A note on the multiplicity expressions in nuclear safeguards ImreP´azsit 1 , Andreas Enqvist 1 and L´ en´ardP´al 2 1 Chalmers University of Technology, Department of Nuclear Engineering, SE-412 96 G¨ oteborg, Sweden 2 KFKI Atomic Energy Research Institute H-1525 Budapest 114, POB 49, Hungary lpal@rmki.kfki.hu Abstract 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 (Ref. [1]), even if the final formulae are correct. These expressions describe the measured multiplicity counting raters, 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. [1] 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. 1. Basic principles The discussion here refers to the“Application Guide to Neutron Multiplicity Counting”, Los Alamos report LA-13422-M by N. Ensslin et al. [1]. More concretely, it concerns the derivations given in Section 5, “Multiplicity Mathematics”. Here, the multiplicities rates, i.e. the S , D, and T rates are derived from analytical expressions for the factorial moments of the detected number of neutrons emitted from a sample by one initial source event. The initial source event can be either a spontaneous fission, leading to a random number of simultaneous source neutrons, or a single neutron generated by an (α, n) reaction. Due to internal multiplication in the sample, adding extra neutrons in an instantaneous manner to those generated in the starting event, the factorial moments of the emitted neutrons will differ from the moments of the spontaneous fission (or more correctly, from the multiplicity of the original source event). Hence, the emitted neutrons are attributed to an artificial event, coined as “superfission” by B¨ohnel [2]. Expressions for the factorial moments of the emitted neutrons were first derived by B¨ohnel [2] and are also available in a recent monograph on neutron fluctuations [3], but are erroneously cited in [1] and in a number of other publications, with or without reference to [1]. Preprint submitted to Nuclear Instruments and Methods A March 2, 2009