Study of a theoretical model for the measured gate moments resulting from correlated detection events and an extending dead time

Neutron emissions from fissioning nuclear material are temporally correlated. The detection of these correlated neutrons is frequently used to quantify plutonium (Pu) and other fissile materials for international nuclear safeguards and related activities. However, detector dead time affects the observed rates of correlated neutrons in a non-trivial manner, and must be accounted for to obtain accurate results. A major simplification made in the most widely used dead time corrections is that the neutron detections are occurring randomly in time. A few previous attempts at providing a dead time model for correlated neutrons have been limited in scope, have made simplifying assumptions early in the derivation, and have, in general, not been implemented in the broader safeguards community. This paper provides an exact dead time model for correlated neutron detections in a single channel system assuming an updating dead time, and therefore a paralyzable system. This dead time model includes the assumption that a single exponential, with one characteristic decay constant, can describe the system neutron die-away profile. An exact model for the effects of dead time on measured gate moments is derived which is extendable to an arbitrary order of neutron correlation. This dead time model predicts the measured gate moments based on the dead time and underlying detection rates, including the effects from detection rates with an arbitrarily high order of correlation. The effects of dead time on the apparent singles, doubles, triples and quadruples rates using either event triggered, random or mixed gate structure is also derived. Either the equations for the measured gate moments or the apparent multiplicity rates can be numerically inverted to find the dead time corrected multiplicity rates. Although the model has been explicitly solved for rates up to and including quadruples, it is directly extendable to any order of correlation. This model is presented from the perspective of neutron counting. However, the model is mathematically applicable to any series of events which are temporally correlated through an exponential probability distribution and which are subject to a dead time-like filter.