Angular and Radial Distributions of Particles in Cascade Showers

Abstract

This paper is concerned with the calculation of the angular and radial distributions of electrons and photons at the maximum of a cascade shower. In Sec. II(A) we calculate the moments of the distribution functions in a shower neglecting collision loss of electrons, i.e., for energies $E$ much greater than the critical energy $\epsilon$. In Sec. II(B) we derive expressions for the moments when collision loss is not negligible. These expressions are in the form of a series in $\frac{\epsilon }{E}$, and are valid down to a few times the critical energy. In Sec. III we use the moments to calculate the distribution functions for energies down to a few times the critical energy.