On the theory of cosmic-ray showers I the furry model and the fluctuation problem

Abstract

The main problems regarding the shower formation by fast electrons are reviewed on the basis of a simplified model first proposed by Furry ( S S 1 and 2). A general method is developed for calculating the fluctuation in the number of particles after a thickness x of matter ( S 3). It is shown in S 4 that can always be found when the average energy distribution F(E, x) is known. Using the approximate "cut-off" method the numerical values of have been computed for the Furry model (see table on p. 358). The approach to the normal value of the fluctuation (corresponding to the Poisson distribution) is much slower than has been expected.