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

Abstract

Optimum distance (R[Formula: see text]) 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 10[Formula: see text]–[Formula: see text][Formula: see text]eV are simulated to find R[Formula: see text] for Alborz-I array located at an altitude of 1200[Formula: see text]m above sea level. It is shown that R[Formula: see text] is approximately independent of characteristics of primary particle and it is only dependent to array configuration. Dependency of R[Formula: see text] 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) R[Formula: see text] for its number of detectors. In this work, R[Formula: see text] for Alborz-I array is obtained about [Formula: see text][Formula: see text]m (from NKG function) and [Formula: see text][Formula: see text]m (from NKG type function). 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.