Theoretical Calculations on Extensive Atmospheric Cosmic-Ray Showers

Large cosmic-ray showers in air, investigated with ionization chambers and coincidence counters, have been explained hitherto as originating from primary electrons of very high energy. In recent experiments at an altitude of 3100 meters Lewis measured the frequency of coincident bursts in two unshielded ionization chambers. The theoretical cumulative frequency $H(P,D)\mathrm{}$ of such coincidences is calculated as a function of the electron density $P$ and the separation $D$ of the chambers for this altitude and for sea level. The cumulative size-frequency distribution $H\left(P\right)\mathrm{}$ for bursts in a single chamber is also computed. All calculations are based on the cascade theory of showers and the theory of the multiple scattering of electrons. The theoretical frequencies compared with those of experiments show (1) a much smaller absolute value, (2) a much slower drop as the chambers are separated, (3) a different form for the cumulative size-frequency distributions, and (4) a smaller increase with altitude. It is pointed out that the large number of narrow showers of high energy observed must originate much nearer to the chamber than the top of the atmosphere if they are to be explained by the cascade theory. It is concluded that the assumption of primary electrons is of little help in explaining the experimental results.