Radiation transport in a cylinder. I. Resolvent of the fundamental integral equation

A new method is presented for calculating spectral line radiation transport in a homogeneous circular cylinder with infinitely long axis for isotropic scattering with complete frequency redistribution or no change in frequency. In addition to the cylinder, scattering in a layer symmetric about its midpoint and in a sphere are also studied. Equations are derived which are satisfied by the resolvent of the fundamental integral equation describing these cases of scattering. By applying a Hankel transform over a finite interval, the resolvent is expressed in terms of an auxiliary function. An equation is derived for this auxiliary function which is easily soluble by iteration, with the speed of its convergence increasing with growth in the radius of the scattering region.Translated from Astrofizika, Vol. 37, No. 1, pp. 111–127, January–March, 1994.This study was carried out with financial support from the Russian Fund for Fundamental Studies (project 93-02-2957).