Radiation length

 ( Experimental Particle Physics ) 

In particle physics, the radiation length is a characteristic of a material, related to the energy loss of high energy particles electromagnetically interacting with it. It is defined as the mean length (in cm) into the material at which the energy of an electron is reduced by the factor 1/ e.

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Definition In materials of high atomic number (e.g. tungsten, uranium, plutonium) the electrons of energies >~10 MeV predominantly lose energy by bremsstrahlung, and high-energy photons by pair production. The characteristic amount of matter traversed for these related interactions is called the radiation length , usually measured in g·cm⁻². It is both the mean distance over which a high-energy electron loses all but of its energy by bremsstrahlung, and of the mean free path for pair production by a high-energy photon. It is also the appropriate length scale for describing high-energy particle shower.

The radiation length for a given material consisting of a single type of nucleus can be approximated by the following expression:

(http://pdg.lbl.gov/)
     

$$X\_0\; =\; 716.4\; \backslash text\{\; g\; cm\}^\{-2\}\; \backslash frac\{A\}\{Z\; (Z+1)\; \backslash ln\{\backslash frac\{287\}\{\backslash sqrt\{Z\}\}\}\}\; =\; 1433\; \backslash text\{\; g\; cm\}^\{-2\}\; \backslash frac\{A\}\{Z\; (Z+1)\; (11.319\; -\; \backslash ln\{Z\})\},$$

where is the atomic number and is mass number of the nucleus.

For , a good approximation is

. $$\backslash frac\{1\}\{X\_0\}\; =\; 4\; \backslash left(\; \backslash frac\{\backslash hbar\}\{m\_\backslash mathrm\{e\}\; c\}\; \backslash right)^2\; Z(Z+1)\; \backslash alpha^3\; n\_\backslash mathrm\{a\}\; \backslash log\backslash left(\backslash frac\{183\}\{Z^\{1/3\}\}\backslash right),$$

where

• is the number density of the nucleus,
• $\backslash hbar$ denotes the reduced Planck constant,
• is the electron rest mass,
• is the speed of light,
• is the fine-structure constant.

For electrons at lower energies (below few tens of MeV), the energy loss by ionization is predominant.

While this definition may also be used for other electromagnetic interacting particles beyond and photons, the presence of the stronger hadronic and Nuclear force makes it a far less interesting characterisation of the material; the nuclear collision length and nuclear interaction length are more relevant.

Comprehensive tables for radiation lengths and other properties of materials are available from the Particle Data Group.

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See also

• Mean free path
• Attenuation length
• Attenuation coefficient
• Attenuation
• Range (particle radiation)
• Stopping power (particle radiation)
• Electron energy loss spectroscopy

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