Numerical computations of Neumann expansion coefficients of Chandrasekhar's H-function for isotropic scattering

Abstract

We present two numerical schemes to compute the Neumann series expansion coefficients of Chandrasekhar's H-function for isotropic scattering. The first scheme involves direct evaluation of the closed-form expression for the expansion coefficients derived by Rutily and Bergeat, while the second scheme is to generate the coefficients by making use of the reflection functions for successive orders of scattering. It is shown that the second scheme is significantly faster than the first, and that its use enables us to extend the computation of the Neumann series coefficients of the H-function to arbitrarily high orders of light scattering. For convenience in practical use, an approximate formula is also given for the computation of the correction term required to represent the total H-function with the Neumann series terminated at the 16th term.