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C. Borges and E. W. Larsen, “The Transversely Inte- grated Scalar Flux of a Narrowly Focused Particle Beam,” SIAM Journal on Applied Mathematics, Vol. 55, No. 1, 1995, pp. 1-22.

has been cited by the following article:

• TITLE: A Closed-Form Formulation for the Build-Up Factor and Absorbed Energy for Photons and Electrons in the Compton Energy Range in Cartesian Geometry

  AUTHORS: Volnei Borges, Julio Cesar Fernandes, Bardo Ernest Bodmann, Marco Túllio Vilhena, Bárbara Rodriguez

  KEYWORDS: Build-Up Factor; Compton Energy; Cartesian Geometry; Fokker-Plank Equation

  JOURNAL NAME: World Journal of Nuclear Science and Technology, Vol.2 No.1, January 16, 2012

  ABSTRACT: In this work, we report on a closed-form formulation for the build-up factor and absorbed energy, in one and two di- mensional 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.