Parameter domains for the existence of Neutron-wave discrete eigenvalues

The report begins with a brief introductory review on the past works of three eignvalue problems in neutron transport, namely the evaluation of pulsed-neutron decay constant, diffusion length and neutron-wave attenuation constant. Then by the scheme of Cercignani and Sernagiotto, the domain of eigenvalue existence is derived for neutron-wave attenuation constant, with various models of reactor physics parameters assumed for moderators. While general functional analyses in the past have clarified the spectral structure of these eigenvalue problems, the present treatment is intended to give rather heuristic and practical illustration of the subject, giving explicit analytical expressions of the domain boundary. The transport theory treatment of Duderstadt’s predicts more stringent condition than the present diffusion theory versions. The variation of the diffusion constant D, and a constant term in the scattering cross section produce considerable shift of the domain boundary. Effect of fission neutrons on this problem is speculated.