Correction to the Exponential Dependence of Neutron Transmissions

Abstract

If the energy spread of the neutron source used in a transmission type of measurement of total neutron cross sections is large compared with the mean spacing of the resonance levels of the sample, these levels may effect a deviation from the simple exponential dependence on sample thickness. The correction to this dependence is derived in the case where capture, inelastic scattering, and Doppler broadening may be neglected. The derivation does not depend upon any special assumption regarding the distributions of the widths and spacings of the levels other than that they have suitable averages, and the correction is found to be proportional to the ratio of these averages, as one would expect. It is noted that by measurement of this ratio for certain elements, it may be possible to distinguish between the predictions of the strong-coupling and complex square-well representations of the neutron-nucleus interaction.