Astroparticle Physics

7.4 Extensive Air Showers 157hadronic, and a neutrino component (see Fig. 7.6). The airshower develops a shower nucleus consisting of energetichadrons, which permanently inject energy into the electromagneticand the other shower components via interactionsand decays. Neutral pions, which are produced in nuclear interactionsand whose decay photons produce electrons andpositrons via pair production, supply the electron, positron,and photon component. Photons, electrons, and positronsinitiate electromagnetic cascades through alternating processesof pair production and bremsstrahlung. The muon andneutrino components are formed by the decay of charged pionsand kaons (see also Fig. 7.6).The inelasticity in hadron interactions is on the order of50%, i.e., 50% of the primary energy is transferred into theproduction of secondary particles. Since predominantly pionsare produced (N(π) : N(K) = 9 : 1) and all chargestates of pions (π + ,π − ,π 0 ) are produced in equal amounts,one third of the inelasticity is invested into the formation ofthe electromagnetic component. Since most of the chargedhadrons and the hadrons produced in hadron interactionsalso undergo multiple interactions, the largest fraction of theprimary energy is eventually transferred into the electromagneticcascade. Therefore, in terms of the number of particles,electrons and positrons constitute the main shower component.The particle number increases with shower depth t untilabsorptive processes like ionization for charged particlesand Compton scattering and photoelectric effect for photonsstart to dominate and cause the shower to die out.The development of electromagnetic cascades is shownin Fig. 7.25 for various primary energies. The particle intensityincreases initially in a parabolical fashion and decaysexponentially after the maximum of the shower has beenreached. The longitudinal profile of the particle number canbe parameterized byhadron, electromagnetic,muon, neutrino componentinelasticitynumber of shower particles10 510 410 310 210110 –110 2 10 3 10 410 6 = E/E 0 C0 10 20 30 40 50shower depth t[ X 0]Fig. 7.25Longitudinal shower developmentof electromagnetic cascades. (Thecritical energy in air isE c = 84 MeV)N(t) ∼ t α e −βt , (7.17)where t = x/X 0 is the shower depth in units of the radiationlength and α and β are free fit parameters. The position ofthe shower maximum varies only logarithmically with theprimary energy, while the total number of shower particlesincreases linearly with the energy. The latter can thereforebe used for the energy determination of the primary particle.One can imagine that the Earth’s atmosphere representsa combined hadronic and electromagnetic calorimeter,longitudinal particle-numberprofile