Restricted Minimum Critical Mass

A continuously varying distribution of fissile material being difficult to realize in a minimum critical mass reactor, restricted distributions varying by steps are investigated in the particular case of “spherical” symmetry. It is shown that the crossing points of the restricted distribution with the unrestricted one are asymptotically distributed like the zeros of the orthogonal polynomials associated with the unrestricted distribution, as weight function. The differences between the minimum masses in the restricted and unrestricted cases are decreasing faster than 4^—p, where p stands for the number of steps of different heights. Other asymptotic properties are examined.