Milne problem for linearly anisotropic scattering and a specularly reflecting boundary

The Milne problem is investigated subject to re¯ecting boundary conditions. The original version of the problem with vacuum boundary condition is generalized assigning, to the sur- face x =ˆ 0, a re¯ection coecient R…04R41†. Linearly anisotropic case is studied using sin- gular eigenfunction method. The cases of non-multiplying and multiplying medium are covered. The separate treatment of non-absorbing medium is also included. The singular eigenfunction method yields good accuracy with an optimized ®rst order approach. Solution of the Milne problem is formulated in terms of characteristic parameters such as extrapolated endpoint, emergent angular distribution and total and asymptotic neutron densities. Numer- ical results for the analytically evaluated parameters are then presented