A solution of the neutron diffusion equation for a hemisphere containing a uniform source

An analytic solution of the diffusion equation for a hemisphere of fissile or non-fissile material is presented which contains a spatially uniform neutron source. Numerical results are given for the flux distribution for one-speed fast neutrons in 235U and also for a non-fissile element of similar scattering properties. We use these results to check the accuracy of the finite element code EVENT. The procedure is also developed for multigroup calculations. In an Appendix we outline the procedure required when the hemisphere contains a source and is also irradiated by an external current of neutrons.