Reinterpreting the development of extensive air showers initiated by nuclei and photons

Understand

Ultra-high energy cosmic rays (UHECRs) interacting with the atmosphere generate extensive air showers (EAS) of secondary particles.

• The depth corresponding to the maximum development of the shower, $\Xmax$, is a well-known observable for determining the nature of the primary cosmic ray which initiated the cascade process.
• In this paper, we present an empirical model to describe the distribution of $\Xmax$ for EAS initiated by nuclei, in the energy range from $10^{17}$ eV up to $10^{21}$ eV, and by photons, in the energy range from $10^{17}$ eV up to $10^{19.6}$ eV.
• Our model adopts the generalized Gumbel distribution motivated by the relationship between the generalized Gumbel statistics and the distribution of the sum of non-identically distributed variables in dissipative stochastic systems.