Electromagnetic shower

An electromagnetic shower is a term from particle physics and describes a cascade of photons and electron - positron pairs. The overarching term is particle shower . The basis of the shower formation are the processes of pair generation and bremsstrahlung , which increase the number of particles in the cascade. In addition to the electromagnetic shower, there are hadronic showers .

Heitler-Schauer model

A simple model of an electromagnetic shower that goes back to Walter Heitler uses the material constants of the radiation length and the critical energy to describe the shower development. The critical energy is the energy at which the energy loss of electrons through ionization and through bremsstrahlung is the same. ${\displaystyle E_{C}}$ ${\displaystyle E_{C}}$

The model is based on the assumption that electrons and photons interact on average after a radiation length and thus the number of particles in the shower doubles, with the energy being distributed equally to the daughter particles. Becomes the dimensionless variable ${\displaystyle X_{0}}$

${\displaystyle t={\frac {X}{X_{0}}}}$

is used, then the energy of the particles decreases by accumulated matter column as ${\displaystyle X}$

${\displaystyle E(t)={\frac {E_{0}}{2^{t}}}}$

write, where is the initial energy of the primary particle. The shower growth ends when the energy of the secondary particles reaches the critical energy . This results in the maximum shower penetration depth ${\displaystyle E_{0}}$ ${\displaystyle E(t)}$ ${\displaystyle E_{C}}$ ${\displaystyle X_{max}}$

${\displaystyle X_{max}=t(E_{c})\cdot X_{0}={\frac {\ln(E_{0})-\ln(E_{c})}{\ln 2}}\cdot X_{0}}$ .

This shows that the depth of penetration of a shower grows logarithmically with the energy. This is particularly important for the design of calorimeters in particle detectors. The maximum number of particles can be found in this model with

${\displaystyle N_{max}=\exp(t(E_{c})\ln 2)={\frac {E_{0}}{E_{c}}}}$

to calculate. It is proportional to the input energy, which allows the primary energy to be measured by measuring the number of particles. ${\displaystyle E_{0}}$

For measurements, more precise Monte Carlo simulations are used, which can also map statistical fluctuations of such a shower. A program that can perform such simulations is e.g. B. Geant4 .

The transverse extent of a shower is determined by the multiple scattering of low-energy particles and is therefore not described by this simple model. The relevant quantity for the transversal extension is the Molière radius .

Applications

The measurement of electromagnetic showers in a calorimeter allows the energy of photons and electrons to be measured in particle physics . The electromagnetic showers in the air can also be used to measure high-energy gamma radiation from space.

See also

• Particle shower
• Air shower

literature

• Wei-Ming Yao et al. (Particle Data Group): 2006 Review of Particle Physics . In: J. Phys. G. 33, 2006 ( Section 27.4 ).
• BR Martin and G. Shaw: Particle Physics . John Wiley & Sons Ltd, Chichester, UK. (2012), chap. 4.4, ISBN 978-0-470-03293-0 .