Method for criticality calculations and estimation of the fissile mass based on the theory of multiplicity counting

Recently, for safeguard purposes, a theoretical model and corresponding numerical framework was elaborated by us for the calculation of the first three factorial moments of the number of neutrons leaving a fissile sample, due to one source event (a spontaneous fission with a random number of neutrons). The method is based on full 3-D transport theory, until recently only in one-speed theory. From the factorial moments, the detection rates of so-called singles, doubles and triples (S, D and T rates, also called multiplicity rates) can be derived. The model can be used for criticality safety applications in two different ways. One is that from the equations for the mean number of neutrons leaving the sample, the k_eff of the system can be determined with the same collision number type iteration as in traditional transport theory, even if the calculated quantities (number of emitted neutrons and the flux inside the system, respectively) are different. The second application is based on the fact that from the knowledge (via measurement) of the S, D and T rates, the mass of both the fissile and the fertile isotope can be extracted. Hence with the application of multiplicity counting, not only the k_eff of the system, but also the amount of fissile material can be determined in principle. (author)