On Fluctuation Phenomena in the Passage of High Energy Electrons through Lead

Abstract

It now seems reasonable on both theoretical and experimental grounds to suppose that the formulae of the present radiation theory are valid in the cosmic-ray energy range. The work of Carlson and Oppenheimer and of Bhabha and Heitler has shown that this assumption is capable of accounting for many of the observed features of cosmic-ray absorption and of shower production. These writers concern themselves principally with the mean behavior of a group of electrons and photons moving through matter. Since the fluctuations around this mean behavior are large and for some purposes very important, it is desirable to investigate their nature, even though this involves a loss of accuracy in dealing with other aspects of the situation. In this paper we consider two fluctuation problems: (1) The fluctuations in size of showers produced by single electrons or photons: In dealing with this problem we take the energetic relations into account only very roughly. (2) Fluctuations in energy loss of electrons: The possible production of secondaries is disregarded. The inadequacies in treatment have for both problems the consequence that the results are applicable only to thin layers of heavy substances. The first problem is discussed in Section II. The conclusion is that the distribution in shower sizes should be essentially of the type $P(n;〈n〉)={\left(〈n〉\right)}^{-1\mathrm{}}{\{1-{\left(〈n〉\right)}^{-1\mathrm{}}\}}^{n-1\mathrm{}}$, where $〈n〉$ is the mean number; but that under ordinary experimental conditions the number of very small showers should be rather greater than indicated by this law. The results account for two observed phenomena which might at first sight be taken as forming serious objections to the multiplicative hypothesis: First, the occasionally observed production of large showers (∼20 or 30 particles) from small thicknesses (∼1 cm) of lead; and second, the appearance which many of the larger showers present of having originated at a single point near the bottom of the lead. In Section III we deal with the second problem, with the purpose of providing a way to use energy loss measurements to provide a more detailed check on the theoretical formulae. A method is given for constructing energy loss distribution curves corresponding to any assumed form of the Bremsstrahlung spectrum. Also a solution is outlined for the problem of using accurate and detailed information on energy losses to compute an empirical spectrum curve.