The effect of atmospheric attenuation on inclined cosmic ray air showers

The increasing cosmic ray statistics collected by present experiments and the future prospects with new large arrays demand accurate calculations of the extensive air shower (EAS) parameters. The energy of the primary particle is estimated by ground arrays fitting a lateral distribution function (LDF) to the particle densities at a given observing level. However, the lack of appropriate parameterization for these distributions, able to reproduce the data collected from all arrival directions, makes the experimental analysis difficult. We propose a method to parametrize particle density distributions of EAS at any incident zenith angle. Starting from analytical LDF for vertical showers we present a detailed study of the atmospheric depth dependence of the shower parameters. The results obtained are used to calculate the corresponding LDF for non-vertical showers including for the first time both, geometrical and atmospheric attenuation effects. We check the method analysing electron and muon LDF generated by Monte Carlo simulations from incident cosmic ray particles at different zenith angles. A comparison of the proposed LDF with experimental results, as well as MC data including detector effects, is also presented.