Generalised Campbell formulae for compound Poisson processes with applications in nuclear safeguards

Abstract: Multiplicity counting is a widely used non-destructive assay method for estimating unknown parameters (primarily the mass) of samples of spontaneously fissioning materials (e.g. plutonium). Traditionally, measurements are performed with thermal neutron detectors operating in pulse counting mode. The method is based on determining the first three lowest order moments of the number of particles emitted simultaneously from the sample, through measuring the so-called singles, doubles and triples detection rates from the counting statistics of the detectors, from which the sought sample parameters can be unfolded with algebraic inversion. The main difficulty with multiplicity counting is its inherent sensitivity to dead time effects, which poses a major constraint on the ability to extract correlated neutron counts. To overcome this difficulty, a new method of multiplicity counting has been developed, which is based on the statistics of the time-resolved signals of detectors operating in current mode. Specifically, the method utilizes information in the auto and cross cumulants of the stationary signals of different groups of detectors. Based on a stochastic theory of fission chamber signals, expressions were derived for the one-, two- and three-point (in time) cumulants of the detector currents. It was shown how the traditional multiplicity count rates can be recovered from the detector currents with the help of these relationships. Although the new approach needs a more involved calibration, its main advantage is that it is insensitive to dead time effects. As a result, no dead-time corrections are required and the sample parameters can be extracted from three (or even fewer) detectors.