Criticality conditions in a multiplying slab with an infinite reflector: an old approach rediscovered

A new form for the critical equation of a slab with an in®nite re¯ector is derived. One speed transport theory is employed and we also make use of a little-known transformation ®rst developed by Wallace (Wallace, P.R., 1944a. Boundary Conditions at Thin Absorbing Shells and Plates I. Canadian National Research Council Report MT-34; Wallace, P.R., 1944b. On the Thermal Utilization of Plates in the Presence of Linear Anistropic Scattering. Canadian National Research Council Report MT-63). Numerical results are obtained which agree well with those reported by others. The main purpose of the paper is to illustrate the Wallace transformation which proves useful in a variety of slab problems and may have possible uses in two- and three-dimensional geometries