Pion and neutron production by cosmic-ray muons underground

The production of positive pions and neutrons by cosmic muons at underground sites of various depths is investigated. We first test the equivalent photon method in the particular case of $\Delta$ excitation by the muon. We find that this method, when it neglects the momentum dependence of the transverse response, reproduces remarkably well the theoretical muon cross-section. This success has lead us to apply the method to higher energies, where it has not been tested. We evaluate in this way the production of positive pions in liquid scintillator from known photo-absorption cross-sections. At a shallow depth of 20 meters our estimate reproduces the measurement. As for the neutron emission, we include the obvious sources, such as the giant-resonance excitation, the quasi-deuteron process, the quasi- free pion production as well as neutrons emitted following pion capture. Our evaluation underestimates the number of neutrons produced and finds a too weak dependence on the depth. This suggests that secondary neutron production is important at all depths.