Chandrasekhar Polynomials and the Solution to the Transport Equation in an Infinite Medium

Abstract

The Chandrasekhar polynomial of the first kind is at the heart of analytical solutions to the neutron and radiative transport equations in finite and infinite media. They form the basis for 1D solutions in plane geometry, which, in turn, enables solutions in spherical and cylindrical geometries. The scalar flux for a point source in spherical geometry permits scalar flux benchmarks for 2D and 3D sources in infinite media. The establishment of benchmarks expressly requires these polynomials to be highly accurate. Here, we focus on the numerical evaluation of Chandrasekhar polynomials for full anisotropic scattering as solutions to a three−term recurrence. When considered in this way, numerical theory guides their evaluation.

Keywords:

• infinite medium
• Green's function
• three-term recurrence
• Chandrasekhar polynomials

ACKNOWLEDGMENTS

While the author did not particularly like the 53 changes asked for by the reviewers, he acknowledges the two reviewers for their obviously thorough reading of the manuscript and pointing out several errors. Seems that no matter how many times the author reads his manuscript, unfortunately typoes remain.