A note on the multiplicity expressions in nuclear safeguards.
Journal article, 2009
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.