Combined use of neutron and gamma multiplicities for determining sample parameters

Expressions for neutron and gamma factorial moments are known in the literature. For neutrons, these 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 multiplicity rates. Here we suggest the combined use of both the individual and joint neutron and gamma multiplicities and the corresponding detection rates. Counting up to third order, there are nine auto- and cross factorial moments, which are all given here explicitly. For the gamma photons, formulae are derived also for the corresponding multiplicity detection rates which, in contrast to the factorial moments, are the measured quantities and which also contain the sample fission rate explicitly. Adding the gamma counting to the neutrons introduces new unknowns, related to gamma generation, leakage, and detection. Despite more unknowns, the total number of measurable moments exceeds the number of unknowns. On the other hand, the structure of the additional equations is substantially more complicated than the neutron moments, hence their analytical inversion 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 redundance in the measured quantities in an effective and accurate way. The use of ANNs is demonstrated with good results on the unfolding of neutron multiplicity rates for the sample fission rate, the leakage multiplication and the ? ratio. Work with using the gamma multiplicity rates is on-going and some results will be reported at the conference.