A priori precision estimation for neutron Triples counting

The nondestructive assay of Plutonium bearing items for criticality, safety, security, safeguards, inventory balance, process control, waste management and compliance is often undertaken using correlated neutron counting. In particular Multiplicity Shift Register analysis allows one to extract autocorrelation parameters from the pulse train which can, within the framework of a simple interpretational model, be related to the effective
²⁴⁰
Pu spontaneous fission mass present. The effective
²⁴⁰
Pu mass is a weighted sum of the
²³⁸
Pu,
²⁴⁰
Pu and
²⁴²
Pu masses so if the relative isotopic composition of the Pu can be established from the measured
²⁴⁰
Pu effective mass one can estimate the total Pu mass and also the masses of the individual isotopes, example the fissile species
²³⁹
Pu and
²⁴¹
Pu. In multiplicity counting three counting rates are obtained. These are the Singles, Doubles and Triples rates. The Singles rate is just the gross, totals or trigger rate. The Doubles and Triples rates are calculated from factorial moments of the observed signal triggered neutron multiplicity distributions following spontaneous fission in the item and can be thought of as the rate of observed coincident pairs and coincident triplets on the pulse train. Coincident events come about because the spontaneous fission and induced fission chains taking place in the item result in bursts of neutrons. These remain time correlated during the detection process and so retain information, through the burst size distribution, about the Pu content. In designing and assessing the performance of a detector system to meet a given goal it is necessary to make a priori estimates of the counting precision for all three kinds of rates. This is non-trivial because the counting does not obey the familiar rules of a Poissonian counting experiment because the pulse train has time correlated events on it and the train is sampled by event triggered gates that may overlap. For Singles and Doubles simple approximate analytical empirical rules for how to estimate the variance have been developed guided by theory and refined by experiment. However, for Triples no equivalent rules have been put forward and tested until now. In this work we propose an analytical expression, the CSH relation, for the variance on the Triples count and exercise it against experimental data gathered for Pu items measured in the Los Alamos National Laboratory's Epithermal Neutron Multiplicity Counter (ENMC). Preliminary results are encouraging and reasonable agreement with observation, considered fit for scoping studies, is obtained. We have also looked at the behavior using Monte Carlo simulations.