Calculation of Multiplicity Moments in Nuclear Safeguards via Explicit Eigenfunctions

Journal article, 2026

Accurate and fast formulations are of particular relevance in applications of multiplicity counting in nuclear safeguards. That is, the final goal is to determine the parameters of the item, primarily the mass of the fissile component. This may be achieved through an inverse procedure by unfolding the parameters of the item from the measured multiplicity rates. However, these rates are directly related to the calculation of multiplicity moments. In a recent work, the forward transport approach, in particular the analytical discrete ordinates (ADO) method, was used to efficiently evaluate factorial moments as an alternative form of the backward integral–type formulation available in the literature. The technique was extended in a subsequent work to consider the mean number of secondary neutrons per collision c > 1, and the first results were established for the multiplicity moments. In both works, the results were compared with the collision number (CN) expansion method. In the present work, seeking to improve even more the speed of calculation, we introduce to the ADO formulation the use of the so-called explicit eigenfunctions to evaluate the factorial moments, and subsequently, the multiplicity moments. Furthermore, thinking of establishing benchmark solutions for the problem, in addition to the CN expansion approach, we present a comparison with additional numerical results available in the literature for the multiplicity moments, including scattering effects, based on an integral formulation. Our method provided very accurate solutions, and it was found that our method is superior in terms of speed in comparison with the originally used CN expansion, for which we have data available. Furthermore, the use of explicit solutions also showed a time computational gain in comparison with the numerical eigenfunctions formulation.