Asymptotic relations in the theory of radiative transfer in a sphere and a spherical shell

Integral relations are obtained for the radiation intensities in homogeneous absorbing and isotropically scattering spherically symmetric media. These relations and some physical arguments are used to find asymptotic expressions for the radiation intensities in the outer layers of a sphere of large optical radius and an optically thick spherical shell. The following cases are considered: central point source, uniform distribution of the sources in the considered media, and conical sources on the outer boundary of the surface