Monte Carlo calculations of nuclear cascades and associated Čerenkov radiation in extensive air showers

We present a Monte Carlo calculation, with observed cross sections and multiplicities, of the nuclear component of small extensive air showers (EAS) with primary energies $E_0\ge {10}^3$ GeV. The simulations were completely three-dimensional and were initiated by cosmic rays sampled from both their primary energy and mass spectra. Resulting particle spectra sampled at 564 g ${\mathrm{cm}}^{-2\mathrm{}}$ agree with extrapolations from observations of EAS with $E_0>{10}^{4-6}$ GeV. The optical Čerenkov radiation calculated for the nuclear-active particles and muons in these EAS is found to be comparable to that expected from the electrons and distinguishable for particular detector configurations. Implications for EAS observations of cosmic $\gamma$ rays and cosmic-ray composition are mentioned.