Thomson scattering formula

If the photon energy is so low that it cannot cause Compton effect, one has elastic scattering on free electrons (Thomson scattering). In the classical limit, the Klein-Nishina formula reduces to the Thomson cross section ... 

But some schemes may be better than others in practice. This raises the question of the best way to define the physical parameters. For pure QED there is an obvious and simple choice. One can show that the exact formula for Thomson scattering becomes... 

This is the Thomson formula for scattering from a free charge. The differential Thomson cross section a is given by the angle-independent part of Eq. (3.25.17) ... 

The Rayleigh scattering cross section for a dilute assembly of N scattering particles per unit volume is N times the cross section per particle. Note that there seems little in common between the formulas for Thomson and Rayleigh scattering. 

The general formula for scattered intensities (away from X-ray absorption edges) in the Thomson formula is... 

This relation is called the Thomson formula [THO 98d]. It has a specific use the scattering power of a given object can be defined as the nmnber of free and independent electrons this object would have to be replaced with, in order to obtain the same scattered intensity. 

This is called the Thomson formula for the scattering of x-rays by a single electron. 

As to the total cross-section of scattering by free electron irradiated by unpolarized light, it is described by the same Thomson formula (5.7) that is easy to check by integrating (5.8) over 20 (from 0 to Jt) and over (p (from 0 to 27t). 

---