The muon energy spectrum at sea level from the intensities deep underground

Abstract

The energy spectrum of muons at sea level is determined from the intensities deep underground. The following three points are different from past treatments: (1) From the energy-loss relation, −(dE/dt) = k(E) + b(E)E, including the effect of nuclear interaction and without the assumption that b is independent of E, the average range–energy relation is derived. (2) The reliable values of the factor which corrects for fluctuations in energy loss of muons passing through a great thickness of material are used. (3) Many authors measured the intensities under their respective rocks. The differences of these rocks are taken into account in the following way. The intensities are directly converted into the energy spectrum at sea level by using the appropriate average range–energy relations and correction factors. The resultant integral exponent of the energy spectrum in the vertical direction is β = 2.541 ± 0.190 with 95% confidence over the energy range 0.4–7 TeV having a weighted mean of 0.7 TeV.