On the Theory of Cosmic-Ray Showers II. Further Contributions to the Fluctuation Problem

Abstract

Further calculations are reported on the problem of the distribution in size of cosmic-ray showers. In §2 it is shown that this distribution is completely determined when the average energy distribution of the particles in a shower is known. In §3 previous calculations of the fluctuation in size of showers have been revised and extended. The main result is that for the simplified model chosen (the so-called Furry model) the fluctuations are small and roughly equal to twice the Poisson value for all values of the thickness (see Table II; Fig. 3). In §4 another simplified model is considered for which it is possible to take the ionization exactly into account. In §5 and §6 the calculations of the fluctuation are extended to the actual cosmicray problem. For one value of the initial energy and for one depth a numerical calculation has been made (see Table III). The result for the fluctuation is again a few times the Poisson value.