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中性子多重相関計数法の数理的基礎; ウラン・プルトニウム混合二酸化物の例

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

細馬 隆   

Hosoma, Takashi

プルトニウム転換技術開発施設では、米国エネルギー省の支援を受けて中性子同時計数法による計量装置の開発・設置・改良を行い、20年にわたり計量管理と保障措置対応に用いてきた。中性子計数による測定の対象は今後、従来とは異なる自発核分裂性核種を含む高質量のウラン・プルトニウム混合二酸化物に拡がると思われる。そこで、中性子多重相関計数法の数理的基礎について現場での経験を含めて再考するとともに、次の点について基礎を拡充した; (a)確率母関数を用いた七重相関までの多重相関分布式の代数的導出; (b)モンテカルロ法に代えて試料内部の任意の点から表面の任意の点までの平均距離とこの間での誘導核分裂反応の確率を用いた漏れ増倍率の評価; (c)Poisson過程が持つ2つの異なる時間軸と同時計数の仕組みの関連付け、結果として確率過程に由来するほぼ同時中性子の導出と評価。分布式については「組合せ」に基づく新しい表現を併記し、実際に取り扱ったウラン・プルトニウム混合二酸化物をスペクトルや平均自由行程の例とした。

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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