A Solution of the Rayleigh Scattering Problem for Plane-Parallel Atmospheres of Large Optical Thickness
The problem of radiative transfer in a plane-parallel, perfectly scattering atmosphere is described. Chandrasekhar's solution applicable to atmospheres of small and moderate optical thickness is outlined. His solution reduces the problem to that of determining the X-, Y-, K-, and L-functions, the scattering functions. Mullikin has extended this method of solution to atmospheres of large optical thickness. Sekera and Kahle have used Mullikin's method of solution for calculating the emergent radiation from plane-parallel Rayleigh-scattering atmospheres of large optical thickness. Their numerical results are reproduced here in the appendix, as tables of scattering functions. The numerical method for determining the intensity and polarization of the radiation emerging from the top and bottom of atmospheres is given, and suggestions for additional uses of the tables are made. Finally, a few examples of representative calculations are presented.