Reflection and transmission of thermal neutrons in polycrystalline slab

Solutions of the neutron transport equation with a one-term degenerate scattering kernel for a polycrystalline plane slab with finite thickness are derived with use made of the eigenfunction expansion method. The effect brought upon the energy spectrum of reflected and of transmitted neutrons by changes in temperature are examined by numerical calculations. No discontinuous change occurs in the spectra upon passage the critical temperature, below which the discrete eigenvalue vanishes, despite the abrupt change undergone at this point by the analytical solution. The spectra of the reflected and the transmitted neutrons differ entirely from each other, particularly below the Bragg energy. The discrepancy between these spectra increases with lowering temperature and widening slab thickness. A sharp peak occurring in the energy spectrum for transmitted neutrons is found to grow significantly with decreasing temperature. (auth.)