ELECTRON DOSE CALCULATIONS USING THE METHOD OF MOMENTS

The Method of Moments is generalized to predict the dose deposited by a prescribed source of electrons in a homogeneous medium. The essence of this method is (i) to determine, directly from the linear Boltzmann equation, the exact mean fluence, mean spatial displacements, and mea n-squared spatial displacements, as functions of energy; and (ii) to r epresent the fluence and dose distributions accurately using this info rmation. Unlike the Fermi-Eyges theory, the Method of Moments is not l imited to small-angle scattering and small angle of flight, nor does i t require that all electrons at any specified depth z have one specifi ed energy E(z). The sole approximation in the present application is t hat for each electron energy E, the scalar fluence is represented as a spatial Gaussian, whose moments agree with those of the linear Boltzm ann solution. Numerical comparisons with Monte Carlo calculations show that the Method of Moments yields expressions for the depth-dose curv e, radial dose profiles, and fluence that are significantly more accur ate than those provided by the Fermi-Eyges theory. (C) 1997 American A ssociation of Physicists in Medicine.