The agreement of the Greisen–Zatzepin–Kuzmin prediction with the extensive air shower measurements of giant surface arrays

Abstract

In very large surface air shower arrays, like AGASA, the primary particle energy has usually been determined via relation to particle densities at 600 m from the shower axis (ρ600). Such a procedure requires a specific treatment for inclined cascades when the maximum of EAS development is close to the array (less than 2–3 radiation lengths above detector). According to the cascade theory and the simulations with the CORSIKA code for primary CR energies above 1019 eV, the exponential function used for ρ600 conversion from inclined to vertical showers is no longer valid. As follows from simulations at energies near to 1020 eV for zenith angles 15–35°, density ρ600 exceeds by about 10% the vertical density, whereas in the previous treatments (using an exponential function) it was usually assumed to be 30% lower. Such treatments generated an artificial increase of the estimated primary cosmic ray energy. The similar behaviour in lateral distributions of muons and photons has an additive contribution to this process. An appropriate algorithm is proposed here to restore the correct primary energy and to amend the previous intensity overestimated for 60–70% of the solid angle inside 45°. We expect that reconstruction of the primary spectrum by the procedure presented here, involving all effects for inclined showers, would eliminate the divergence between measurements at ultra-high energies and confirm the validity of the Greisen–Zatzepin–Kuzmin prediction.