On the Space-Energy Separability of the Fundamental Mode of the Neutron Transport Operator with Isotropic Scattering

We report the results of some calculations of the fundamental mode decay constant (and the corresponding eigenfunction) of the neutron transport operator in slabs and spheres of various sizes. The assemblies are assumed to be homogeneous and nonmultiplying with absorption cross section varying as 1/v. The scattering is assumed to be isotropic in the laboratory system, and parameters are chosen to represent the scattering by beryllium. The integral equations were solved by the multigroup technique, and calculations show that the fundamental mode eigenvalue for a slab is bounded by (v ∑)_min whereas no bound exists for a spherical assembly. The solutions wherever possible are compared with the corresponding exp(iBx) theory results, and the implications for experiments are discussed. The nonseparability of the energy and space dependence of the asymptotic flux has been shown explicitly, and its consequences on the extrapolation distance have been pointed out.