On the energy estimation of ultra-high-energy cosmic rays observed with the surface detector array

A Monte Carlo simulation has been carried out to look for a suitable parameter as the energy estimator for large extensive air showers (EAS) at Akeno. For primaries of fixed energy, the fluctuation of the electron density at several hundred metres from the EAS core is smaller than that near the core, as has been pointed out by Hillas et al. (1971). The present simulation shows that the fluctuation of the electron density at 600 m (S(600)) from the core is within 20%, irrespective of the primary composition, for zenith angles less than 35 degrees and primary energies above 10 18 eV. The conversion factor from S(600) to the primary energy is independent of primary composition and interaction models within a certain zenith angle (<or=35 degrees ), but depends on the lateral distribution function of electrons. By using the interaction model (QCD) and the lateral distribution function which give the best fit to Akeno experimental data, the conversion factor at Akeno level (920 g cm -2 ) is E 0 (eV)=(2.03+or-0.10)*10 17 S(600) 1.02+or-0.02 for vertical showers with energy greater than 10 17 eV.