Mass uncertainty in neutron multiplicity counting associated with the uncertainty on the fission multiplicity factorial moments

Passive neutron multiplicity counting relies on measurement of the spontaneous fission neutron yield, to estimate the amount of ²⁴⁰Pu in the tested sample. To account for additional neutron sources in the sample, typically (α,n) reactions and induced fissions in the odd fissionable isotopes, the first three sampled moments of the neutron count distribution are used in an inversion formula that quantifies the amplitude of all three neutron sources. When solving the set of equations corresponding to the inversion formula, the first three factorial moments of the fission multiplicity distribution (both the spontaneous and induced fission) are used. Thus, any uncertainty on the nuclear data and the numeric values of the neutron multiplicity moments, is bound to create a parametric uncertainty on the estimated mass. So far, most studies on the uncertainty associated with the nuclear data are experimental by nature, often focusing on a better estimation of the factorial moments and a viable uncertainty estimation on the reported values. Since the inversion formula is non-linear, the error propagation from the multiplicity moments to the mass is also non-linear, and might have a very strong dependence on the sample parameters. In the present study, we formulate mathematical formulas that describe the error propagation from the factorial moments of the fission multiplicity to the mass, and implement the formulas to quantify the uncertainty in terms of the sample characteristics. For validation, the computational results are then compared with experimental results.