Diffusion of photons in the frame of the integral form of the transport equation

In this paper the 3D photon transport equation is considered to give a detailed description of the fluorescence photon emission from a homogeneous slab. As an example we study, with a complete 3D spatial description in plane geometry, the distribution both in physical and momentum space of the primary photons, induced by a radiation beam crossing the slab. Then we will see how the 3D geometry influences the shape of the continuous spectra due to a second Compton collision which modifies the distribution of the primaries due to photoelectric effect. The possibility of isolating the effect of a particular interaction is one of the strength points of the multiple-scattering scheme in the framework of transport techniques, which allows a better understanding of the photon diffusion. In order to evaluate the effects of the boundary conditions, we will use the integral transport equation instead of the integro-differential one, which has the advantage of treating the flow of the photons from the outer space as an external source. The results will be compared with those obtained in the case of a half-infinite medium uniformly irradiated with a plane infinite slant source of monochromatic photons previously solved in 1D.