View source for Radiation length

{{short description|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 [[elementary particle|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 (mathematical constant)|''e'']].<ref name=Gupta/>

==Definition==
In materials of high atomic number (e.g. [[tungsten]], [[uranium]], [[plutonium]]) the [[electrons]] of energies >~10 MeV predominantly lose energy by {{lang|de|[[bremsstrahlung]]}}, and high-energy [[photons]] by {{chem2|[[Positron|e+]][[electron|e-]]}} pair production. The characteristic amount of matter traversed for these related interactions is called the radiation length {{math|''X''<sub>0</sub>}}, usually measured in g·cm<sup>−2</sup>. It is both the mean distance over which a high-energy electron loses all but {{math|{{frac|1|[[e (mathematical constant)|''e'']]}}}} of its energy by {{lang|de|bremsstrahlung}},<ref name=Gupta>
{{cite journal
  |author=M. Gupta
  |title=Calculation of radiation length in materials
  |journal=PH-EP-Tech-Note
  |year=2010
  |volume=592
 |issue=1–4
 |page=1
 |doi=10.1016/j.physletb.2004.06.001
 |arxiv=astro-ph/0406663
 |display-authors=etal|bibcode=2004PhLB..592....1P
  }}</ref> and {{frac|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 [[particle shower|electromagnetic cascade]]s.

The radiation length for a given material consisting of a single type of nucleus can be approximated by the following expression:<ref name=pdg>
{{cite journal
  |author=S. Eidelman
  |title=Review of particle physics
  |journal=Phys. Lett. B
  |volume=592
  |issue=1–4
  |pages=1–5
  |year=2004
  |doi=10.1016/j.physletb.2004.06.001
  |display-authors=etal|bibcode=2004PhLB..592....1P
  |arxiv=astro-ph/0406663
  }} (http://pdg.lbl.gov/)</ref>

<math display=block>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})},</math>

where {{mvar|Z}} is the [[atomic number]] and {{mvar|A}} is [[mass number]] of the nucleus.

For {{math|''Z'' > 4}}, a good approximation is<ref>
{{cite book
 |first1=Alessandro
 |last1=De Angelis
 |first2=Mário
 |last2=Pimenta
 |title=Introduction to Particle and Astroparticle Physics
 |year=2018
 |edition=2
 |publisher=Springer
 |isbn=978-3-319-78180-8
 |doi=10.1007/978-3-319-78181-5
|bibcode=2018ipap.book.....D
 }}</ref>
{{Inconsistent|date=October 2020|reason=dimension inconsistent; maybe given in different convention and mass density rho is missing.}}.
<math display=block>\frac{1}{X_0} = 4 \left( \frac{\hbar}{m_\mathrm{e} c} \right)^2 Z(Z+1) \alpha^3 n_\mathrm{a} \log\left(\frac{183}{Z^{1/3}}\right),</math>

where 
*{{mvar|n{{sub|a}}}} is the [[number density]] of the nucleus, 
*<math>\hbar</math> denotes the reduced [[Planck constant]], 
*{{mvar|m{{sub|e}}}} is the [[electron rest mass]], 
*{{mvar|c}} is the [[speed of light]], 
*{{mvar|&alpha;}} 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 [[lepton]]s and photons, the presence of the stronger [[strong interaction|hadronic]] and [[Nuclear force|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]].<ref name=pdg /><ref>{{cite web|title=AtomicNuclearProperties on the Particle Data Group|url=http://pdg.lbl.gov/AtomicNuclearProperties|access-date=2008-01-26|archive-date=2021-07-24|archive-url=https://web.archive.org/web/20210724105007/https://pdg.lbl.gov/AtomicNuclearProperties/|url-status=dead}}</ref>

==See also==
* [[Mean free path]]
* [[Attenuation length]]
* [[Attenuation coefficient]]
* [[Attenuation]]
* [[Range (particle radiation)]]
* [[Stopping power (particle radiation)]]
* [[Electron energy loss spectroscopy]]

==References==
{{Reflist|2}}

[[Category:Experimental particle physics]]


{{particle-stub}}