One-speed criticality problems for a bare slab and sphere: Some benchmark results

Benchmark results for the two canonical problems of critical slab and sphere are reported. Three different approaches, use of the X-function and Neumann iteration, FN method, and discrete-ordinate method, are explored. It is found that to the orders of the approximations considered here, the critical half-thickness and critical radius values obtained through the three approaches are consistently accurate from 9 to 12 significant figures, and agree amongst themselves. The accuracy for the corresponding values for neutron density using X-function, and discrete-ordinate method (the only two explored for the density computations) is 9-10 figures. In several instances, the results constitute an improvement on the previously reported benchmark results in literature.