The Scattering of Resonance-line Radiation in the Limit of Large Optical Depth

It is shown that the essential features of the transfer of resonance-line radiation in very optically thick media of low density are described by the Poisson equation. The solution of this equation is presented in the form of an eigen-function expansion. Simple closed expressions are given for the mean number of scatterings for escape and for the line profile at both the centre and surface of the medium. In the case of a medium with a finite probability of photon destruction upon scattering, we obtain the fraction of the photons which escape and the limiting intensity at the centre as the optical depth tends to infinity. These analytic results are shown to agree well with the available numerical solutions.