Thompson scattering

Thixotropy, 77 306, 27 707-709, 3 729 estimating, 27 709 Thomas equation, 75 688-689 Thomas steelmaking process, 76 150 Thompson scattering, 7 339 Thompson-Stewart process, 74 794 Thompson, William (Lord Kelvin), 24 433-434... 

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... 

When a beam of x-rays strikes an electron, some of the energy is momentarily absorbed, displacing the electron from its unperturbed position. This sets the electron in periodic motion with the same frequency as that of the exciting radiation. As a result the electron radiates an electromagnetic wave in all directions with the same frequency as the exciting radiation. This leads to the experimental observation that the incident radiation is scattered by the electron. A theoretical analysis (10, 11) of these events leads to the Thompson scattering equation which relates the intensity of x-rays scattered by a single electron, Ie, to that of the incident non-polarized x-radiation, I0 ... 

To this point we have assumed that an atom, be it heavy or otherwise, scatters as a point source of scattering power fj having phase 0j. Although the detailed physical explanation is outside the scope of this book and involves quantum mechanical properties, it must be pointed out that this is not entirely true. An atom scatters X rays in a somewhat more complex fashion, in that its scattered radiation is composed of two components. The major component, which arises from normal Thompson scattering, and is by far the largest component, has phase 0 dependent on the atom s position as we have assumed. But there is also a minor component of the scattering that has phase 0 + jt/2. This is because the electrons of the atom also absorb a small amount of radiation due to electron resonance phenomena and re-emit it with a phase change. This second component is called the anomalous dispersion, and to be entirely correct, we should properly describe the radiation scattered by an atom as a complex number,... 

Compton scattering will also occur under the experimental conditions used, but will produce a slowly increasing isotropic background as resolution increases. This background is isotropic and monotonic for the biological molecules and only starts to dominate the Thompson scattering at higher resolutions (>0.5A-1). 

The scattering of radiation, i,e, its diffusion in different directions, which has two components, one coherent with the incident radiation Thompson scattering) and the other incoherent with a longer wavelength Compton scattering). The term coherent indicates a precise relation between the phases of the incident and scattered wave. The coherent scattering by a periodic structure, hence by a crystal, is called diffraction. This may be elastic or inelastic (Section 3,1.1),... 

For SAXS, the neutron scattering length density p ) is replaced by the product of the electron density (pe) and the Thompson scattering length (/j = 0.282 x 10 cm), and vice-versa. 

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. 

In the case of X-rays (A w 1 A), resultant frequency factor becomes equal to 1 as the phase of scattered wave is Jt shifted and the ampUtude of the scattered wave becomes independent of frequency. The phenomenon is called Thompson scattering. Equation (6.5), thus reduces to... 

Like crystallography, SAXS is also based on the elastic (Thompson) scattering of photons by electrons of the macromolecular entities. As the monochromatic beam of X-rays hits the object, the electrons of its atoms (except for heavy atoms, which play no role in small-angle scattering) resonate with the frequency of X-rays and become sources of coherent secondary waves. The intensity of the secondary waves is given by the Thompson formula ... 

For X-rays or neutrons of wave vector k the refractive index, n, of a medium can be simply related to the scattering properties of the medium, see, e.g., appendix of Ref. 3. For X-rays the relevant parameters are the Thompson scattering length of a single electron, ro, and the electron density, pei ... 

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