Differential scattering intensities

Relevant quantities of interest, e.g. differential scattered intensities A/, are obtained from the formulae in Table 1 by an appropriate choice of K. The difference between the intensity of right (R) and left (L) circularly polarized scattered light in a backscat-tering SCP experiment with unpolarized (u) exciting light from Equation [8] is... 

The intensity of SS /. from an element in the solid angle AD is proportional to the initial beam intensity 7q, the concentration of the scattering element N., the neutralization probability P-, the differential scattering cross section da(0)/dD, the shadowing coefficient. (a, 5j ) and the blocking coefficient(a,5 ) for the th component on the surface ... 

For simplicity, consider a single unit of structure with a cylindrical differential polarizability tensor. The scattered intensity Is is then... 

For a cylindrical differential polarizability tensor we can write ax = a2 and r = v.3l[Pg.91]

In normal transmission geometry16 any mathematical treatment of calibration to absolute units [87-90] starts from the basic differential relation among the scattering intensity in the detector, the primary intensity and the structure... 

It is also interesting to note that circular differential Raman scattering, circular intensity differential (CID), has been reported for a series of optically active sulfoxides and a correlation found between the absolute configuration at sulfur and the differential scattering (240). Thus, all (/ )-alkyl p-tolyl sulfoxides investigated show a common (positive) CID feature in the 300 to 400 cm" region. 

To enable detection of fine mineral particles (<20pm),back-scattered electron imaging was used. Once the minerals were detected, EDS was used for analysis. Selected lignite particles were scanned to determine the distribution of minerals. Mineral types were then differentiated by variation in back scatter intensity and identified using EDS. The relative proportions (major, minor) and size and spatial distributions of the minerals were recorded. The overall surface of the polished section was viewed and massive minerals were analyzed and their distribution and size recorded. 

Raman vibrational frequencies and intensities for both complexes 5 and 7 are compared in Table II. The relative Raman scattering intensities were calculated from the differential cross sections. For their evaluation we used the wavelength of 613.33 nm (105). Polarizabilities were calculated in the limit of a static perturbation. 

The neutron scattered intensity (macroscopic differential scattering cross section d (Q)/dfi) is given by ... 

The zero angle differential scattering cross-section for the completely inter-diffused couple is calculated from equations 1 and 3 to be roughly 1100 cm The SANS intensity from the blend will approach this at a rate governed by the respective inter-diffusion... 

The relation which describes the intensity of a Raman band is determined by the number of scattering molecules per unit volume N, the differential scattering cross section dff/df , and the intensity of the incident laser beam Iq ... 

Another commonly-used normalisation procedure is to use the relative flow technique. In this method the elastic differential cross section for a particular species may be obtained by comparing the scattered intensity under the same conditions with that from another target with a known cross section. It is important to ensure, for both the gas under study and the reference gas, that the electron flux density and distribution, the detector efficiency, and the target beam flux distribution are the same for both gases during the measurement. 

In a system where the Brownian motion is not intermpted by sedimentation or particle-partide interaction, the movement of particles is random. Hence, the intensity fluctuations observed after a large time interval do not resemble those fluctuations observed initially, but rather represent a random distribution of particles. Consequently, the fluctuations observed at a large time delay are not correlated with the initial fluctuation pattern. However, when the time differential between the observations is very small (a nanosecond or a microsecond), both positions of particles are similar and the scattered intensities will be correlated, and when the time interval is increased then the correlation will be decreased. The decay of correlation is particle size-dependent that is, the smaller the particles the faster the decay. 

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