Scattering equations

The generalized scattering equation can be expressed by a complex exponential fomi... 

The ADT matrix for the lowest two electronic states of H3 has recently been obtained [55]. These states display a conical intersection at equilateral triangle geometi ies, but the GP effect can be easily built into the treatment of the reactive scattering equations. Since, for two electronic states, there is only one nonzero first-derivative coupling vector, w5 2 (Rl), we will refer to it in the rest of this... 

This result was published by Debye in 1946. Since we shall also encounter a light-scattering equation associated with his name, we shall refer to Eq. (2.56) and its variations as the Debye viscosity equation. 

The term I scattering (equation 6) is dominant when the excitation laser wavelength is resonant with an allowed electronic transition (M° / 0, M° M ). The... 

The term II scattering (equation 7) from vibronic activity in allowed electronic transitions mainly results in fundamental transitions of non-totally symmetric vibrations. This term corresponds to the B and C terms of the Albrecht theory25. 

The term III scattering (equation 8) is the weakest in the three scattering mechanisms, as shown by two derivative terms (M ) in the electronic transition integrals. Clearly, for a dipole forbidden transition (M° = 0) the only non-zero term is term III. The term in scattering results in binary overtone and combination transitions of vibronically active modes. It is noted that no fundamental transition survives. 

Basilevsky, M. V. and Ryaboy, V. M. Two approaches to the calculation of molecular resonance states Solution of scattering equations and matrix diagonalization, J.Comp.Chem., 8 (1987), 683-699... 

The light scattering equation for molecular weight-heterodisperse samples which are compositionally homogeneous simplifies if dn/dc is constant for all species ... 

What is the significance of the virial constant B in osmometry and light-scattering equations ... 

For analysis by means of the most general graphical treatment of light scattering measurements (the Zimm plot), the scattering equation (5.23) is rewritten in the following easy-to-use form (Burchard. 1994 Evans, 1972 Tanford, 1961) ... 

Finally, at the level of pair interactions, after the differentiation of the osmotic pressure Ft with respect to biopolymer concentration c, we get the following widely used form of the scattering equation, showing clearly the relationship between AR and the measured quantities Mw, RG... 

General solutions of light scattering equations generate oscillating curves when x is plotted... 

Analysis from Light Scattering Experiments. When = 4rB, then the light scattering equation becomes... 

This expression for cMwa is quite similar to the expression obtained in light scattering experiments. When irA = B (and vA = vB), the light scattering equation becomes... 

When a beam of x-rays strikes an electron, some of the energy is momentarily absorbed, displacing the electron from its unperturbed position. This sets the electron in periodic motion with the same frequency as that of the exciting radiation. As a result the electron radiates an electromagnetic wave in all directions with the same frequency as the exciting radiation. This leads to the experimental observation that the incident radiation is scattered by the electron. A theoretical analysis (10, 11) of these events leads to the Thompson scattering equation which relates the intensity of x-rays scattered by a single electron, Ie, to that of the incident non-polarized x-radiation, I0 ... 

Light-scattering Equations. From the light-scattering data the Mw value can be found since it is related to the scattering in the following manner (23) ... 

The scattering equations are illustrated in Figs. 10.6b and 10.7. In linear predictive coding of speech, this structure is known as the Kelly-Lochbaum scattering junction,... 

Systematic improvements in the trial wave function were achieved by increasing the value of w, and investigations of the convergence of the phase shifts revealed a similar pattern to that described earlier for positron-hydrogen scattering, equation (3.54), with extrapolation to infinite u expected to yield essentially exact results for the particular helium model being used. 

N. When this is combined with the light scattering equation of Rayleigh, and allowance made for a distribution in the particle size because of the stochastic nature of the process, one obtains (37)... 

Zeller, R. (1988). Empty-lattice test for non-muffin-tin multiple-scattering equations, Phys. Rev. B 38, 5993-6002. 

Although the mathematics required to transform the scattered fight patterns into a particle size distribution are complicated, it is beneficial to examine the basic scattering equation of fight by a single particle, as certain optical properties of the powder... 

Gustav Mie was able to solve this equation for. Sj(0) and S2(6) using a rigorous mathematical solution, assuming the scattering objects were spheres.8 To apply Mie s solution to the scattering equation, as most laser diffraction instruments do, the refractive index of the material must be known (both the real and imaginary component) The refractive index is expressed as ... 

The average diameter(s), as representative of the population behavior, should satisfy the analytic behavior of the scattering equations (ie the resulting equations should have the same functional form as equations 1 1 and 16). 

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