Electromagnetic Shower

  Bremsstrahlung and electron pair production are the dominant processes for high-energy electrons and photons; their cross-sections become nearly independent of energy above 1 GeV. The dominance of these electromagnetic processes and their small fluctuations distinguish the electromagnetic showers (initiated by e's and 's) hadronic shower. The , decaying electromagnetically, produces two, possibly three, electromagnetic showers ( Dalitz pair).

The cross-sections can be described in units of a scaling variable, radiation length X₀.

Secondaries produced in electromagnetic processes are again mainly and , and most of the energy is consumed for particle production (inelasticity 1). The cascade develops through repeated similar interactions. The shower maximum, with the largest number of particles, is reached when the average energy per particle becomes low enough to stop further multiplication. From this point the shower decays slowly through ionization losses for e^-, or by Compton scattering for photons. This change is characterized by the critical energy in the absorber material. is the electron energy for which energy loss by radiation equals the collision and ionization losses, and is approximately 550 MeV/Z. Nuclear interactions (photonuclear effects) play a negligible role.

The electromagnetic shower shape, to a good approximation, scales longitudinally with the radiation length, and laterally with the Moliere radius. Experimental results on shower shape have been parameterized in the following way (see [Fabjan82]):

Shower maximum:

with

Shower depth for 95% longitudinal containment:

Transverse shower dimension (95% radial containment):

For the average differential longitudinal energy deposit over the volume of the cascade a reasonable longitudinal parametric approximation is given by:

with a and b fitted from Monte Carlo or experimental data ( [Bock81] or [Longo75]) and

t = depth starting from shower origin in units of X₀

k =

For the average lateral electromagnetic shower development, double exponentials and Breit-Wigner distributions have been shown to fit experimental data (see [Acosto92]).