Theoretical Approach to Pseudo-Mode Neutron Waves in a Moderator

Abstract

An analysis is presented on neutron wave propagation in moderators in the frequency region above the limiting frequency for discrete eigenvalues, and the distribution of the modulated neutrons in the medium is described by integrals over the continua.When a discrete eigenvalue reaches the edge of a continuum, a singularity appears in the angular distribution of the waves and causes the discrete mode waves to disappear. Further pursuit of the root of the dispersion law making use of the analytic continuation in the angular integral locates the root on a branch of the complex eigenvalue planes that adjoins the principal branch. This root on the adjacent branch can in certain cases bring about a sharp resonance_ i.e. a " pseudo-discrete wave eigenvalue" in the continuum. The conditions for the effectiye excitation of this kind of pseudo-mode wave were examined, which revealed that for this it is essential that the neutrons causing the limiting frequency have a weak coupling and that their injection be light. It was also demonstrated that the distance from source affects the pseudodiscrete eigenvalue.An application of this analysis to the case of graphite is also presented.