Astroparticle Physics

50 4 Physics of Particle and Radiation Detection4.1 Interactions of Astroparticles“Observations are meaningless withouta theory to interpret them.”Raymond A. Lyttletonmeasurementof primary nucleiFig. 4.1Cross section for proton–airinteractionsmean free pathλ =A ≈ 93 g/cm 2 . (4.3)N A σ AThis means that the first interaction of protons occurs in theupper part of the atmosphere. If the primary particles are notprotons but rather iron nuclei (atomic number A Fe = 56),the first interaction will occur at even higher altitudes becausethe cross section for iron–air interactions is correspondinglylarger.Primary high-energy photons (energy ≫ 10 MeV) inter-act via the electromagnetic process of electron–positron pairproduction. The characteristic interaction length 1 (’radiation1 The radiation length for electrons is defined in (4.7). It describesthe degrading of the electron energy by bremsstrahlungaccording to E = E 0 e −x/X 0. This ‘interaction length’ X 0 isalso characteristic for pair production by photons. The interactionlength for hadrons (protons, pions, ...) is defined through(4.3), where σ A is the total cross section. This length is sometimesalso called collision length. If the total cross section in(4.3) is replaced by its inelastic part only, the resulting lengthis called absorption length.detection of primary photonsThe primary particles carrying astrophysical information arenuclei (protons, helium nuclei, iron nuclei, ...), photons, orneutrinos. These three categories of particles are characterizedby completely different interactions. Protons and othernuclei will undergo strong interactions. They are also subjectto electromagnetic and weak interactions, however, thecorresponding cross sections are much smaller than thoseof strong interactions. Primary nuclei will therefore interactpredominantly via processes of strong interactions. Atypical interaction cross section for inelastic proton–protonscattering at energies of around 100 GeV is σ N ≈ 40 mb(1 mb = 10 −27 cm 2 ). Since high-energy primary protonsinteract in the atmosphere via proton–air interactions, thecross section for proton–air collisions is of great interest.The dependence of this cross section on the proton energy isshown in Fig. 4.1.For a typical interaction cross section of 250 mb, themean free path of protons in the atmosphere (for nitrogen:A = 14) is, see Chap. 3, (3.54),