Radiation field of an optically finite homogeneous atmosphere with internal sources

The equation of radiative transfer in an optically finite homogeneous atmosphere with different internal sources is solved using the method of kernel approximation the essence of which is to approximate the kernel in the equation for the Sobolev resolvent function by a Gauss-Legendre sum. This approximation allows to solve the equation exactly for the resolvent function while the solution is a weighted sum of exponents. Since the resolvent function is closely connected with the Green function of the integral radiative transfer equation, the radiation field for different internal sources can be found by simple integration. In order to simplify the obtained formulas we have defined the x and y functions as the generalization of the well-known Ambarzumian-Chandrasekhar X and Y functions.For some types of internal sources the package of codes in Fortran-77 can be found at http://www.aai.ee/∼viik/HOMOGEN.FOR.