Simple method for solving transport equations describing the propagation of cosmic-ray nucleons in the atmosphere

A simple and efficient method is proposed for solving transport equations t hat describe the propagation of cosmic-ray protons and neutrons in the atmo sphere at high energies. It is shown that, upon taking into account a non-p ower-law character of the primary spectrum, a growth of total cross section s for inelastic nucleon-nucleus interactions, and violation of scaling in s uch interactions, the effective absorption ranges of nucleons come to be de pendent not only on energy but also on the depth in the atmosphere. The res ults of the calculations are compared with available experimental data. (C) 2000 MAIK "Nauka/Interperiodica".