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快中子多重性测量技术是军控核查领域一项重要的无损检测技术, 可用于核材料的质量衡算. 但该方法是基于点模型假设建立的, 会造成系统偏差. 为修正偏差提升测量精度, 本文对两种不同形状的样品进行了快中子多重性模拟测量, 得到了材料空间体积内中子产生、吸收和净增长随位置的变化关系, 发现了中子泄漏增殖系数的空间变化规律. 根据中子多重性阶乘矩与待测参数间的函数关系, 提出了一种基于空间增殖系数修正的方法, 通过引入修正因子$ {g_n} $, 推导了快中子多重性加权点模型方程. 为验证该方法的准确性, 本文通过Geant4搭建了一套测量模型, 对球体和圆柱体两种形状的公斤级钚样品进行了模拟测量. 结果表明, 快中子多重性加权点模型方程的测量精度高于点模型方程, 测量偏差缩小至6%以内, 提供了一种求解公斤级钚样品质量的优化方法, 推动了快中子多重性测量技术向前发展.Fast neutron multiplicity measurement technology is an important non-destructive testing technology in the field of arms control verification. In the technique, the liquid scintillation detector is used to detect the fission neutron and combined with the time correlation analysis method to extract multiplicity counting rates from the pulse signals. This technique is commonly used to measure the mass of nuclear materials, however, it is based on the point model that assumes that the neutron multiplication coefficient keeps constant in the whole spatial volume, which will lead to overestimation of the multiplication coefficient and result in system deviation. To correct the deviation and improve the measurement accuracy, the fast neutron multiplicity simulation measurements are carried out on spherical and cylindrical samples in this work. The relationship among the position of neutron generation, absorption and net growth in the space volume of the material is obtained. According to the definition of the leakage multiplication coefficient, the leakage multiplication coefficients at different positions in the space volume of the material are calculated. On this basis, a method based on spatial multiplication coefficient correction is proposed according to the functional relationship between neutron multiplicity factorial moments and the unknown parameters. In this method, the n-order multiplication coefficient is modified by introducing a weight factor $ {g_n} $, and the fast neutron multiplicity weighted point model equation is derived. To verify the accuracy of this method, a set of fast neutron multiplicity detection model is built by Geant4, and the fast neutron multiplicity simulation measurement is carried out on the spherical and cylindrical samples. The results show that the solution accuracy of the weighted point model equation is higher than that of the standard point model equation, and the measurement deviation is reduced to less than 6 %. This work provides an optimization method for solving plutonium samples with several kilograms in mass, and promotes the development of the fast neutron multiplicity measurement technology.
[1] Fulvio A D, Shin T H, Jordan T, Sosa C, Ruch M L, Clarke S D, Chichester D L, Pozzi S A 2017 Nucl. Instrum. Meth. A 855 92
Google Scholar
[2] Li S F, Qiu S Z, Zhang Q H 2016 Appl. Radiat. Isot. 110 53
Google Scholar
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[4] Piau V, Litaize O, Chebboubi A, Oberstedt S, Gook A, Oberstedt A 2023 Phys. Lett. B. 837 137648
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Google Scholar
[6] Fraïsse B, Bélier G, Méot V, Gaudefroy L, Francheteau A, Roig O 2023 Phys. Rev. C 108 014610
Google Scholar
[7] Zhang Q H, Yang J Q, Li X S, Li S F, Hou S X, Su X H, Zhou M, Zhuang L, Lin H T 2019 Appl. Radiat. Isot. 152 45
Google Scholar
[8] 黎素芬, 李凯乐, 张全虎, 蔡幸福 2022 物理学报 71 091401
Google Scholar
Li S F, Li K L, Zhang Q H, Cai X F 2022 Acta Phys. Sin. 71 091401
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[18] Zhang Q H, Li S F, Zhuang L, Huo Y G, Lin H T, Zuo W M 2018 Appl. Radiat. Isot. 135 92
Google Scholar
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图 3 中子产生量和吸收量 (a)球体; (b)圆柱体
Fig. 3. neutron production and absorption: (a) Sphere; (b) cylinder.
图 4 中子泄漏增殖系数空间分布 (a)球体; (b)圆柱体
Fig. 4. Spatial distribution of neutron multiplication coefficient: (a) Sphere; (b) cylinder.
表 1 中子净增殖量
Table 1. Net increase of neutron.
样品 第1层 第2层 第3层 第4层 第5层 第6层 第7层 第8层 第9层 第10层 球体 173663 156111 142509 131236 121585 110940 102358 92682 82744 72978 圆柱体 212847 201300 189675 177980 165286 154546 140224 128419 113419 97833 
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表 2 离散修正因子
Table 2. Discrete correction factor.
样品 $ \overline {M_{\text{L}}^n} $ $ {(\overline {{M_{\text{L}}}} )^n} $ $ {g_n} $ $ \overline {{M_{\text{L}}}} $ $ \overline {M_{\text{L}}^{2}} $ $ \overline {M_{\text{L}}^{3}} $ $ \overline {M_{\text{L}}^{4}} $ $ \overline {M_{\text{L}}^{5}} $ $ {(\overline {{M_{\text{L}}}} )^1} $ $ {(\overline {{M_{\text{L}}}} )^2} $ $ {(\overline {{M_{\text{L}}}} )^3} $ $ {(\overline {{M_{\text{L}}}} )^4} $ $ {(\overline {{M_{\text{L}}}} )^5} $ $ {g_1} $ $ {g_2} $ $ {g_3} $ $ {g_4} $ $ {g_5} $ 球体 2.03 4.21 8.87 18.97 41.24 2.03 4.14 8.42 17.13 34.84 1 1.017 1.053 1.107 1.184 圆柱体 2.38 5.76 14.16 35.36 89.52 2.38 5.66 13.45 31.99 76.09 1 1.017 1.052 1.105 1.176
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表 3 离散修正效果
Table 3. discrete correction effect.
