Abstract
Starting from the fcmiliar integro-differential equation describing the slowing-down and diffusion of neutrons, the critical radius of a two-region thermal neutron reactor with spherical symmetry has been calculated by the Wiener-Hopf method. The only assumption is that the diffusion coefficient is proportional to the slowing-down length, which may be less restrictive than generally made. Using the Fermi slowing-down model, the critical radius of the internal region is calculated from an asymptotic solution in each region in which the external region is finitely extended. In that expression the extrapolation distance for the internal region can be also found. The integrals appearing in those expressions is numerically evaluated with little labor. Finally, two numerical examples are given and the results are compared with those obtained by the elementary diffusion approximation.
