In particle physics, a shower is a cascade of secondary particles produced as the result of a high-energy particle interacting with dense matter. The incoming particle interacts, producing multiple new particles with lesser energy; each of these then interacts, in the same way, a process that continues until many thousands, millions, or even billions of low-energy particles are produced. These are then stopped in the matter and absorbed.
Types
There are two basic types of showers. Electromagnetic showers are produced by a particle that interacts primarily or exclusively via the electromagnetic force, usually a photon or electron. Hadronic showers are produced by hadrons (i.e. nucleons and other particles made of quarks), and proceed mostly via the strong nuclear force.
Electromagnetic showers An electromagnetic shower begins when a high-energy electron, positron or photon enters a material. At high energies (above a few MeV), in which the photoelectric effect and Compton scattering are insignificant, photons interact with matter primarily via pair production — that is, they convert into an electron-positron pair, interacting with an atomic nucleus or electron in order to conserve momentum. High-energy electrons and positrons primarily emit photons, a process called bremsstrahlung. These two processes (pair production and bremsstrahlung) continue, leading to a cascade of particles of decreasing energy until photons fall below the pair production threshold, and energy losses of electrons other than bremsstrahlung start to dominate. The characteristic amount of matter traversed for these related interactions is called the radiation length X 0 {\displaystyle X_{0}} . X 0 {\displaystyle X_{0}} is both the mean distance over which a high-energy electron loses all but 1/e of its energy by bremsstrahlung and 7/9 of the mean free path for pair production by a high energy photon. The length of the cascade scales with X 0 {\displaystyle X_{0}} ; the "shower depth" is approximately determined by the relation
X = X 0 ln ( E 0 / E c ) ln 2 , {\displaystyle X=X_{0}{\frac {\ln(E_{0}/E_{\mathrm {c} })}{\ln 2}},}
where X 0 {\displaystyle X_{0}} is the radiation length of the matter, and E c {\displaystyle E_{\mathrm {c} }} is the critical energy (the critical energy can be defined as the energy in which the bremsstrahlung and ionization rates are equal. A rough estimate is E c = 800 M e V / ( Z + 1.2 ) {\displaystyle E_{\mathrm {c} }=800\,\mathrm {MeV} /(Z+1.2)} ). The shower depth increases logarithmically with the energy, while the lateral spread of the shower is mainly due to the multiple scattering of the electrons. Up to the shower maximum the shower is contained in a cylinder with radius < 1 radiation length. Beyond that point electrons are increasingly affected by multiple scattering, and the lateral size scales with the Molière radius R M {\displaystyle R_{\mathrm {M} }} . The propagation of the photons in the shower causes deviations from Molière radius scaling. However, roughly 95% of the shower are contained laterally in a cylinder with radius 2 R M {\displaystyle 2R_{\mathrm {M} }} . The mean longitudinal profile of the energy deposition in electromagnetic cascades is reasonably well described by a gamma distribution:
d E d t = E 0 b ( b t ) a − 1 e − b t Γ ( a ) {\displaystyle {\frac {dE}{dt}}=E_{0}b{\frac {(bt)^{a-1}e^{-bt}}{\Gamma (a)}}}
where t = X / X 0 {\displaystyle t=X/X_{0}} , E 0 {\displaystyle E_{0}} is the initial energy and a {\displaystyle a} and b {\displaystyle b} are parameters to be fitted with Monte Carlo or experimental data.
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