Mathematical Problems of Nuclear Reactor Theory

Abstract

The unanswered mathematical questions of reactor theory can be divided roughly into two classes. The first class concerns the mathematical theory of the basic transport equations and of the approximations thereto. Thus, the multiplication and criticality equations are characteristic value equations but their operators do not belong to the class for which the characteristic value theory is well established: they are not normal. Much progress was made recently concerning the character and properties of the highest characteristic value and the corresponding characteristic vector but the properties of the lower characteristic values and vectors are not known. In particular, the extent of a continuous spectrum and the completeness of the whole set of characteristic vectors are not established in general. A simple example is given in which the transport operator has a continuous spectrum which has not been recognized to date. The need for a generalization of the characteristic value problem is pointed out and such a generalization is proposed.