Thompson scattering amplitude

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. 

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 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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