Radiation length

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.

Definition

In materials of high atomic number (e.g. tungsten, uranium, plutonium) the electrons of energies >~10 MeV predominantly lose energy by Template:Lang, and high-energy photons by Template:Chem2 pair production. The characteristic amount of matter traversed for these related interactions is called the radiation length Template:Math, usually measured in g·cm⁻². It is both the mean distance over which a high-energy electron loses all but Template:Math of its energy by Template:Lang, and Template:Frac of the mean free path for pair production by a high-energy photon. It is also the appropriate length scale for describing high-energy electromagnetic cascades.

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

$$X_0=716.4{\text{ g cm}}^{-2}\frac{A}{Z(Z+1)\ln \frac{287}{\sqrt{Z}}}=1433{\text{ g cm}}^{-2}\frac{A}{Z(Z+1)(11.319-\ln Z)},$$

where Template:Mvar is the atomic number and Template:Mvar is mass number of the nucleus.

For Template:Math, a good approximation is Template:Inconsistent. $$\frac{1}{X_0}=4{\left(\frac{\hslash }{m_{\mathrm{e}}c}\right)}^{2}Z(Z+1){\alpha }^3{n}_{\mathrm{a}}\log \left(\frac{183}{Z^{1/3}}\right),$$

where

• Template:Mvar is the number density of the nucleus,
• $\hslash$ denotes the reduced Planck constant,
• Template:Mvar is the electron rest mass,
• Template:Mvar is the speed of light,
• Template:Mvar 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 leptons and photons, the presence of the stronger hadronic and nuclear interaction 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.

See also

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

References

Template:Particle-stub