Time eigenvalues for one–speed neutrons in reflected spheres

Abstract

The spectrum of time eigenvalues has been studied for one-speed neutrons in isotropically scattering spheres with a reflexion coefficient R in the interval −1 ≤ R ≤ 1. It is proved that a continuous spectrum exists in the Hilbert space. This continuum disappears if we suitably enlarge the function space. It is also proved that for R ≤ 0 there are only discrete eigenvalues on the real axis. However, for R > 0 there is a continuum of eigenvalues beyond the Corngold limit. An expression is given for the lower boundary of the continuum, and it is supported through numerical calculations.