assumed that this dependence is but weak as compared with the terms 0 and exp(—Ed/RT), and therefore it cannot be accurately enough determined from the experimental data which usually exhibit a considerable scatter. 

These parameters, which describe the topology of a branched structure are determined from a static scattering experiment, and the branch content can be calculated in terms of fraction of material occupied in the branches and is given as [83],... 

In the scattering theory approach, the stopping power, or energy loss per unit length for a projectile of energy Ep, can be written in terms of a differential scattering cross section da/dQ as... 

In linear imaging theory, it is assumed that the object is a weak scatterer, so that the quadratic term in equation 5 is small and can be neglected... 

In the vicinity of the atomic absorption edges, the participation of free and bound excited states in the scattering process can no longer be ignored. The first term in the interaction Hamiltonian of Eq. (1.11) leads, in second-order perturbation theory, to a resonance scattering contribution (in units of classical electron scattering) equal to (Gerward et al. 1979, Blume 1994)4... 

The atom-centered models do not account explicitly for the two-center density terms in Eq. (3.7). This is less of a limitation than might be expected, because the density in the bonds projects quite efficiently in the atomic functions, provided they are sufficiently diffuse. While the two-center density can readily be included in the calculation of a molecular scattering factor based on a theoretical density, simultaneous least-squares adjustment of one- and two-center population parameters leads to large correlations (Jones et al. 1972). It is, in principle, possible to reduce such correlations by introducing quantum-mechanical constraints, such as the requirement that the electron density corresponds to an antisymmetrized wave function (Massa and Clinton 1972, Frishberg and Massa 1981, Massa et al. 1985). No practical method for this purpose has been developed at this time. 

---