Abstract
Passive methods of nuclear safeguards determine the important parameters of an unknown sample from the statistics of the detection of the neutrons emitted from the item. These latter are due to spontaneous fissions and (α,n) reactions, enhanced by internal multiplication before leaking out. Based on the original work of Böhnel, the methodology of traditional multiplicity counting is based on the first three factorial moments of the number of neutrons, emitted from the sample due to one source event. These “Böhnel moments” were derived in the so-called “point model”, in which no space-dependence is accounted for, rather a uniform first collision probability is assumed for each neutron, irrespective of the position of its birth and its velocity direction, and, more important, it is assumed to be the same for all generations in the fission chain as for the source neutrons. The purpose of the present work is to derive the same factorial moments in a one-speed space-dependent model, in which the position and direction of the neutrons is accounted for, but (similarly to the original Böhnel model), no energy dependence is assumed. The integral equations for the moments are solved numerically with a collision number expansion. It is shown that compared to the space-dependent calculations, the unfolding method using the point model underestimates the fissile mass and the underestimation increases with increasing both of fissile mass and the value of α.
Highlights
The principles of determining the singles, doubles and triples neutron count rates used in identifying and quantifying unknown items of special nuclear materials are well known (Böhnel, 1985; Ensslin et al, 1998; Pázsit and Pál, 2008; Pázsit et al, 2009)
In this paper we present a derivation of the equations for the same factorial moments, but instead of using the point model and postulating a universal first collision probability, the interactions of the neutrons will be treated in a space-angle dependent one-speed transport model
Equations were derived for the probability distribution of the number of neutrons, leaving a sample of fissile material with spontaneous fission as the neutron source, in a space and angle dependent one-speed transport model
Summary
The principles of determining the singles, doubles and triples neutron count rates used in identifying and quantifying unknown items of special nuclear materials are well known (Böhnel, 1985; Ensslin et al, 1998; Pázsit and Pál, 2008; Pázsit et al, 2009). Work to determine the bias of the point model with Monte-Carlo simulations, and to derive empirical correction factors has been performed in the past by introducing the so-called Weighted Point Model (Burward-Hoy et al, 2004) This fact does not diminish the value of the type of investigations presented in this paper, whose goal is to provide both quantitative results, as well as insight. This goal can be achieved in a fundamental way by the transport model applied here, quantifying the bias, and lending insight into its origin in terms of neutron transport theory Another aspect is that by using the same stochastic formalism as the point model, but extended to spatial and angular effects, the point model and the space dependent model are based on equivalent premises, it is easier to ensure a consistent comparison between the two models. But not least, the insight given by the analytical model, and the ease and speed of a deterministic calculation, makes it easier to suggest a correction procedure for the bias which is due to the neglection of space dependence in the point model
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