The number distribution of neutrons and gamma photons generated in a multiplying sample

Diffusion theory model of the neutron number probability distribution in a subcritical multiplying assembly

“…However, in the application of interest here, namely, highly subcritical fissile systems, the probability of obtaining neutron numbers in excess of a few tens is known to be vanishingly small. In this case, the approach demonstrated by Böhnel (1985) and Enqvist et al (2006) for the lumped model is extensible to the non-lumped case, as we demonstrate next.…”

“…While the resulting neutron number distribution provides valuable insight into the branching process and the conditions under which the population may become extinct or diverge asymptotically in time, a complete characterisation of the random neutron population in the presence of randomly emitting neutron sources inherent to the system, such as spontaneous fission, requires consideration of multiple concurrent chains. We note that spontaneous fission neutron multiplicity plays a key role in distinguishing the presence of fissile material from background neutrons in detection systems (Enqvist et al, 2006). An explicit source cannot be included in the backward Master equation formulation but the neutron number distribution from a single chain is an essential ingredient in constructing the corresponding distribution in the presence of a random intrinsic source, as we demonstrate next.…”

“…Measurement and modelling of neutron multiplicity distributions play a key role in the identification and characterisation of small samples of special nuclear material that is important in the nonproliferation and safeguards space (Böhnel, 1985;Enqvist et al, 2006;Mattingly, 2012). A knowledge of the neutron multiplicity distribution makes possible the estimation of integral properties such the strength of the inherent random source, and the mass and composition of an unknown sample (Mattingly, 2012;Enqvist et al, 2006).…”

“…A knowledge of the neutron multiplicity distribution makes possible the estimation of integral properties such the strength of the inherent random source, and the mass and composition of an unknown sample (Mattingly, 2012;Enqvist et al, 2006). Moreover, because the neutronic signature of fissile materials deviates from the Poisson distribution, multiplicity distributions can help distinguish background neutrons arising from (α, n) reactions from those arising from fission chains.…”

“…These are precisely the conditions that arise when dealing with small, highly subcritical samples and hence the approach is relevant to nonproliferation and safeguards work. Thus far, however, numerical work based on the Master equation has been restricted to computing neutron and photon distributions in lumped or point systems for a single source realisation (Enqvist et al, 2006). While useful for developing insight into the statistics of neutron multiplication and quantifying the effect of random sources, lumped models are unable to describe spatial effects originating from nonuniformity in the distribution of fissile material and the presence of neutron reflectors and absorbers.…”