Exact Solution of Chandrasekhar's H Function For the Isotropic Case

TL;DR

This paper derives an exact analytical solution for Chandrasekhar's H function in isotropic scattering, enhancing the precision of radiative transfer models.

Contribution

It introduces a novel exact solution to the nonlinear integral equation governing the H function for isotropic scattering.

Findings

Exact expression for the H function derived and validated.

Numerical results closely match Chandrasekhar's previous approximations.

Differences between the new and previous solutions are quantitatively presented.

Abstract

This study provides an exact solution to Chandrasekhar's H function for isotropic scattering. The H function, which is governed by a nonlinear integral equation, plays a central role in radiative transfer theory. To facilitate the solution, the differential form of the integral equation is derived using classical integral techniques. The resulting differential equation is then solved to yield an exact expression for the H function. Numerical results obtained from the exact solution are compared with those reported by Chandrasekhar, and the differences are presented in tabular format.