Cosmic-ray spectra of primary protons and high altitude muons deconvolved from observed atmospheric gamma rays

Abstract

We have observed atmospheric gamma rays from 30 GeV to 8 TeV, using emulsion chambers at balloon altitudes, accumulating the largest total exposure in this energy range to date, $S\ensuremath{\Omega}T\ensuremath{\sim}6.66\text{ }\text{ }{\mathrm{m}}^{2}\text{ }\mathrm{sr}\text{ }\mathrm{day}$. At very high altitudes, with residual overburden only a few $\mathrm{g}\text{ }{\mathrm{cm}}^{\ensuremath{-}2}$, atmospheric gamma rays are mainly produced by a single interaction of primary cosmic rays with overlying atmospheric nuclei. Thus, we can use these gamma rays to study the spectrum of primary cosmic rays and their products in the atmosphere. From the observed atmospheric gamma-ray spectrum, we deconvolved the primary cosmic-ray proton spectrum, assuming appropriate hadronic interaction models. Our deconvolved proton spectrum covers the energy range from 200 GeV to 50 TeV, which fills a gap in the currently available primary cosmic-ray proton spectra. We also estimated the atmospheric muon spectrum above 30 GeV at high altitude from our gamma-ray spectrum, almost without reference to the primary cosmic rays, and compared the estimated flux with direct muon observations below 20 GeV.