泄漏增殖系数 计算质量 计算偏差/% 球体 圆柱体 球体 圆柱体 球体 圆柱体 修正前 2.16 2.51 161.05 243.06 –28.04 –27.6 修正后 2.07 2.40 236.03 344.30 5.5 2.6
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表 4 拟合修正因子
Table 4. Fitting correction factor.
样品 $ \overline {M_{\text{L}}^n} $ $ {(\overline {{M_{\text{L}}}} )^n} $ $ {g_n} $ $ \overline {{M_{\text{L}}}} $ $ \overline {M_{\text{L}}^{2}} $ $ \overline {M_{\text{L}}^{3}} $ $ \overline {M_{\text{L}}^{4}} $ $ \overline {M_{\text{L}}^{5}} $ $ {(\overline {{M_{\text{L}}}} )^1} $ $ {(\overline {{M_{\text{L}}}} )^2} $ $ {(\overline {{M_{\text{L}}}} )^3} $ $ {(\overline {{M_{\text{L}}}} )^4} $ $ {(\overline {{M_{\text{L}}}} )^5} $ $ {g_1} $ $ {g_2} $ $ {g_3} $ $ {g_4} $ $ {g_5} $ 球体 2.03 4.18 8.76 18.64 40.22 2.03 4.11 8.35 16.93 34.34 1 1.016 1.049 1.101 1.171 圆柱体 2.37 5.74 14.08 35.09 88.61 2.37 5.64 13.39 31.78 75.47 1 1.017 1.052 1.104 1.174
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表 5 拟合修正效果
Table 5. Fitting correction effect.
泄漏增殖系数 计算质量 计算偏差/% 球体 圆柱体 球体 圆柱体 球体 圆柱体 离散修正 2.07 2.40 236.03 344.30 5.45 2.55 拟合修正 2.08 2.39 231.24 343.02 3.32 2.13
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[1] Fulvio A D, Shin T H, Jordan T, Sosa C, Ruch M L, Clarke S D, Chichester D L, Pozzi S A 2017 Nucl. Instrum. Meth. A 855 92
Google Scholar
[2] Li S F, Qiu S Z, Zhang Q H 2016 Appl. Radiat. Isot. 110 53
Google Scholar
[3] Stewart J, Menlove H, Mayo D, Geist W, Carrillo L, Herrera G D 2000 The Ephithermal Neutron Multiplicity Counter Design and Performance Manual: More Rapid Plutonium and Uranium Inventory Verifications by Factors of 5–20 (United States: Los Alamos National Lab) p168
[4] Piau V, Litaize O, Chebboubi A, Oberstedt S, Gook A, Oberstedt A 2023 Phys. Lett. B. 837 137648
Google Scholar
[5] Clark A, Mattingly J, Favorite J 2020 Nucl. Sci. Eng. 194 308
Google Scholar
[6] Fraïsse B, Bélier G, Méot V, Gaudefroy L, Francheteau A, Roig O 2023 Phys. Rev. C 108 014610
Google Scholar
[7] Zhang Q H, Yang J Q, Li X S, Li S F, Hou S X, Su X H, Zhou M, Zhuang L, Lin H T 2019 Appl. Radiat. Isot. 152 45
Google Scholar
[8] 黎素芬, 李凯乐, 张全虎, 蔡幸福 2022 物理学报 71 091401
Google Scholar
Li S F, Li K L, Zhang Q H, Cai X F 2022 Acta Phys. Sin. 71 091401
Google Scholar
[9] Shin T H, Hutchinson J, Bahran R 2019 Nucl. Sci. Eng. 193 663
Google Scholar
[10] Croft S, Alvarez E, Chard P, McElroy R, Philips S 2007 48th INMM Annual Meeting (Tucson) p89
[11] Li S F, Li K L, Zhang Q H, Cai X F 2022 Nucl. Instrum. Meth. A 1027 166314
Google Scholar
[12] Liu X B, Chen L G 2021 Nucl. Instrum. Meth. A 1016 165779
Google Scholar
[13] Zhang Q H, Su X H, Hou S X, Li S F, Yang J Q, Hou L J, Zhuang L, Huo Y G, Li J J 2020 J. Nucl. Sci. Technol. 57 678
Google Scholar
[14] Li K L, Li S F, Zhang Q H 2021 AIP Adv. 11 165
[15] Enqvist A, Pázsit I, Avdic S 2010 Nucl. Instrum. Meth. A 615 62
Google Scholar
[16] Burward-Hoy J M, Geist W H, Krick M S, Mayo D R 2004 Achieving Accurate Nuetron-Multiplicity Analysis of Metals and Oxides with Weighted Point Model Equations (United States: Los Alamos National Lab) p132
[17] Fulvio A D, Shin T H, Basley A, Swenson C, Sosa C, Clarke S D, Sanders J, Watson S, Chichester D L, Pozzi S A 2018 Nucl. Instrum. Meth. A 907 248
Google Scholar
[18] Zhang Q H, Li S F, Zhuang L, Huo Y G, Lin H T, Zuo W M 2018 Appl. Radiat. Isot. 135 92
Google Scholar
[19] Bai H Y, Xiong Z H, Zhao D S, Su M, Gao F, Xia B Y, Li C G, Pang C G, Mo Z H, Wen J 2023 Nucl. Instrum. Meth. A 1056 168652
Google Scholar
[20] Böhnel K 1985 Nucl. Sci. Eng. 90 75
Google Scholar
[21] Brown D A, Chadwick M B, Capote R 2018 Nucl. Data Sheets 148 142
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