Neutron Multiplicity Counting Moments for Fissile Mass Estimation in Scatter-Based Neutron Detection Systems

Neutron multiplicity counting (NMC) techniques are widely used for nuclear materials accountability and international safeguards applications to quantitatively evaluate characteristic properties pertaining to fissile material. Mathematical models for NMC moments have been previously derived for systems that use capture-based detectors; however, these models are not applicable when scatter-based detectors are used because of “neutron cross talk.” Neutron cross talk occurs when a single neutron scatters and deposits energy above threshold into multiple detectors causing spurious increase in multiplicity counts; this, in turn, has caused fissile mass to be overestimated when not treated. In this paper, we propose new mathematical models derived from point kinetics to correct for neutron cross-talk effects up to any arbitrary order N, where N denotes the maximum number of counts a single neutron can cause. The new models were used to estimate the fissile mass of plutonium metal and oxide samples with effective ²⁴⁰Pu mass ranging from 2.5 to 250 g. The adequacy of the models was confirmed using simulations of a conceptual scatter-based neutron multiplicity counter (e.g., organic scintillators) using MCNPX v2.7e with the PoliMi fission event generating extension. The fissile mass estimates with no correction for neutron cross-talk events yielded an average relative deviation from the true ²⁴⁰Pu_eff mass of 55.94% and 84.56% for metal and oxide samples, respectively. When neutron cross-talk events of order N = 2 are included in the model, the fissile mass estimates yielded an average relative deviation of 11.89% for metal and 13.21% for oxide samples. Accounting for neutron cross-talk events of order N = 3 resulted in fissile mass estimates with an average relative deviation of 9.58% and 10.51% for metal and oxide samples, respectively. These mass estimates were compared to a reference case (i.e., no neutron cross-talk effects) that yielded an average relative deviation of 6.81% and 4.77% for metal and oxide samples, respectively. The discrepancy between the estimates from the proposed model and the reference case is attributed to the assumed value of N, which sets a finite upper bound on the order of cross-talk events the model treats (i.e., the model for N = 3 assumes that a neutron will never cause more than three counts).