Primary Cosmic-Ray Spectrum at High Energies and Spectra ofγRays and Muons in the Atmosphere

The shape of the primary cosmic-ray spectrum at very high energies and its connection with the spectra of high-energy $\gamma$-rays and muons in the atmosphere have been discussed. Using a simple formulation for calculating secondary spectra arising from power-law primary spectra cutoff at arbitrary points, it is shown that a specific two-component model for the primary spectrum explains the present observations on the high-energy $\gamma$-ray spectrum at all altitudes and the muon spectrum at sea level, without invoking any change in the character of the interactions at high energies. Such a spectrum is also consistent with air-shower observations.