Second‐order multiple‐scattering theory for charged‐particle teletherapy beams

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Abstract
The Fermi‐Eyges theory of multiple scattering, applicable to charged‐particle teletherapy beams, has been generalized to second order in small quantities representing deviations from the particles’ initial lines of travel and direction. This second‐order multiple‐scattering theory provides increased accuracy, and in particular it takes into account the skewness of the particles’ paths, in calculating dose. Only the assumptions and certain results of the second‐order theory are presented in this communication, for the immediate use of other investigators. An application to rectangular fields shows that the second‐order theory predicts one component of the buildup of electron central axis depth dose, which the (first‐order) Fermi–Eyges theory cannot do. (The other major component of buildup, which is not yet incorporated into this theoretical work, is due to high‐energy secondary electrons.) Various approximate calculations of electron central axis depth dose are compared with the second‐order calculation.