A Monte Carlo Calculation of Muon Flux at Ground Level from Primary Cosmic Gamma Rays

The Monte Carlo program FLUKA was used to calculate the number of muons reaching detection level in events initiated by primary cosmic gamma ray interactions in the atmosphere. The calculation was motivated by the desire to gauge the sensitivity of arrays like that of Project GRAND to primary gamma cosmic rays while measuring single muons at detection level. Because direct gamma pair production is not a significant source of muons, normally the presence of muons is not considered as a signal for gamma rays. However, due to their non-negligible cross section for hadron production, high-energy gamma rays can initiate hadronic showers containing a large number of pions. These can decay producing secondary muons which then have a good chance of reaching detection level. The complete kinetic energy and space distribution of such muons can be predicted by simulating in detail the whole process by means of Monte Carlo techniques. However, the code used must be capable of handling both hadron-nucleus and photon-nucleus interactions. Unlike most available Monte Carlo particle transport programs, such interactions are implemented in FLUKA, up to several tens of TeV, based on Dual Parton and Vector Meson Dominance models. The FLUKA capability to describe hadronic cascades generated in the atmosphere by primary cosmic hadrons has already been shown in several studies. In the present paper, the investigation has been extended to primary gamma rays. The number of muons per photon is presented as a function of the primary energy in the region between 3 GeV and 10 TeV. As the energy of primary photons rises, their flux falls, whereas the number of muons per gamma rises. Combining these two effects, it can be predicted that gamma ray energies in the 30 GeV region produce the most muons at detection level. The radial and kinetic energy distributions of the muons are also presented.