A new method for calculating energy spectrum of cosmic ray muons under thick layers of matter

An effective analytical method to solve the transport equation for energy spectrum of cosmic ray muons at large depths of homogeneous media is developed. It allows to include an arbitrary (decreasing) muon spectrum at the medium boundary and the real energy dependence of both discrete (radiative and photonuclear) and continuous (ionization) muon energy losses, with reasonable requirements for the high-energy behavior of initial spectrum and differential cross sections of muon-matter interactions