Two-Half-Space Milne Problem in Two-Group Neutron Transport Theory

The singular-eigenfunction-expansion method and the principle of invariance are combined to reduce the two-half-space Milne problem to a regular computational form in the two-group isotropic scattering model. The method used here consists in considering a problem of two contiguous half-spaces with surface sources at the interface. The problem is equivalent to the Milne problem in the sense that the expansion coefficients are to be determined from the same equation. The emergent distributions are obtained from coupled regular integral equations. The expansion coefficients can then be obtained using the halfrange orthogonality relation of the eigenfunctions. Numerical results are reported for light-water media.