Analysis of the Feynman Variance to Mean Ratio Using Nonlinear Regression

Neutron multiplicity counting is an established measurement technique for estimating properties of special nuclear material (SNM). Point kinetics models of neutron multiplicity measurements are frequently applied to estimate the kinetics parameters of fissile sources (such as neutron source strength, multiplication, lifetime, and detection efficiency) because the models can generally be used to derive closed form expressions for the moments of the neutron count distribution in terms of the kinetics parameters. Most applications of point kinetics models derive explicit algebraic expressions for the kinetics parameters in terms of the distribution’s moments measured for a single coincidence gate width. Uncertainties in kinetics parameters are typically estimated by propagating counting uncertainties in the moments through the algebraic expressions for the kinetics parameters. Alternatively, it is possible to implicitly solve for the kinetics parameters by fitting point kinetics models of the moments (or related quantities, like the Feynman variance to mean ratio) using nonlinear regression. Furthermore, it is relatively straightforward to apply nonlinear regression to fit the point kinetics models to the moments measured for all coincidence gate widths. This paper demonstrates nonlinear regression analysis applied to the Feynman variance to mean ratio ( ) measured for a 4.4 kg weapons-grade plutonium metal sphere reflected by varying thicknesses of polyethylene. The analysis estimates the neutron multiplication factor ( ), the neutron time-constant ( ), and their respective uncertainties. Relative to approaches that explicitly solve for the point kinetics model using a single coincidence gate, the approach presented in this paper should yield reduced uncertainties for the kinetics parameters.