Equivalent scattering particles

Earlier studies of positron-molecule elastic scattering did not involve such detailed descriptions of the scattering process as do the variational and R-matrix formulations. Instead, the interaction between the positron and the molecule was represented by a relatively simple model potential, and the positron wave function F(r 1) was assumed to satisfy the equivalent single-particle Schrodinger equation... 

D-4464 Particle Size Distribution of Catalytic Material by Laser Light Scattering Particle size distribution of catalyst particles (20 to equivalent spherical diameter) as ascertained by laser scattering 150/im light... 

Figure 4 shows the impact of the number of primary particles per aggregate and the coefficient of penetration on the result of a dynamic light-scattering particle sizing of those aggregates. The impact of /is very low. Therefore, it is now very easy to give the number of primary patticles as a result of a PSD measurement rather than the equivalent spherical diameter 2 n,yd. 

Scatter in adhesive force may be because of various factors. Solid surfaces are energetically inhomogeneous. Because of this inhomogeneity, the constant of molecular interaction (see Section 7) may be different for identical contiguous bodies, and this will cause a scatter in adhesive force. As an example, we may cite the data shown in Table II. 1 for the adhesion of glass particles to glass surfaces, where the molecular interaction constant may assume values from 0.2 lO to 32 10 erg, i.e., it may vary by a factor of 160. In accordance with Eq. (11.24), this change can produce an equivalent scatter in adhesive force if the adhesive force is caused solely be molecular interaction. 

B.2.1.1. Transit Particles pass support region repeatedly in particles finite steps. This produces an equivalent scattering and diffusion process. 

Although most modem particle characterization methods are developed, validated and presumably used for spherical particles or equivalent spherical particles, real particles are rarely such ideal. In many instances, particle shape affects powder packing, bulk density, and many other macroscopic properties. Shape characterization of particulate systems only scatters in the literature [60], since there are hardly any universal methodologies available. Several methods exist that use shape coefficients, shape factors, Fourier analysis, or fractal analysis to semi-quantitatively describe shape [Ij. 

If each particle has a plane of symmetry or, equivalently, the particles and their mirror-symmetric particles are present in equal numbers, the scattering... 

Rayleigh s results do not apply fully to solutions. He had assumed that each particle acted as a point source independent of all others, which is equivalent to assuming that the relative positions of the particles are random. This is true in the gases with which he worked, but is not true in liquids. Hence, for solutions, the scattered light is less intense by a factor of about 50 due to interference of the light scattering from different particles. 

Optical devices, based upon particle attenuation of a light beam or measurement of scattering angles, also give equivalent spherical diameters. 

Methods for calculating scattering by particles are physically equivalent to the procedure outlined above, although their mathematical form may obscure the underlying physics. For certain classes of particles, however, the scattered... 

Relative measurements are considerably easier to make and are the type most commonly reported. However, absolute measurements are of importance, for example, in comparing measured scattering cross sections of nonspherical particles with calculations for equivalent spheres. Note that absolute as we are using the term here means that scattering is not normalized to some arbitrary reference angle it does not mean that absolute irradiances are measured, as with calibrated detectors. In both relative and absolute measurements, it is relative (i.e., dimensionless) irradiances that are determined. 

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