Electron dose calculation using multiple‐scattering theory. A. Gaussian multiple‐scattering theory

This article is the first in a series on the calculation of electron dose using multiple‐scattering theory. In it we develop a unified theory, which we term Gaussian multiple‐scattering theory, starting from a number of contributions already in the literature: the Fermi–Eyges multiple‐scattering theory, the Yang path length distribution, the second‐order multiple‐scattering theory of Jette [Med. Phys. 12 , 178 (1985)], and the diffusion theory of Bethe et al . [Proc. Am. Philos. Soc. 78 , 573 (1938)]. After examining in detail the ramifications and limitations of Gaussian multiple‐scattering theory, we derive basic formulas generalizing the Fermi–Eyges theory, for use in subsequent articles. We also find explicit, accurate expressions for incorporating the scattering power into the theory.