Symmetries in the Superposition Model of Extensive Air Shower Development

Abstract

According to the superposition principle, an extensive air shower initiated by a nucleus with energy E and mass number A can be approximated as the superposition of A proton-initiated showers each with energy E/A. The superposition principle for interactions of atomic nuclei proposes to describe nucleus-initiated extensive air showers using simulations performed for proton showers. Single detectors and systems working in tight coincidence mainly register events initiated by particles with very low energies, which are affected by major statistical fluctuations, such as those used in high schools for education and outreach purposes. Verifying whether the superposition principle is still a good approximation in the low-energy region is important for the validity of the interpretation of such measurements. We present results of the comparison of results of the superposition model with detailed simulations of showers with the CORSIKA program from the energy of 10 GeV. While the energy dependence of the mean shower parameters satisfies the superposition principle, the higher moments do not. A modification of the superposition model based on the wounded nucleon model, reducing these discrepancies, is proposed. The semi-analytical description of showers in the modified superposition model can give the density spectrum of cosmic ray particles, which is consistent with the measurements. In this paper, we present results both consistent with the superposition model and indicating the need for its modification. This modification is proposed and tested.