Va. Naumov et al., A NEW METHOD FOR CALCULATING THE ENERGY-SPECTRUM OF COSMIC-RAY MUONS UNDER THICK LAYERS OF MATTER, Physics of atomic nuclei, 57(3), 1994, pp. 412-424
An effective analytical method for solving the transport equation for
the energy spectrum of cosmic ray muons at large depths of homogeneous
media is developed. It makes it possible to consider an arbitrary (de
creasing) muon spectrum at the medium boundary and the real energy dep
endence of both discrete (radiative and photonuclear) and continuous (
ionization) muon energy losses with regard for reasonable requirements
on the high-energy behavior of the initial spectrum and differential
cross sections of the muon-matter interactions.