Incorporating delayed neutrons into the point-model equations routinely used for neutron coincidence counting in nuclear safeguards

We extend the familiar Bӧhnel point-model equations, which are routinely used to interpret neutron coincidence counting rates, by including the contribution of delayed neutrons. After developing the necessary equations we use them to show, by providing some numerical results, what the quantitative impact of neglecting delayed neutrons is across the full range of practical nuclear safeguards applications. The influence of delayed neutrons is predicted to be small for the types of deeply sub-critical assay problems which concern the nuclear safeguards community, smaller than uncertainties arising from other factors. This is most clearly demonstrated by considering the change in the effective (α,n)-to-spontaneous fission prompt-neutron ratio that the inclusion of delayed neutrons gives rise to. That the influence of delayed neutrons is small is fortunate, and our results justify the long standing practice of simply neglecting them in the analysis of field measurements.