On the Non-Uniqueness of Solutions of Chandrasekhar's S-Equation in Radiative Transfer

The non-uniqueness of solutions of the non4inear integral equation for Chandrasekhar's S-function for a homogeneous semi-infinite atmosphere is discussed. Heuristic arguments, based upon the singular eigensolutions of the equation of transfer, are used to re-derive the singular integral equation for the S-function. 8imilarly, the regular eigensolutions lead to IullWin's linear constraints, which select the "physical" solution. It is also shown that an "unphysical" solution differs from the "physical" one hy a term corresponding to the solution of a generalized Iilne problem.