Can We Understand High Energy Cosmic-Ray Spectra on the Basis of the Scaling Hypothesis?

Abstract

Using the essential point of Feynman's hadronic scaling hypothesis, we have made a calculation of atmospheric cosmic-ray spectra, i.e., spectra of muons, hadrons and electromagnetic component. The results are compared with emulsion chamber data on the three components. In doing so, various factors related to the primary cosmic-ray spectrum are carefully examined. It is shown that the scaling feature of particle production in the entire energy region (up to several times 10¹⁶ eV) is compatible with the data only when one assumes i) very large inelastic cross-sections (∼ 380 mb for p-air collisions) and ii) the steepening of the (proton equivalent) primary cosmic-rays above several times 10¹⁴ eV, of which the intensity is much less than some air shower data. Another feasible way of understanding the phenomena is discussed by hypothesizing a break of the scaling feature in the fragmentation region at high energies (≳ 10¹⁴ eV).