Klein–Nishina formula

The Klein-Nishina cross section is a cross section indicating the angular distribution of photons scattered from stationary electrons ( Compton scattering). It was calculated in 1929 by Oskar Klein and Yoshio Nishina, and was one of the first results of quantum electrodynamics. He agrees with the experimental results.

Definition

In the photon -electron scattering define energy and momentum conservation, such as the energy of the scattered photon on the scattering angle and the original photon energy dependent:

In which

However, from the laws of conservation does not follow how often this or that scattering angle occurs. This frequency is indicated by the differential cross section, with the solid angle.

For incident photon energy of the Klein-Nishina cross section is

This is

The classical electron radius.

For photon energies that are small compared to the rest energy of the electron, applies

Then, the Klein-Nishina cross-section is against the cross-section

Joseph Thomson was calculated for the scattering of an electromagnetic wave at a point charge. For small energies forward scattering of the photon is therefore just as likely as backward scattering at higher energies forward scattering is more likely ( see illustration).

Total cross section

The total cross section is obtained by integration of the angle.

If the photon energy large compared to the rest energy of the electron, the total cross section coincides with the energy from:

For low-energy photons of the total cross section is up to a factor of 8/3 the area of ​​a circular disk whose radius is the classical electron radius:

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