Three-Dimensional Monte Carlo Simulation of Extensive Air Showers

Abstract

We have carried out a three-dimensional Monte Carlo simulation of extensive air showers (EAS) with primary energies between ${10}^{14}$ and ${10}^{16}$ eV. The experimentally observable effects of three interaction models and two primary particles (Fe and proton) have been determined. In all, some 500 simulated EAS at three primary energies were analyzed at two atmospheric depths: 530 and 970 g ${\mathrm{cm}}^{\ensuremath{-}2}$. This analysis yielded average lateral distributions and energy spectra of nuclear-active particles (n.a.p.) and muons, together with the extent of the fluctuations in these quantities. The calculations also yielded the size of each EAS. This, in turn, enabled us to calculate measurable quantities normalized to shower size for comparison with experimental dat. Our principal results and conclusions are as follows: (1) The extent of the fluctuations in shower size ${N}_{e}$ for a fixed primary energy ${E}_{0}$ is about a factor of 2 at mountain altitudes (530 g ${\mathrm{cm}}^{\ensuremath{-}2}$) and as much as a factor of 30 at sea level. Thus, at 530 g ${\mathrm{cm}}^{\ensuremath{-}2}$, ${N}_{e}$ is a good measure of the primary energy. (2) The extent of the fluctuations in the total n.a.p. energy per shower normalized to ${N}_{e}$, for EAS with Fe primaries (Fe-EAS), is less than $\frac{1}{25}$ of that for EAS with proton primaries ($p$-EAS). Data from a n.a.p. detector of large area and good energy resolution could thus yield meaningful results concerning the primary composition. (3) The relative number of high-energy nucleons to pions at 530 g ${\mathrm{cm}}^{\ensuremath{-}2}$ is significantly greater for Fe-EAS than for $p$-EAS. However, our calculations do not take into account the possibility of copious nucleon-antinucleon production at high energies in EAS. (4) The effect of introducing a few very highenergy pions (from isobar decay) into a two-center production spectrum is small compared to the effect of substituting Fe primaries for proton primaries. (5) The distribution of transverse momentum that we adopted [$f({p}_{t})\ensuremath{\propto}\mathrm{exp}(\ensuremath{-}\frac{{{p}_{t}}^{2}}{{{p}_{0}}^{2}})$, ${〈{p}_{t}〉}_{\mathrm{av}}=350$ MeV/c] yields steeper lateral distributions than those observed experimentally. It is thus deficient in particles of large ${p}_{t}$.