Solutions for collision densities in a slab with an energy- and angle-dependent degenerate scattering kernel are developed. The slab distribution is expanded in a set of regular and singular eigenfunctions and the expansion coefficients are obtained as solutions of a matrix integral equation. From invariance principles, this integral equation depends upon the half-space generalized Milne solution. To obtain this solution one must solve a nonlinear matrix equation for a generalization of the Chandrasekhar H-function. Approximate solutions and numerical calculations for the heavy-gas scatterer are presented, including emergent distributions for the slab.