Scalar Green's function for penetrable or dielectric scatterers

In a series of former papers we developed the so-called self-consistent Green's function formalism (SGFF) for acoustic and light scattering on impenetrable or ideal metallic scatterers. With the paper at hand we will extend the application of this formalism to penetrable or dielectric scatterers. The concept of the Green's function of the third kind is utilized which was introduced first by Chen-To Tai. It must be slightly generalized to allow the treatment of nonspherical scatterers. The following considerations reveal the conceptual equivalence between the Green's function of the third kind and Waterman's T-matrix method. It is another goal of this paper to demonstrate that the conventional boundary and volume integral equations can be also derived within the developed Green's function formalism