Calculation of the Stopping-Muon Rate Underground

A detailed calculation is given for the rate of stopping cosmic-ray muons underground. An important source of such muons, dominant at depths ≳ 1.5×${10}^5$ g/${\mathrm{cm}}^2$, is the decay of slow pions which are the end products of hadronic cascades in the rock initiated by the photonuclear interactions of fast muons. The cross section for the production of such cascades is obtained by extrapolating accelerator data to higher energies. The multiplicity of stopping pions is taken from a detailed Monte Carlo calculation. The results agree with the observed rates of stopping muons and of identified stopping pions at shallow depths. An explanation is offered for the Turin measurements of stopping muons made at shallow depths and various inclined zenith angles. However, for the Turin point at 4.27×${10}^5$ g/${\mathrm{cm}}^2$ (which is uniquely sensitive to a possible anomalous source of stopping muons) the predictions fall short by a factor of 4, and we are unable to account for the discrepancy even under the most extreme assumptions for the conventional processes considered.