Range fluctuations for muons of energy up to 106 GeV

Recent measurements on cosmic rays deep underground have led to the necessity of studying the effect of fluctuations in range for muons of energy to some 106 GeV and ranges down to 15 000 m.w.e. The results of such calculations are given here; in these calculations, which are more extensive than hitherto, an examination is made of the effect on the muon survival probabilities deep underground of different assumptions as to the form of the cross section for the contributions from nuclear and bremsstrahlung losses and different magnitudes of the energy loss coefficients. Survival probability curves are given from which the enhancement in underground intensity can be calculated for any sea-level muon spectrum, and results are also given of the actual enhancement factors for sea-level spectra having constant exponents.