Neutron diffusion in a plane uranium-water lattice

The diffusion lengths for a plane uranium-water lattice are calculated for thermal-neutron diffusion parallel (L) and perpendicular (L) to the layers. The calculation of L is carried out in the diffusion approximation but can be used without the introduction of nondiffusion corrections since it is correct in the limiting cases (thick and thin layers). The calculation of L is carried out both in the diffusion and nondiffusion approximation: in the latter case, however, it is assumed that the absorption is small. In the case of thick layers, the ratio may reach 1.9. It is shown that if a uranium-aluminum alloy is used the anisotropy becomes still larger. As the layer thickness is reduced the anisotropy is reduced and finally vanishes.