Astroparticle Physics

154 7 Secondary Cosmic RaysFig. 7.21Variation of the exponent n of thezenith-angle distribution of muonswith depthFig. 7.22Ratio of stopping to penetratingmuons as a function of depth incomparison to some experimentalresults. (1) Stopping atmosphericmuons, (2) stopping muons fromnuclear interactions, (3) stoppingmuons locally produced byphotons, (4) neutrino-inducedstopping muons, and (5) sum ofall contributions(Fig. 7.21). For large depths the exponent n in this distribution,however, gets very large, so that it is preferable to use(7.14) instead.The average energy of muons at sea level is in the rangeof several GeV. Absorption processes in rock reduce predominantlythe intensity at low energies. Therefore, the averagemuon energy of the muon spectrum increases withincreasing depth. Muons of high energy can also produceother secondary particles in local interactions. Since lowenergymuons can be identified by their (µ → eνν) decaywith the characteristic decay time in the microsecond range,the measurement of stopping muons underground providesan information about local production processes. The flux ofstopping muons is normally determined for a detector thicknessof 100 g/cm 2 and the ratio P of stopping to penetratingmuons is presented (Fig. 7.22).A certain fraction of stopping muons is produced locallyby low-energy pions which decay relatively fast into muons.Since the flux of penetrating muons decreases strongly withincreasing depth, the ratio P of stopping to penetratingmuons is dominated by neutrino interactions for depthslarger than 5000 m w.e.The knowledge of the particle composition at largedepths below ground represents an important informationfor neutrino astrophysics.Also remnants of extensive air showers, which developedin the atmosphere, are measured underground. Electrons,positrons, photons, and hadrons are completely absorbedalready in relatively shallow layers of rock. Therefore,only muons and neutrinos of extensive air showerspenetrate to larger depths. The primary interaction vertexof particles which initiate the air showers is typically atan atmospheric altitude of 15 km. Since secondary particlesin hadronic cascades have transverse momenta of about300 MeV/c only, the high-energy muons essentially follateralspread of muonslike 1/ cos θ. Therefore, at large depths and from inclineddirections neutrino-induced muons dominate.For not too large zenith angles and depths the zenithangledependence of the integral muon spectrum can still berepresented byI(θ) = I(θ = 0) cos n θ (7.16)underground low the shower axis. For primaries of energy around 10 14eV lateral displacements of energetic muons (≈ 1TeV)