A closed-form formulation for the build-up factor and absorbed energy for photons and electrons in the Compton energy range in Cartesian geometry

In this work, we report on a closed-form formulation for the build-up factor and absorbed energy, in one and two dimensional Cartesian geometry for photons and electrons, in the Compton energy range. For the one-dimensional case we use the LTSN method, assuming the Klein-Nishina scattering kernel for the determination of the angular radiation intensity for photons. We apply the two-dimensional LTSN nodal solution for the averaged angular radiation evaluation for the two-dimensional case, using the Klein-Nishina kernel for photons and the Compton kernel for electrons. From the angular radiation intensity we construct a closed-form solution for the build-up factor and evaluate the absorbed energy. We present numerical simulations and comparisons against results from the literature. (author)