Astroparticle Physics

148 7 Secondary Cosmic Raysmuonsfrom inclined directionssea-level muon spectrumup to 20 TeV/clong distances in rare parts of the atmosphere. Because ofthe low area density at large altitudes for inclined directionsthe decay probability is increased compared to the interactionprobability. Therefore, for inclined directions pions willproduce predominantly high-energy muons in their decay.The result of these considerations is in agreement withobservation (Fig. 7.14). For about 170 GeV/c the muon intensityat 83 ◦ zenith angle starts to outnumber that of thevertical muon spectrum. The intensity of muons from horizontaldirections at low energies is naturally reduced becauseof muon decays and absorption effects in the thickeratmosphere at large zenith angles.The sea-level muon spectrum for inclined directions hasbeen measured with solid-iron momentum spectrometers upto momenta of approximately 20 TeV/c (Fig. 7.15). Forhigher energies the muon intensity decreases steeply.Fig. 7.14Sea-level muon momentum spectrafor vertical and inclined directionsFig. 7.15Momentum spectrum of muons atsea level for large zenith angles. Inthis figure the differential intensityis multiplied by p 3 µThe total intensity of muons, however, is dominated bylow-energy particles. Because of the increased decay probabilityand the stronger absorption of muons from inclineddirections, the total muon intensity at sea level varies likeI µ (θ) = I µ (θ = 0) cos n θ (7.2)charge ratio of muonsfor not too large zenith angles θ. The exponent of the zenithangledistribution is obtained to be n = 2. This exponentvaries very little, even at shallow depths underground, ifonly muons exceeding a fixed energy are counted.An interesting quantity is the charge ratio of muons atsea level. Since primary cosmic rays are positively charged,this positive charge excess is eventually also transferred to