Energy Deposition by Electron Beams and $\delta$ Rays

The product of two empirical relations, for the practical range and the transmission probability of normally incident electrons through plane sheets of matter, may be differentiated to yield a simple formulation of the energy deposition by electron beams, in agreement with more complex formulations and with experimental data. When combined with the $\delta$-ray distribution formula, these results provide a theory of the spatial distribution of ionization energy about the path of a rapidly moving ion, which is basic to theories of radiation damage and detection.