Multi-velocity corrections in the theory of neutron detecting foils

Abstract

The accuracy of the one-velocity, average cross section, approach in the theory of neutron detecting foils has been assessed. This has been achieved by treating the full energy-dependent Boltzmann equation and forming a variational functional for the foil activation. The use of simple but realistic trial functions enables this functional to be reduced to tractable integrals. In the case of graphite, at room temperature or above, it is concluded that the one-velocity method is adequate. However, for moderators with rapidly varying scattering cross sections in the thermal region—water, for example, discrepancies arise which cannot be neglected. Also for cold moderators (i.e. temperature around 100°K or less), particularly crystalline ones, the effect of the Bragg cut-off and the corresponding increase of the mean free path below this, can lead to a large increase in the foil activation. This effect is not predicted by the one-velocity approximation.