Particles, general scattering theory

At the present time the electromagnetic scattering theory for a sphere, which we have called Mie theory, provides the only practical method for calculating light-scattering properties of finite particles of arbitrary size and refractive index. Clearly, however, many particles of interest are not spheres. It is therefore of considerable importance to know the extent to which Mie theory is applicable to nonspherical particles. To determine this requires generalizing from a large amount of experimental data and calculations. We summarize... 

Because there is no general microscopic theory of liquids, the analysis of inelastic neutron scattering experiments must proceed on the basis of model calculations. Recently1 we have derived a simple interpolation model for single particle motions in simple liquids. This derivation, which was based on the correlation function formalism, depends on dispersion relation and sum rule arguments and the assumption of simple exponential decay for the damping function. According to the model, the linear response in the displacement, yft), satisfies the equation... 

We will present the approximate analytical formulas used for calculating the cross sections of different processes of the interaction of charged particles with molecules, and discuss the limits within which they are valid. In this connection let us first dwell on the general formulation of the problem in the framework of the scattering theory. 

When the extinction is measured at different frequencies/, this equation becomes a linear equation system, which can be solved for Cpp and q2(x). The key for the calculation of the particle-size distribution is the knowledge of the related extinction cross section K as a function of the dimensionless size parameter c = iTOifk. For spherical particles K can be evaluated directly from the acoustic scattering theory. A more general approach is an empirical method using measurements on reference instruments as input. 

To study scattering effects by solid particles in a fluid and adapt previous existing methods in generalized transport theory (the discrete ordinate method or DOM) (Duderstadt and Martin, 1979) to solve the RTE (Alfano etai, 1995). 

First we shall discuss the SAXS-analysis of latex particles consisting of a homopolymer. This system serves as a check for the accuracy of the measurements and for a comparison with the general prediction of scattering theory as outlined in Sect. 2. 

According to the molecular scattering theory, a particle incident to the surface has a certain probability for a certain amount to stay on the surface, and the rest is scattered back into the gas phase, a is an initial attaching probability and is a parameter to be determined through a molecular dynamics simulation based on quantum chemistry. Although in surface chemistry, a thermal accommodation coefficient is also used, in atmospheric chemistry a mass accommodation coefficient is solely used so that here it is simply called an accommodation coefficient. In general a cannot be determined directly by experiments, and the experimentally determined parameter of intake of a gaseous molecule to the particle surface is an uptake coefficient y defined by... 

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