On Multiregion Problems in Plane Geometry and the Use of Half-Range Orthogonality Relations

A general systematic method to reduce multiregion problems in plane geometry to regular integral equations for the coefficients of singular-eigenfunction expansions is proposed. The method is based on the half-range orthogonality relations of the eigenfunctions and is applicable in two-groups as well as one-group theory. The method is used to solve two problems in one-group theory for isotropic scattering: the Milne problem for a half-space bounded by a slab of dissimilar medium and a problem of neutron transmission through two slabs. Numerical results are reported for several sets of parameters.