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

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Abstract
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.