Simulation of atmospheric cascades and deep-underground muons

We describe a new hadronic-interaction model for the calculation of high-energy cosmic-ray cascades in the atmosphere. High-energy muons above 0.5 TeV at production are transported through 7000 ${\mathrm{h}\mathrm{g}/\mathrm{c}\mathrm{m}}^2$ of rock in order to obtain the multiplicity and lateral distributions at different depths. These distributions are parametrized to facilitate the calculation of the muon-bundle rates deep underground. As an illustration, these results are applied to calculate the rates of coincident multiple muons in a detector of finite area at the Gran Sasso Laboratory. We study in particular the sensitivity of rates of high-multiplicity events to chemical composition of the primary cosmic radiation and to uncertainties in the interaction model. Our results point to the importance of the coincident measurement of showers at the surface to maximize the power of an underground detector to study the primary composition.