During the development of nuclear energy, a number of apparent anomalies have become evident in nuclear criticality. Some of these have appeared in the open literature and some have not. Yet, a naive extrapolation of existing data, without knowledge of the “anomalies,” could certainly lead to potentially serious consequences. The known “anomalies” include, but are not limited to,

  1. relationship between criticality in finite spheres and reflected cubes
  2. effect of added scatterers on the criticality of infinite slabs
  3. a small mass concept whereby criticality could be achieved with less than an ounce of fissile material in the form of a single small foil ≃0.2 mil thick
  4. effects of progressive water flooding on the criticality of interacting arrays of fissile materials in storage vaults
  5. effect of mixing metal and fissile bearing aqueous solutions together in the same vault
  6. criticality of coupled fast-thermal systems composed of small plutonium metal spheres surrounded by aqueous plutonium-bearing solutions
  7. criticality of slightly enriched uranium and the negative buckling core
  8. effects of density changes in spherical cores with weakly absorbing reflectors (external moderation)
  9. appearance of critically unbounded regions (of infinite masses) for slightly enriched uranium
  10. criticality in the earth
  11. criticality in the universe
  12. criticality of even-n nuclides beginning with the naturally occurring element,
  13. beyond Californium projection of the “micro” critical mass for the doubly-closed shell super heavy magic nuclei of the future.
There can be as many as three different fuel concentrations with the same critical volume, and perhaps four different fuel concentrations may result in the same critical mass. Contrary to the usual expectation, the sphere, after all, may not be the configuration of least mass; the reflected cube may be somewhat less under certain circumstances. In some cases, the effect of added scatterers can significantly reduce the critical dimension; whereas, in others, the result can be precisely the opposite.Reducing the core density can, under some circumstances, actually decrease the critical mass, contrary to the usual expectation that the mass will be increased. Surprising as it may seem, a system with k∞ < unity might be made critical by reducing the core size and adding a finite reflector of D2O, etc. (in the latter case keff > k∞!). In some cases the effect of moderation results in the smallest critical mass; whereas, in others (dependent on the evenness or oddness of the nuclide), the effect is again precisely the opposite. Still other anomalies are known. Several of these anomalies constitute “autocatalytic reactions,” for in the event of criticality, the reactivity would be increasingly enhanced as a consequence of the reaction.