The eigenfunctions for thetransport of radiation between concentric spheres are proved to be the sphericalharmonics and Legendre polynomials. The corresponding eigenvalues arethen derived for the cases of both an outer emitting sphere and aninner absorbing sphere, and an inner emitting sphere and an outerabsorbing sphere. Simple approximations to these eigenvalues are found and their various properties are derived. These results are then applied tothe problem of ICF capsules inside hohlraums.