The problem of space dependent thermalization of neutrons is solved for a slab lattice of heavy moderator and fuel. Fuel slabs are replaced by negative plane sources whose strength is computed by transport-theoretical arguments. The Fourier space-transform of the spectrum is obtained by iteration of an integral equation and the solution correct to the order O(Δ2mod) is shown to reduce, in the absence of fuel, to the one found by Hurwitz et al. The influence of the hardening of the spectrum incident on the fuel slab is studied by means of the thermal utilization factor.