The role of diffusion theory to describe multiplicity moments

• Multiplicity moments of safeguards are calculated using diffusion theory. • The results are compared with exact transport solutions and with the point model. • The error of the diffusion theory increases with the size of the item. • An explanation of the behaviour of the error is offered. • For large items diffusion theory still supplies better results than the point model. The factorial moments of the neutrons emitted from a multiplying item due to one internal source event (also called multiplicity moments), are traditionally calculated in the so-called point model. Recently, interest arose in the calculation of these moments in a space-dependent model, using one-speed transport theory (Pázsit and Pál, 2021). In this work, a comparison of work in the space dependent model on multiplet evaluation ( Pázsit et al., 2023 , Williams, 2025 ) has been made using diffusion theory. The method of solution uses the scalar form of the transport equation reduced to diffusion theory form to calculate the singlet, doublet and triplet moments. It is well-known that diffusion theory is an approximation to transport theory but in general is much simpler to use. For the sake of completeness, we compare the results from transport theory with those of the corresponding diffusion theory solutions. As expected, the diffusion results differ from those of transport theory and we find that they are in significant error as the body radius increases; an explanation is advanced for this defect. At the same time, for large item sizes, the diffusion results still represent an improvement over the point model.