The shape of the electron and muon lateral distribution functions of extensive air showers

Abstract: The lateral density data obtained for different secondaries of an extensive air shower (EAS) from an array of detectors are usually described by some suitable lateral density functions (LDFs). Analyzing non-vertical simulated EASs generated with the CORSIKA code, it is found that the lateral and polar density distributions of electrons and muons are asymmetric in the ground plane. It means that typical expressions for symmetric lateral density functions (SLDFs) (\emph{e.g.} the Nishimura-Kamata-Greisen function) are inadequate to reconstruct the lateral and polar dependencies of such asymmetric electron or muon densities accurately. In order to provide a more consistent LDF for non-vertical shower reconstruction in the ground plane, the paper considers the issue of the modification of the SLDF analytically. The asymmetry arising from additional attenuation and correction of the positional coordinates (radial and polar) of cascade particles causes a gap length between the center of concentric equidensity ellipses and the EAS core. A toy function is introduced as a basic LDF to describe the asymmetric lateral and polar density distributions of electrons or muons of EASs, thereby predicting the gap length parameter. Consequently, the desired LDF describing the asymmetric density distributions of electrons and muons of EASs has emerged. We compare results from detailed simulations with the predictions of the analytical parametrization. The LDF derived in this work is found to be well-suited to reconstruct EASs in the ground plane directly.