Energy Spectrum and Positive Excess of Muons in Cosmic-Ray Air Showers

A magnet spectrometer and an array of 15 large scintillator disks have been used to examine the distribution of the muon component of extensive air showers with respect to both energy and distance from the axis. An empirical function which has been found to be consistent with the observations is ${\rho }_{\mu }(N, r, \ge E)=\frac{14.4r^{-0.75\mathrm{}}}{{(1+\frac{r}{320})}^{2.5}}{\left(\frac{N}{{10}^6}\right)}^{0.75}\left(\frac{51}{E+50\mathrm{}}\right){\left(\frac{3}{E+2\mathrm{}}\right)}^{a\left(r\right)\mathrm{}},$ with $a\left(r\right)=0.14\mathrm{}{r}^{0.37}$, where ${\rho }_{\mu }$ gives the average number of muons per square meter with energy exceeding $E$ Bev at $r$ meters from the axis of a shower that contains $N$ charged particles. According to this relation, the mean energy at sea level of the muons in air showers is 7 Bev, and they carry, in a shower of $N$ particles, an energy of $0.9\times {10}^{15}{\left(\frac{N}{{10}^6}\right)}^{0.75}$ ev. The positive excess which has been observed in muons examined independently of air showers was not found in the muons detected in the air showers. We conclude that $\pi$-meson production dominates $K$-meson production by a factor of at least 10 in a region of meson energies about 10 Bev.