Errors in Electromagnetic Cascade Measurements Due to the Transition Effect

The transition of an electromagnetic cascade which passes from one material to another having a different critical energy is discussed using Rossi and Greisen's approximation B. It is shown that an infinitely rapid change in the total number of particles takes place at the boundary layer. This leads in certain geometries to a strong dependence of the signal measured on the transition effect. A few of these arrangements are discussed and it is shown that they cause difficulties if measurements are made on cascades in ionization spectrometers or air-shower arrays. As a result, it appears to be strongly advisable to have no appreciable change in the critical energy over dimensions of more than several times ${10}^{-3\mathrm{}}$ radiation length prior to the depth at which the cascade is measured.