Benchmark results for the critical slab and sphere problem in one-speed neutron transport theory

Research highlights: → The critical slab and sphere problem in neutron transport under Case eigenfunction formalism is considered. → These equations reduce to integral expressions involving X functions. → Gauss quadrature is not ideal but DE quadrature is well-suited. → Several fold decrease in computational effort with improved accuracy is realisable. - Abstract: In this paper benchmark numerical results for the one-speed criticality problem with isotropic scattering for the slab and sphere are reported. The Fredholm integral equations of the second kind based on the Case eigenfunction formalism are numerically solved by Neumann iterations with the Double Exponential quadrature.