Subcritical Problems in Spherical Geometry

The results of high-order P_N calculations for the one-speed albedo and Milne problems in spherical geometry are presented. The computations were performed by the transfer matrix approach. The analysis is included in the paper. Reflection probabilities are given for spheres of various radii and for the region exterior to spheres: reflection and transmission probabilities for spherical shells and extrapolation lengths for the exterior Milne problem. The method is found to diverge for sufficiently high values of N—the smaller the radius, the more rapidly divergence sets in. For moderate and large radii (≳2 mfp), the method nevertheless gives generally excellent results.