Analytic derivation of the multiplicity moments in Active Neutron Coincidence Counting with a non-Poissonian interrogation source

Active Neutron Multiplicity Counting (ANMC) methods utilize an inversion formula to extract the intensity of a fission source. This is achieved by analyzing the sampled moments of the count distribution, which are generated through the process of inducing fissions in the sample using an external interrogation source. ANMC serves as a powerful tool for quantifying fissile mass e.g., for uranium quantification in mines, fuel fabrication facilities, and reprocessing plants. Typical ANMC methods employ Poissonian interrogation neutron sources, such as AmLi, which emit a single neutron at each source event. In this study, we expand upon the conventional formulas used in ANMC inversion to accommodate non-Poissonian interrogation sources. Specifically, we derive analytical expressions for the rates of Singles and Doubles events in ANMC systems. This advancement holds practical significance as it enables the future implementation of ANMC methods utilizing external sources with correlated neutrons, such as AmBe or ²⁵²Cf. Aligned with established formulas, the derived formulas in this study adhere to the single-group model and incorporate the influence of fission chains through the widely recognized Bohnel method.