Scattering cross section wavelength dependence

A major source of the problem for systems with wide size distributions (and therefore relatively small numbers of small particles) is the strong dependence of the scattering cross section on particle diameter in the nonabsorbing wavelength range. Calculations have indicated that a means for improving relative resolution is to choose a wavelength where the particles can absorb as well as scatter (27). 

X-ray and neutron scattering experiments yield direct information on the atomic pair-correlation functions, gj/fj, fj,). by the help of the scattering cross-section do/dQ 241,242) gj. reduced intensity I both of which depend on the scattering angle 6, which is expressed as the scattering vector k = [4n sin (0/2)]/X. X is the wavelength of the incident radiation. The intensity of the radiation scattered by each atom i depends on its scattering factor fj. 

Different types of radiation interact elastically with different structural units of the material to be investigated. So x-rays are scattered on electronic cloud, while electrons are deflected in the electric field of atomic nuclei. An exception includes neutron scattering where wavelength of incident radiation is larger than the diameter of atomic nuclei, so that scattering is independent on diffraction angle but depends on differences of scattering cross sections of atomic nuclei. 

Since, the size of the scattereis is much smaller than the scattered wavelength, the Rayleigh scattering formalism should be used. In this approach, the losses due to scattering are sc(A) = p.a JX), where p is the density of scatterers and is the wavelength dependent scattering cross section (Van de Hulst, 1981). For the sake of simphcity we consider the scatterer to be a dielectric sphere of radius r. Thus, can be calculated according to the equation (Wu et al., 2004) ... 

The differential scattering cross sections given in Equations (5.21) and (5.31) allow us to deduce the optical wavelength dependence. Note that, basically, for nematics... 

When an X-ray beam falls on an atom, it may either pass through unaffected or interact with the electrons. This interaction takes one of two forms the X-ray photon is absorbed, with electrons and photons being emitted by the atom, or alternatively the beam is scattered. Scattering cross sections are generally rather small, while the absorption cross section is very dependent on the X-ray wavelength. 

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