Neutron Wave Analysis in Finite Media

Energy-dependent diffusion theory with a modified one-term degenerate kernel is employed to derive an expression for the detector response in neutron-wave experiments performed in a slab and a cylinder of crystalline moderator. The Watson transform and the Laplace transform modified to finite systems are used and different mathematical representations of the detector output are discussed. From the derived expressions, various decaying modes, including the continuum mode, are calculated for a 100-cm graphite slab. The condition for the existence of the discrete mode is studied, and the maximum frequencies obtained are 7440 cps for graphite and 9300 cps for beryllium. The experiment reported by Utsuro et al. is interpreted and the observed interference pattern is reproduced analytically with a slight discrepancy in the resonance frequency. The potential of this experiment for measuring moderator properties is also discussed.