The method for solving time-independent one-speed half-space transport problems, which was explained in earlier papers, is applied to find the emerging distributions for the albedo and Milne problems for thermal neutrons with the isotropic degenerate kernel. By using the principle of invariance and the reciprocity theorem, these distributions are expressed in terms of the H-matrix. This matrix is a generalization of the one-speed Ambarzumian-Chandrasekhar H-function and satisfies a nonlinear integral equation. The conditions, which uniquely determine the physical solution of this equation, are derived. At the end, the possibilities for calculating the H-matrix by iteration are discussed.