Minimizing the statistical error in capture cross-section measurements

Measurements of the neutron capture cross-section are performed by measurement of the capture rate of a sample placed in a neutron beam. The capture rate is measured by surrounding the sample with gamma-ray detectors. The capture rate is corrected for background and divided by the rate of neutrons incident on the sample in order to obtain the capture yield. The neutron capture cross-section can be obtained from the capture yield if additional information such as the total or scattering cross-section is known. An error analysis was performed on the measured capture cross-section. The error was minimized with respect to the experimental time split of the capture, background and incident neutron rates and also with respect to the sample thickness. These calculations are useful for the planning of an efficient capture cross-section experiment. The derived equations are compared to experimental data and show excellent agreement. This type of error analysis and minimization is also valid for other types of partial cross-section measurements such as fission and scattering which have similar expressions for the measured yield.