A note on the multiplicity expressions in nuclear safeguards

The purpose of this note is to point out notational inconsistencies and actual errors in some of the basic and often cited expressions of Ensslin et al. [Application Guide to Neutron Multiplicity Counting, Los Alamos Report LA-13422-M, 1998], even if the final formulae are correct. These expressions describe the measured multiplicity counting rates, i.e. singles, doubles, and triples rates S, D, and T, as parameters of a multiplying sample, through analytical expressions of the factorial moments of the neutrons generated in the sample by one initial source event. They serve as the basis of unfolding these parameters by the inversion of the formulae. The motivation for this brief communication is twofold. First, Ref. [N. Ensslin,W.C. Harker, M.S. Krick, D.G. Langner, M.M. Pickrell, J.E. Stewart, Application guide to neutron multiplicity counting, Los Alamos Report LA-13422-M, 1998] is the most widely available and by far the most cited source of the derivation, which is supposedly also used as a tutorial for newcomers. Hence it is important that the correct derivation is available. Indeed it can be seen that the erroneous expressions have already propagated widely in citations. Second, similar derivations have become recently interesting for the multiplicities of gamma photons. Hence we want to create both a citable reference as well as guidance for such on-going work in further applications of the theory.