Solution of the Initial-Value Neutron-Transport Problem for a Slab with Infinite Reflectors

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Abstract
The initial‐value transport problem of monoenergetic neutrons migrating in a thin slab surrounded by infinitely thick reflectors is solved for isotropic scattering by using the normal‐mode expansion technique of Case. The results obtained indicate that the reflector may give rise to a branch‐cut integral term typical of a semi‐infinite medium while the central slab may contribute a summation over discrete residue terms. Exact expressions are obtained for these discrete time eigenvalues, and sample numerical results are presented showing the behavior of real time eigenvalues as a function of the material properties of the slab and reflector. In the limit of purely absorbing reflectors or a bare slab, the present solution has the properties which have been previously reported by others who used the approach of Lehner and Wing.