Effect of Distribution of Fissile Material on Critical Mass

The influence of the distribution of ²³⁵U, ²³⁹Pu, and ²³³U in water on the minimum critical mass, the minimum critical concentration per unit length of cylinder, and the minimum critical mass per unit area of slab surface is calculated. Two energy groups are employed in the calculations with parameters normalized to force agreement between calculations and experiments performed with water-reflected spheres containing uniform aqueous solutions having a wide range of concentrations. Calculations made with these parameters for a water-reflected cylinder, in which the optimum distribution for minimum mass was approximated within five coaxial regions, agree well with experimental results. Minimum critical masses, concentrations per unit length of cylinder, and masses per unit area calculated for ²³⁵U, ²³⁹Pu, and ²³³U are, respectively, 768 g, 16.9 g/cm, 0.417 g/ cm²; 492 g, 10.6 g/cm, 0.266 g/cm²; and 571 g, 13.5 g/cm, 0.362 g/cm².