Estimating primary energy of cosmic rays by calculating secondary particles density in optimum distance from shower core

TL;DR

This study uses simulations to determine the optimal distance from the shower core for energy estimation of cosmic rays, showing that this distance is mainly influenced by array configuration rather than primary particle type.

Contribution

The paper introduces a method to identify the optimal distance for density measurement in cosmic ray showers, improving primary energy estimation accuracy.

Findings

Optimal distance (Ropt) is approximately 9 m for Alborz-I array.

Ropt depends mainly on array configuration, not primary particle type.

A new energy estimation function based on density at Ropt is proposed.

Abstract

Optimum distance (Ropt) is a distance from the shower core in which the density calculated by lateral distribution function, has its minimum uncertainty. In this paper, Using CORSIKA code, proton, carbon and iron primary in the energy range between 1013 - 3*1015eV are simulated to find Ropt for Alborz-I array located at an altitude of 1200 m above sea level. It is shown that Ropt is approximately independent of characteristics of primary particle and it is only dependent to array configuration. Dependency of Ropt on layout and detector spacing for 20 Alborz-I array detectors, are studied. It is shown that the Alborz-I array layout and its detector spacing result into the best (minimum uncertainty) Ropt for its number of detectors. In this work Ropt for Alborz-I array is obtained about 9 m. In addition, it is shown that, by finding dependency of primary energy to density in optimum distance, energy of primary particle can be estimated well. An energy estimation function is suggested and the function is examined by another set of simulated showers.