Unfolding sample parameters from neutron and gamma multiplicities using artificial neural networks.

Expressions for neutron and gamma factorial moments have been known in the literature. The neutron factorial moments have served as the basis of constructing analytic expressions for the detection rates of singles, doubles and triples, which can be used to unfold sample parameters from the measured neutron multiplicity rates. The gamma factorial moments can also be extended into detection rates of multiplets, as well as the combined use of joint neutron and gamma multiplicities and the corresponding detection rates. Counting up to third order, there are nine auto- and cross factorial moments. Adding the gamma counting to the neutrons introduces new unknowns, related to gamma generation, leakage, and detection. Despite of having more unknowns, the total number of independent measurable moments exceeds the number of unknowns. On the other hand, the structure of the additional equations is substantially more complicated than that of the neutron moments, hence the analytical inversion of the gamma moments alone is not possible. We suggest therefore to invert the non-linear system of over-determined equations by using artificial neural networks (ANN), which can handle both the non-linearity and the redundancies in the measured quantities in an effective and accurate way. The use of ANN is successfully demonstrated on the unfolding of neutron multiplicity rates for the sample fission rate, the leakage multiplication and the ratio. The analysis is further extended to unfold also the gamma related parameters. The stability and robustness of the ANNs is further investigated to verify the applicability of the method. The ANN approach enables extraction of additional important information on the fissile sample compared to the application of the analytical method.