High-Energy Cosmic-Ray Muons Under Thick Layers of Matter I. a Method to Solve the Transport Equation

An effective analytical method for calculating energy spectra of cosmic-ray muons at large depths of homogeneous media is developed. The method allows to include an arbitrary (decreasing) muon spectrum at the medium boundary and the energy dependence of both discrete (radiative and photonuclear) and continuous (ionization) muon energy losses, with resonable requirements for the high-energy behavior of the initial spectrum and differential cross sections of the muon-matter interactions. (To be published in the Proceedings of the Second NESTOR International Workshop, 19 -- 21 October 1992, Pylos, Greece.)