Transport solutions to the monoenergetic constant source and the Milne problems for the forward-backward-isotropic scattering (FBIS) kernel are obtained by method of singular expansion modes. The monoenergetic linear transport equation for extremely anisotropic scattering with constant source is reduced to a transport equation with isotropic scattering. The expansion coefficient is obtained in a form involving exact integral equations and determined by the accompanying new boundary conditions and the half-range orthogonality relations. In the zeroth order approximation, the analytical expressions for neutron density and the emergent angular distributions are also obtained as a function of forward scattering.
GÜLEÇYÜZ, M.Ç .. and KAŞKAŞ, A. (1998) "The Milne and the Constant Source Problems for the FBIS Kernel," Turkish Journal of Physics: Vol. 22: No. 6, Article 2. Available at: https://journals.tubitak.gov.tr/physics/vol22/iss6/2