Astroparticle Physics

144 7 Secondary Cosmic RaysFig. 7.6Transformation of primary cosmicrays in the atmosphereFig. 7.7Decay probabilities for chargedpions and kaons in the atmosphereas a function of their kineticenergyshower component is absorbed relatively easily and is thereforealso named a soft component. Charged pions and kaonscan either initiate further interactions or decay.The competition between decay and interaction probabilityis a function of energy. For the same Lorentz factorcharged pions (lifetime 26 ns) have a smaller decayprobability compared to charged kaons (lifetime 12.4ns).The decay probability of charged pions and kaons in theatmosphere is shown in Fig. 7.7 as a function of theirkinetic energy. The leptonic decays of pions and kaonsproduce the penetrating muon and neutrino components(π + → µ + + ν µ , π − → µ − +¯ν µ ; K + → µ + + ν µ ,K − → µ − +¯ν µ ). Muons can also decay and contributevia their decay electrons to the soft component and neutrinosto the neutrino component (µ + → e + + ν e +¯ν µ ,µ − → e − +¯ν e + ν µ ).The energy loss of relativistic muons not decaying in theatmosphere is low (≈ 1.8 GeV). They constitute with 80%of all charged particles the largest fraction of secondary particlesat sea level.Some secondary mesons and baryons can also survivedown to sea level. Most of the low-energy charged hadronsobserved at sea level are locally produced. The total fractionof hadrons at ground level, however, is very small.Apart from their longitudinal development electromagneticand hadronic cascades also spread out laterally in theatmosphere. The lateral size of an electromagnetic cascadeis caused by multiple scattering of electrons and positrons,while in hadronic cascades the transverse momenta at productionof secondary particles are responsible for the lateralwidth of the cascade. Figure 7.8 shows a comparison of theshower development of 100 TeV photons and 100 TeV protonsin the atmosphere. It is clearly visible that transversemomenta of secondary particles fan out the hadron cascade.The intensity of protons, electrons, and muons of all energiesas a function of the altitude in the atmosphere is plottedin Fig. 7.9. The absorption of protons can be approximatelydescribed by an exponential function.The electrons and positrons produced through π 0 decaywith subsequent pair production reach a maximum intensityat an altitude of approximately 15 km and soon after are relativelyquickly absorbed while, in contrast, the flux of muonsis attenuated only relatively weakly.