Astroparticle Physics

7.1 Propagation in the Atmosphere 143of scientific balloons (≈ 35–40 km) corresponds to approximatelyseveral g/cm 2 . For inclined directions the thicknessof the atmosphere increases strongly (approximately like1/ cos θ, with θ – zenith angle). Figure 7.4 shows the variationof atmospheric depth with zenith angle at sea level.For the interaction behaviour of primary cosmic rays thethickness of the atmosphere in units of the characteristic interactionlength for the relevant particles species in questionis important. The radiation length for photons and electronsin air is X 0 = 36.66 g/cm 2 . The atmosphere therefore correspondsto a depth of 27 radiation lengths. The relevantinteraction length for hadrons in air is λ = 90.0g/cm 2 ,correspondingto 11 interaction lengths per atmosphere. Thismeans that practically not a single particle of original primarycosmic rays arrives at sea level. Already at altitudes of15 to 20 km primary cosmic rays interact with atomic nucleiof the air and initiate – depending on energy and particlespecies – electromagnetic and/or hadronic cascades.The momentum spectrum of the singly charged componentof primary cosmic rays at the top of the atmosphereis shown in Fig. 7.5. In this diagram the particle velocityβ = v/c is shown as a function of momentum. Clearly visibleare the bands of hydrogen isotopes as well as the lowflux of primary antiprotons. Even at these altitudes severalmuons have been produced via pion decays. Since muon andpion mass are very close, it is impossible to separate themout in this scatter diagram. Also relativistic electrons andpositrons would populate the bands labeled µ + and µ − .Onegenerally assumes that the measured antiprotons are not ofprimordial origin, but are rather produced by interactions ininterstellar or interplanetary space or even in the residual atmosphereabove the balloon.The transformation of primary cosmic rays in the atmosphereis presented in Fig. 7.6. Protons with approximately85% probability constitute the largest fraction of primarycosmic rays. Since the interaction length for hadronsis 90 g/cm 2 , primary protons initiate a hadron cascade alreadyin their first interaction approximately at an altitudecorresponding to the 100 mbar layer. The secondary particlesmost copiously produced are pions. Kaons on the otherhand are only produced with a probability of 10% comparedto pions. Neutral pions initiate via their decay (π 0 → γ +γ )electromagnetic cascades, whose development is characterizedby the shorter radiation length (X 0 ≈ 1 3λ in air). Thisatmospheric depth [g/cm ]210 510 410 30°20° 40° 60° 80°zenith angle Fig. 7.4Relation between zenith angle andatmospheric depth at sea levelradiation lengthinteraction lengthelectromagneticand hadronic cascadesFig. 7.5Identification of singly chargedparticles in cosmic rays at a flightaltitude of balloons (̂= 5 g/cm 2residual atmosphere) {21}