The need for thermal and fast neutron fluxes in the range of 1 to 5 x l0/ sup 15/ neutrons/cm/sup 2/(sec) for the production of heavy elements such as Cf/ sup 252/ and other special isotopes and for improving the quality of beam experiments, reactor materials testing work, and solid state research has led to plans for the construction of three ultra high flux research reactors. The designs of these and other high flux research reactors are based on the general technology of enriched tank-type reactors; however, they utilize the principle of separate fuel and moderator regions to achieve flux peaking in these regions. Thus, proposed designs take the form of an annular fuel region with internal and external moderating regions or an under moderated core with an external moderator or reflector. In such arrangements, the thermal flux peaks in the moderating regions and the fast flux peaks in the fuel region, which results in maximum fast and thermal fluxes per unit of power. Since most of the moderation of fast neutrons takes place outside of the fuel region, the thermal flux peaking depends on the number of fast neutrons leaking from the reactor core, which in turn depends on …