Revisiting the form of dead time corrections for neutron coincidence counting

A standard nondestructive assay technique for determining the mass of plutonium in an item is passive neutron coincidence counting. In passive neutron coincidence counting, the dead time or rate loss corrections for the singles and doubles neutron counting rates are routinely made using empirical relationships that are based on the design and performance of the individual counter used to make the measurements. The empirical methods were developed ahead of any supporting theory for dead time losses and have worked well to date for the majority of safeguards measurement scenarios. Modern applications using highly efficient systems with short neutron lifetimes together with the challenges posed by highly multiplying items mean dead time corrections of higher fidelity are needed. While many attempts have been made to develop dead time corrections that are based on the physical principles of the measurements being performed, these corrections have often been found to be difficult to implement in a real system. For instance, Matthes and Haas developed an approach in 1985 which did not gain favor largely because the form of the doubles correction apparently required numerical integration which was difficult to implement with the computer technology of that time. A recent review into the approach that was developed by Matthes and Haas has determined that a straightforward analytical expression can be derived for the doubles correction that is similar to the singles rate correction that was developed in their original work. An analysis of the expressions is presented here to show how they relate to the traditional empirical methods. Further, we illustrate their implications and limitations. For instance the empirical methods do not address within burst losses i.e. rate related losses due to the correlated neutron bursts from fission, whereas the Matthes and Hass expression for singles counting does exhibit such an effect.