Molière radius

The Molière radius is a material constant and describes the transverse expansion of an electromagnetic shower , which is mainly caused by multiple scattering. The radius is defined as

${\displaystyle R_{\text{m}}={\frac {21\,{\text{MeV}}}{E_{\text{C}}}}X_{0}}$

with the critical energy of the material and its radiation length . If the radiation length is given as mass coverage , for example in units of , then this must be divided by the density of the material. The critical energy is defined as the particle energy at which the energy loss due to bremsstrahlung is equal to that due to ionization : ${\displaystyle E_{\text{C}}}$ ${\displaystyle X_{0}}$ ${\displaystyle [{\text{g}}/{\text{cm}}^{2}]}$ ${\displaystyle \varrho }$

${\displaystyle \left({\frac {{\text{d}}E}{{\text{d}}x}}\right)_{\text{Brems.}}=\left({\frac {{\text{d}}E}{{\text{d}}x}}\right)_{\text{Ionis.}}\qquad {\text{für }}E=E_{\text{C}}}$

The following equation represents an approximation for : ${\displaystyle E_{\text{C}}}$

${\displaystyle E_{\text{C}}={\frac {800\,{\text{MeV}}}{Z+1{,}2}}}$

with the atomic number . ${\displaystyle Z}$

To a good approximation, the lateral width of a shower is independent of its depth and thus its energy. 90% (95%) of the energy is deposited within a very narrow shower core, which can be described by means of an idealized cylinder around the shower axis. Its radius is estimated as (or ). This quantity is primarily used in the development and application of calorimeters in particle physics. A small Molière radius indicates a good shower position resolution, and there is less overlap of nearby showers. ${\displaystyle R(90\,\%)=R_{\text{m}}}$ ${\displaystyle R(95\,\%)=2R_{\text{m}}}$

literature

• Dan Green: The Physics of Particle Detectors . Cambridge University Press, 2000, ISBN 0-521-66226-5 , p. 251 ( limited preview in Google Book Search).

Individual evidence

1. ^ Claus Grupen: Particle Detectors. Wissenschaftsverlag, 1993, p. 298.
2. ^ WR Leo: Techniques for Nuclear and Particle Physics Experiments. Springer-Verlag, 1994, p. 41 ( limited preview in the Google book search).