Astroparticle Physics

170 7 Secondary Cosmic Rays5. Figure 7.23 shows a muon shower in the ALEPH experiment.Typical energies of muons in this shower are100 GeV. What is the r.m.s. scattering angle of muons inrock for such muons (overburden 320 m w.e., radiationlength in rock X 0 = 25 g/cm 2 ̂= 10 cm)?6. Narrow muon bundles with muons of typically 100 GeVoriginate in interactions of primary cosmic rays in theatmosphere. Estimate the typical lateral separation ofcosmic-ray muons in a bundle at a depth of 320 m w.e.underground.7. Due to the dipole character of the Earth’s magnetic fieldthe geomagnetic cutoff varies with geomagnetic latitude.The minimum energy for cosmic rays to penetrate theEarth’s magnetic field and to reach sea level can beworked out to beE min = ZeM4R 2 cos4 λ,where Z is the charge number of the incident particle,M is the moment of the Earth’s magnetic dipole, R isthe Earth radius, λ is the geomagnetic latitude (0 ◦ at theequator). For protons one gets E min = 15 GeV cos 4 λ.The Earth’s magnetic field has reversed several timesover the history of our planet. In those periods when thedipole changed polarity, the magnetic field went throughzero. In these times when the magnetic shield decayed,more cosmic-ray particles could reach the surface of theEarth causing a higher level of radiation for life developingon our planet. Whether this had a positive effecton the biological evolution or not is the object of muchdebate. The estimation of the increased radiation levelfor periods of zero field can proceed along the followinglines:• the differential energy spectrum of primary cosmicrays can be represented by a power law N(E) ∼ E −γwith γ = 2.7.• in addition to the geomagnetic cutoff there is also anatmospheric cutoff due to the energy loss of chargedparticles in the atmosphere of ≈ 2GeV.Work out the increase in the radiation level using theabove limits!8. Neutrons as candidates for the highest-energy cosmicrays have not been discussed so far. What are the problemswith neutrons?