Spatial and energy distribution of muons inγ-induced air showers

Abstract

The FLUKA Monte Carlo program is used to calculate the effects of hadroproduction by primary gamma rays incident upon the Earth's atmosphere; for the results presented in this paper, only primary angles at $0\ifmmode^\circ\else\textdegree\fi{}$ from zenith are considered. The FLUKA code is believed to be quite accurate in reproducing experimental photon hadroproduction data in the 1 GeV to 10 TeV energy range studied. The charged pions which are so produced can decay to muons with sufficient energy to reach ground level. The number of these muons and their radial and energy distribution are studied for incident gamma ray energies from 1 GeV to 10 TeV. The number of these muons is not negligible; they can, in certain circumstances, be used to study potential sources of gamma rays such as gamma ray bursts. It is found, for example, that a 10 TeV incident primary gamma ray produces, on average, 3.4 muons which reach ground level; the gamma ray energy which produces the maximum number of muons at ground level depends on the spectral index of the primary gamma spectrum, a constant which describes how the primary gamma flux rises with decreasing primary energy. For example, for a differential spectral index of 2.7, there is a broad maximum number of muons coming from $\ensuremath{\approx}30$ GeV primary gamma ray energy.