Density Transform Method for Particle Transport Problems in Spherical Geometry with Linearly Anisotropic Scattering

Abstract

We develop the density transform method for treating particle transport problems in spherical geometry with linearly anisotropic scattering. We consider both, the interior and exterior problems of a homogeneous sphere and show that the transform satisfies an equation that resembles particle transport equation in slab geometry. The boundary conditions for these two problems are different. We also work out the density transform method for linearly anisotropic scattering for a region of arbitrary shape.

Keywords:

• Density transform
• transport equation
• spherical geometry
• linearly anisotropic scattering

Acknowledgments

The problem was initiated during my stay at Kirikkale University, Kirikkale, Turkey on a TUBITAK fellowship. It evolved out of discussions with my colleague, Prof. R. G. Tureci. Helpful discussions with him and financial support from TUBITAK are gratefully acknowledged. Numerical work is being carried out in collaboration with him and Mr. A. Z. Bozkir of Kirikkale University. My thanks are also due to my close colleague and friend, Dr. B. Dahl of Chalmers University of Technology, Sweden for helpful discussions.