Critical Mass Variation of ²³⁹Pu with Water Dilution

The critical mass of an unreflected solid sphere of ²³⁹Pu is ∼10 kg. The increase in critical mass observed for small water dilutions of unreflected ²³⁹Pu spheres is paradoxical. Introducing small amounts of water uniformly throughout the sphere increases the spherical volume containing the same amount of ²³⁹Pu as the critical solid sphere. The increase in radius decreases the surface-to-volume ratio of the sphere, which has the effect to first order of decreasing the neutron leakage, which is proportional to the surface, relative to the fissions, which are proportional to the volume. The reduction in neutron leakage is expected to reduce the critical mass, but instead, the critical mass is observed to increase. It is discussed how changes in the fast neutron spectrum with corresponding changes in the nuclear parameters result in an increase in critical mass for small water dilutions.