The KleinNishina formula was derived in 1928 by Oskar Klein and Yoshio Nishina, and was one of the first results obtained from the study of quantum electrodynamics.

KleinNishina distribution of scattering-angle cross sections over a range of commonly encountered energies.

Nishina, "On the Scattering of Radiation by Free Electrons According to Dirac's New Relativistic Quantum Dynamics The Oskar Klein Memorial Lectures, Vol.

At low frequencies (e.g., visible light ) this yields, thomson scattering ; at higher frequencies (e.g., x-rays and gamma-rays ) this yields, compton scattering.

Compton wave length of the electron (0.38616 pm m e displaystyle m_e is the mass of an electron (511 gömda nakna killar keV / c 2 displaystyle /c2 and P ( E, ) displaystyle P(E_gamma,theta ) is the ratio of photon energy after and before the collision:.Evans, The Atomic Nucleus, McGraw-Hill, New York, 1955,. .Bethe and Alan.Note that this result may also be expressed in terms of the classical sex är noll online-film electron radius r e r c displaystyle r_ealpha r_c.Ltd., Singapore, 1994,. .

The final energy of the scattered photon, E displaystyle E_gamma ', depends only on the scattering angle and the original photon energy, and so it can be computed without the use of the KleinNishina formula: E ( E, ) E P ( E, ) displaystyle.

Note that if E m e c 2 displaystyle E_gamma ll m_ec2, P ( E, ) 1 displaystyle P(E_gamma,theta )rightarrow 1 and the KleinNishina formula reduces to the classical Thomson expression.

While this classical quantity is not particularly relevant in quantum electrodynamics, it is easy to appreciate: in the forward direction (for displaystyle theta 0 photons scatter off electrons as if these were about r e r c displaystyle r_ealpha r_c (2.8179 fm) in linear dimension.

However, scattering experiments showed significant deviations from the results predicted by the Thomson cross section.

The Quantum Theory of Fields.Guth with Translated Reprints by Oskar Klein,.2: Lectures by Hans.For an incident photon of energy E displaystyle E_gamma, the differential cam porr flickor cross section is: 2 d d 2 r c 2 P ( E, ) 2 P ( E, ) P ( E, ) 1 sin 2 ( ) / 2 displaystyle frac dsigma dOmega.Further scattering experiments agreed perfectly with the predictions of the KleinNishina formula.Further reading edit.Melissinos, Experiments in Modern Physics, Academic Press, New York, 1966,. .Consideration of relativistic and quantum mechanical effects allowed development of an accurate equation for the scattering of radiation from a target electron."Über die Streuung von Strahlung durch freie Elektronen nach der neuen relativistischen Quantendynamik von Dirac".The, kleinNishina formula 1 gives the differential cross section of photons scattered from a single free electron in lowest order of quantum electrodynamics.

Before this derivation, the electron cross section had been classically derived by the British physicist and discoverer of the electron,.J.