Essentials of neutron multiplicity counting mathematics. An example of U-Pu mixed dioxide

Several neutron coincidence counting assay systems for small and unshaped uranium-plutonium dioxide remained in some of glove boxes or contained in solid wastes have been developed, installed and improved in the last two decades for nuclear materials accounting and for safeguards at the Plutonium Conversion Development Facility supported by the U.S. Department of Energy. Objects to be measured by neutron counting would extend to high-mass uranium-plutonium dioxide containing ²⁴⁴Cm etc. by an innovation of higher order multiplicity counting technique, therefore essentials of neutron multiplicity counting mathematics were reconsidered into where experiences in the field were taken, then expanded in regard to the following subjects : formulae of multiplicity distribution were algebraically derived up to septuplet using a probability generating function ; leakage multiplication was evaluated not by Monte Carlo method but by an average length from an arbitrary point inside a sample to an arbitrary point on its surface ; and a mechanism of coincidence counting was associated with a couple of different time axes in Poisson process as a renewal process, consequently a pair of close-to-coincident neutrons from the process was derived and evaluated. In this report, conventional bases were included to view all the mathematics. For the multiplicity distribution formulae, new expressions using combination which is easy-to-understand were wrote down with the conventional ones. For spectrum and mean free path, actually treated uranium-plutonium dioxide was selected as an example of composition and size. Primary multiplicity distribution and other basic data for representative spontaneous fission nuclei and induced fission nuclei were reviewed and attached. (author)