Thompson scattering equation

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 ... 

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... 

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Considerable scatter in the neighborhood of the critical point is a result of the difficulty of measurement and the deviation amplifying effect of the function A (Pr) for Pr near unity. In the case of smoothed data, a smoothing j3c which departs from Equation 11 will lead to a singularity in A at the critical point. Similarly, deviant critical properties Pc and Vc will lead to a singularity in A at the critical point (for a detailed discussion, see Thompson (20)). 

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

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