In physics, the radiation length is a characteristic of a material, related to the energy loss of high energy, electromagnetic-interacting particles with it.

## Definition

In materials of high atomic number (e.g. W, U, Pu) 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 X0, usually measured in g·cm−2. It is both the mean distance over which a high-energy electron loses all but 1e of its energy by bremsstrahlung, and 79 of the mean free path for pair production by a high-energy photon. It is also the appropriate scale length for describing high-energy electromagnetic cascades.

The radiation length for a given material consisting of a single type of nuclei can be approximated by the following expression:[1]

$X_0 = \frac{716.4\cdot A}{Z (Z+1) \ln{\frac{287}{\sqrt{Z}}}}\;\mathrm g\cdot \mathrm{cm}^{-2} = \frac{1432.8\cdot A}{Z (Z+1) (11.319 - \ln{Z})}\;\mathrm g\cdot \mathrm{cm}^{-2}$,

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

Or exactly using:[2] $\frac{1}{X_0} = \frac{4\alpha N_A Z(Z+1)r_e^2 \log(183Z^{-1/3})}{A}$

For electrons at lower energies (below few tens of MeVs), 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 [3] [4]