Straggling of Electrons near the Critical Energy

Abstract

The straggling of electrons caused by loss of energy by radiation and collision is discussed. The paper is essentially in three parts. In Section III we have found the "straggling probability" for an electron that loses energy only by radiation, and give curves corresponding to various approximations to the expression for the radiative cross section. In Section IV collision loss is also taken into account and a formal expression for the straggling probability is found in the form of a series whose terms decrease rapidly for energies not too small and not too large thickness. No proof of the convergence is given however and, in fact, for very small energies the terms increase and some higher order terms become infinite at zero energy. In Section V some remarks are made on the small "showers" initiated by a particle of energy near the critical energy.