On the resolvent of Milne's integral equation for a spherical,isotropically-scattering medium

Recently, determination of the resolvent kernel of Milne's integral equation for a spherical, isotropically-scattering medium with internal sources has been made by several authors (cf. Heaslet and Warming;⁽¹⁾Nagirner;⁽²⁾Wilson and Sen⁽³⁾). In this paper, it is shown how to compute the resolvent kernel of the above Milne's equation in terms of the modified Sobolev's Φ-function, which is reduced to the angular integration of the source function in the diffuse radiation field by a finite slab. In other words, once the X- and Y-functions of a slab with twice the optical radius of the sphere have been computed and a Cauchy system for the source function has been solved, the resolvent kernel under consideration can be determined by integration of the modified Sobolev Φ-function.