Experimental determination of the muon range–energy relation

Calculations of the zenithal distribution of cosmic-ray muons indicate the appearance of peaks at near-horizontal directions in the relative muon intensity I(θ)/I0 for Eμ > a few tens of GeV. The magnitude of the peak value of I(θ)/I0 increases monotonically with energy, representative values being 1.15 for Eμ > 50 GeV and 1.58 for Eμ > 120 GeV. Using this phenomenon, an independent evaluation can be made of the muon range–energy relation. Absolute measurements of the muon flux underground at zenith angles of 69° to 77° are compared to the calculated zenithal distribution to determine the muon range–energy relation in rock at 25–100 GeV. Suggestions are advanced for extending the energy range to a few thousand GeV and for making a purely experimental determination by utilizing magnetic spectrometer results in a context which would avoid the need to normalize the spectrometer data and would largely eliminate the problem of possible energy bias. The usefulness of these data in determining the pion attenuation length in the atmosphere is discussed.