Parametrization of atmospheric muon angular flux underwater

The analytical expression for the angular integral flux of atmospheric muons in matter with an explicit relation of its parameters with those of the sea level spectrum is obtained. The fitting formula for the sea level muon spectrum at different zenith angles for a spherical atmosphere is proposed. The concrete calculations for pure water are presented. Fluctuations of muon energy losses are taken into account by means of a parametrized correction factor calculated using survival probabilities resulting from Monte Carlo simulations. Parametrizations of all continuous energy losses are obtained using the most recent expressions for muon interaction cross sections. The corresponding parametrization errors and field of method application are comprehensively discussed. The proposed formulas could be useful primarily for experimentalists processing data of arrays located deep under water or ice.