Abstract
Synopsis The eigenvalue problem defining the exponential time decay of a thermal neutron distribution is investigated. It is found that the decay constant is bounded whenever the neutron transit time is unbounded. For the particular case of spherical geometry, isotropic scattering and a simple thermalization model, the fundamental mode decay constant reaches its upper bound for a finite sphere radius. This implies that there are no discrete eigenvalues of the thermal neutron transport operator for a sufficiently small sphere. This is in contrast to the result for mono-energetic neutrons obtained by Jorgens. The problem is first illustrated by reviewing the results for mono-energetic neutrons for a single fourier component in an infinite medium, for a slab and for a sphere. Only the last of these has a bounded neutron transit time, and this also becomes unbounded when the possibility of zero velocity neutrons in a thermal neutron velocity distribution is considered. It is indicated, but not proved, that the conclusions drawn from the special model studied apply to more realistic models of slow neutron interaction with matter. The relevance to pulsed neutron experiments in small moderating samples is discussed.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call