Two-region Milne problem with anisotropic scattering

We consider the two-region Milne problem, defined as the steady-state monoenergetic linear transport problem for two adjoining homogeneous source-free half-spaces, with particle source coming from infinity in the positive half-space. The integral version of the transport equation is solved using trial functions based on Case’s eigen modes and exponential integral function. The solution of the Milne problem is formulated in terms of characteristic parameters such as the extrapolation length, the fractional scalar flux discontinuity and the fractional current discontinuity. Numerical results for the analytically evaluated parameters are then presented. Some of our numerical results are compared with the available published results.