AbstractCorrections to the extrapolation distance and angular emergent distribution for the Milne problem have been obtained by means of a perturbation method. The exact solution for a simple kernel has been taken as the unperturbed state, and the method has been applied to more realistic scattering models: numerical results are given for hydrogen gas.By means of a combined use of numerical and analytical methods some very accurate values have been obtained for the emergent angular energy spectrum for the Milne problem in the case of hydrogen gas.