HIGHER-ORDER MULTIPLE-SCATTERING THEORIES FOR CHARGED-PARTICLE TRANSPORT

The Fermi pencil beam formula and the higher-order multiple scattering theory due to Jette are shown to result from a perturbative treatment of the linear Boltzmann equation with Fokker-Planck scattering. Using asymptotic one-dimensional solutions for the transverse integrated (s pherical) fluence as well as its variance, approximate higher-order pe ncil beam theories are constructed. These simple and explicit formulae are shown, by comparison with benchmark Monte Carlo results, to be si gnificantly more accurate than the Fermi and Jette equations, particul arly at large distances from the beam axis. (C) 1996 American Associat ion of Physicists in Medicine.