Derivation of muon range spectrum under rock from the recent primary spectrum

Abstract

The muon range spectra under Mont Blanc Tunnel and Kolar Gold Field rocks have been calculated from the recently measured primary cosmic ray spectrum. The scaling hypothesis of Feynman has been used for the calculation of pion and kaon spectra in the atmosphere. The meson atmospheric diffusion equation has been solved by following the method of Bugaev et al. The derived muon energy spectrum has been found to be in good agreement with the measured data of the Kiel, Durham, DEIS, and Moscow University groups. The calculated muon energy spectra at large polar angles have been compared with the different experimental results. The integral muon spectrum up to 20 TeV supports the MARS burst data favourably. Using the procedure of Kobayakawa, the muon energy loss in rock due to ionization, pair production, and bremsstrahlung and nuclear interactions from Bezrukov and Bugaev, we have constructed the range–energy relation in Mont Blanc and Kolar Gold Field rocks. The estimated range spectra have been corrected for range fluctuations and have been compared with the Mont Blanc Tunnel data of Castagnoli et al., Bergamasco et al., and Sheldon et al. and the Kolar Gold Field data compilation by Krishnaswamy et al.