A numerical method for the calculation of the diffusion of high energy electrons in a heterogeneous medium (Q756390)

In clinical applications of electron beams it is important to calculate an absorbed dose. The so-called pencil beam method is often used for it. One part of this method is the calculation of the diffusion of high energy electrons. After sketching the Fermi-Eyges theory for a broad beam of electrons and for a medium with slab-geometry the authors propose to solve numerically the Fermi's diffusion equation in the case of an arbitrary heterogeneous medium. In order to make it they approximate the directional distribution of the electrons by a Gaussian function multiplied by a linear combination of shifted Hermite polynomials. Numerical results both for homogeneous and heterogeneous media are given. In appendices some properties of the shifted Hermite polynomials and the extension of the method to the three-dimensional case are briefly discussed. The paper is written very clear.