Electron penetration depth at which its energy is reduced by 1/e

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.^{[1]}

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 e^{+}e^{−} pair production. The characteristic amount of matter traversed for these related interactions is called the radiation length X_{0}, usually measured in g·cm^{−2}. It is both the mean distance over which a high-energy electron loses all but 1⁄e of its energy by bremsstrahlung,^{[1]} and 7⁄9 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:^{[2]}

$X_{0}=716.4{\text{ g cm))^{-2}{\frac {A}{Z(Z+1)\ln {\frac {287}{\sqrt {Z))))}=1433{\text{ g cm))^{-2}{\frac {A}{Z(Z+1)(11.319-\ln {Z}))),$