A multi-region multi-energy formalism for Neutron Multiplicity Counting

The stochastic transport equation, which describes the dynamics in time of neutron popula- tion in a nuclear system, is used to gain expressions for higher moments of the neutron population. This type of analysis is of utmost importance for Neutron Multiplicity Counting (NMC), where the first three moments of the detected neutrons are used to separate between neutrons originat- ing from spontaneous fission and neutrons originating form induced fissions and alpha-neutron reactions, in order to estimate the mass of fissile material in a sample. In the present study, we extend the currently used single energy point wise formalism into the most general setting of N regions and M energy groups. The basic idea which allows simplifying the formulas is the simple observation that from a mathematical point of view, there is almost no difference between spatial and energetic distribution. Or, in other words, we could treat the system, at least from a formal point of view, as a single vector of ”space-energy” cells, distinguished only by their cross sections. In the study, we introduce and solve a stochastic transport equation for a multi energy multi region system, and verify our results through computer based simulations.