Analytical solution of the radiative transfer equation in the two-stream approximation

The analytical solution of the plane-parallel radiative transfer equation i s obtained in the two-stream approximation for a large class of continuous distributions of the de-excitation coefficient epsilon (constant, linear, p arabolic, with spikes etc.). We present also the method of the discrete spa ce theory for obtaining solutions of the transfer equation in the media wit h strong density inhomogeneities. These sets of the analytical solutions ca n be used for the solution of the inverse problem. The deduction of the int ernal distribution of epsilon from observational data is facilitated in the case of isothermal media. since the characteristic behavior of the solutio n refers to the certain behavior of epsilon. As an example, we find the cor responding parameters of the constant and linear distributions of epsilon p recisely.