Intranuclear cascading in photographic emulsion at accelerator and cosmic-ray energies

The data on the interactions of cosmic-ray protons in nuclear emulsion have been analyzed in light of the results of recent exposures of emulsion to accelerator protons. Plots of $〈{log}_{10}tan\theta 〉$ as a function of the number of evaporation prongs, $N_h$, display an energy-independent behavior which is exploited to determine the energies of cosmic-ray events. It is found that the energies quoted in the literature are generally too high. The average charged multiplicity is linearly related to $N_h$ from 30 GeV to 5 TeV. While a model of nuclear cascading based on direct production is consistent with these data from 30 GeV to 500 GeV, a model proceeding through an intermediate state gives better agreement at cosmic-ray energies.