In this paper we study, using Monte Carlo simulations, the possibility to discriminate the mass of the Ultra High Energy Cosmic Rays (UHECRs) by combining information obtained from the maximum $X_{max}^{\mu}$ of the muon production rate longitudinal profile of Extensive Air Showers (EAS) and the number of muons, $N^{\mu}$, which hit an array of detectors located in the horizontal plane. We investigate the sensitivity of the 2D distribution $X_{max}^{\mu}$ versus $N^{\mu}$ to the mass of the primary particle generating the air shower. To this purpose we analyze a set of CORSIKA showers induced by protons and iron nuclei at energies of $10^{19}$eV and $10^{20}$eV, at five angles of incidence, $0^{\circ}$, $37^{\circ}$, $48^{\circ}$, $55^{\circ}$ and $60^{\circ}$. Using the simulations we obtain the 2D Probability Functions $Prob(X_{max}^{\mu},N^{\mu} \ | \ p)$ and $Prob(X_{max}^{\mu},N^{\mu} \ | \ Fe)$ which give the probability that a shower induced by a proton or iron nucleus contributes to a specific point on the plane ($X_{max}^{\mu}$, $N^{\mu}$). Then we construct the probability functions $Prob(p\ | \ X_{max}^{\mu},N^{\mu})$ and $Prob(Fe \ | \ X_{max}^{\mu},N^{\mu})$ which give the probability that a certain point on the plane ($X_{max}^{\mu}$, $N^{\mu}$) corresponds to a shower initiated by a proton or an iron nucleus, respectively. Finally, a test of this procedure using a Bayesian approach, confirms an improved accuracy of the primary mass estimation in comparison with the results obtained using only the $X_{max}^{\mu}$ distributions.
↧
