Neutron-Wave Propagation Through a Crystalline Moderator-I: Beryllium

The propagation of neutron waves through crystalline moderator beryllium has been studied. The two simultaneous integral equations in the real and imaginary part of the flux are reduced to a single homogeneous integral equation in an extended energy interval and this is solved by an iterative procedure to determine the fundamental-mode eigenvalues and eigenfunctions for various angular frequencies of the source. We show that for frequencies exceeding a certain critical frequency ω^*, no discrete mode exists. Various parameters have been deduced including D₀, the diffusion constant, and C, the diffusion cooling constant. These values are compared with the values obtained from pulsed-neutron experiments.