Classical Thompson scattering

The anomalous contribution to the real part of the scattering amplitude can be separated by subtraction of the classical Thompson scattering, —e2/mc2, from the first term of Eq. (1.29) to give... 

The total scattering per electron (incoherent plus coherent) is given by the classical Thompson equation. 

A scattering process will also result in polarization of x-rays according to the classical Thompson theory expressed by Eq. (2.1). For an unpolarized primary beam, scattering at an angle (26) of 90° results in nearly complete plane polarization of the scattered x-rays. Thus, crystal diffraction of x-rays produces plane-polarized radiation. If the diffraction angle (26) approaches 90°, polarization becomes nearly complete. 

Neutrons are scattered isotropically from individual nuclei, whereas, for LS and SAXS, the scattering originates in the electron cloud, so the atomic form factors are in principle (2-dependent. However, the variation is small in practice (<1% for Q < 0.1 A ) and is usually neglected for SAXS and LS [36]. The Thompson-scattering amplitude of a classical electron is rj = 0.282 x 10 cm [65], so the X-ray scattering length of an atom, /, is proportional to the atomic number (/ = rjZ) and increases with the number of electrons per atom. For neutrons, values of b vary from isotope to isotope (see below). If the nucleus has nonzero spin, it can interact with the neutron spin, and the total cross section (atot) splits into coherent and incoherent components as explained below. 

Raff, L.M. and Thompson, D.L. (1985). The classical trajectory approach to reactive scattering, in Theory of Chemical Reaction Dynamics, Vol. Ill, ed. M. Baer (CRC Press, Bow Ruton). 

D. G. Truhlar and J. T. Muckerman, Reactive scattering cross sections. Ill Quasiclassical and semiclassical methods, Atom-Molecule Collision Theory (R. B. Bernstein, ed.), Plenum, New York, 1979 L. M. Raff and D. L. Thompson, The classical approach to reactive scattering, Theory of Chemical Reaction Dynamics (M. Baer, ed.), CRC, Boca Raton, FL, 1985. 

The theory of coherent scattering by a classical free electron was developed by J, J, Thompson in 1898. The electron is considered to be a classical free particle of charge - e and of mass m accelerated by the oscillating electric field of the... 

Raff, LM, Thompson DL. The classical approach to reactive scattering. In Baer M, Editor. Theory of chemical reaction dynamics, Vol. 3. Boca Raton CRC Press 1985. pp. 1-121. Truhlar, DG, Muckerman JT. Reactive scattering cross section. Ill Quasiclassical and semi-classical methods. In Bemtein RB, Editor. Atom-molecule collision theory. New York Plenum Press 1979, pp. 505 6. 

The elastic scattering intensity produced by an isolated electron was derived by Thompson. The amplitude of the wave elastically scattered by each electron has a well-defined phase relation with the amplimde of the incident wave, thus making interference effects possible. The scattering intensity produced by one electron per imit solid detection angle, 7, is a function of the scattering angle e but it can be considered constant at small angles, i.e., F e)= krf, where Jq is the intensity of the direct beam and is the classical... 

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