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

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. The 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.