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Essentials of neutron multiplicity counting mathematics; An Example of U-Pu mixed dioxide

Hosoma, Takashi 

Neutron coincidence counting assay systems have been developed in the last two decades. Objects would extend to high-mass uranium-plutonium dioxide containing other spontaneous fission nuclei, so essentials of neutron multiplicity counting were reconsidered and expanded: (a) Formulae of multiplicity distribution were algebraically derived up to septuplet using a probability generating function; (b) 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 probability of induced fission within the length; (c) Mechanism of coincidence counting was associated with a couple of different time axes in Poisson process, and consequently a pair of close-to-coincident neutrons from the process was derived. For the formulae, new expressions using combination were wrote down. For spectrum and mean free path, actually treated uranium-plutonium dioxide was selected as an example.

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