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## Experimental study on material discrimination based on muon discrete energy

Li Yu-Peng, Tang Xiu-Zhang, Chen Xin-Nan, Gao Chun-Yu, Chen Yan-Nan, Fan Cheng-Jun, Lü Jian-You
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• #### 摘要

宇宙射线缪子具有穿透力强、对重核材料敏感的特点, 近年来被广泛应用于核材料检查等领域. 缪子与不同原子序数材料发生的多重库仑散射效果不同, 利用这点可以对被测物体进行成像以及材料鉴别, 而在该过程中引入缪子的能量信息可以提高材料鉴别的准确度. 本文基于原子能院研制的缪子成像装置开展了5种样品的材料鉴别实验, 使用离散能量拟合近似连续能量的缪子散射角分布, 进而测量出各材料的辐射长度并以此作为特征量进行材料鉴别. 实验结果表明, 在约1400个有效缪子事例下, Al-Fe和Fe-Pb可以在95%的置信水平下有效区分, 该方法相比于不引入缪子能量信息对Pb-W鉴别的准确率提高了18.5%.

#### Abstract

Cosmic-ray muon is a kind of charged particle with strong penetrating capability and sensitivity to high atomic number materials. In recent years, muongraphy emerged as a novel technique by using cosmic-ray muon to image unknown volume, and is widely applied to nuclear security, geosciences, archaeology and civil engineering. The effect of multiple Coulomb scattering between muons and materials with different atomic number is different, and the scattering angle is related to material Z and muon energy. If we can measure muon scattering angle and muon energy, we can identify the category of material interacted with muon. However, it is difficult to measure the energy of each muon in real time, most of the researches use the mean muon energy ~4 GeV to alternate each muon energy which causes image to blurred and material discrimination accuracy to decrease. This article introduces a method of using the discrete muon energy to fit the scattering angle distribution derived from continuous muon energy and estimate the weight of each discrete muon energy. Then measure the scattering angle of the material to be identified, histogram the scattering angle and couple it with the calibrated scattering angle distribution by discrete muon energy. The last step is to calculate the radiation length from the above equation. The radiation length is a characteristic quantity of the material, and used to identify materials in this method. We carry out the experiment on material’s discrimination based on the apparatus of cosmic-ray muon tomography made by China Institute of Atomic Energy. The system contains 6 layers, consisting of several drift tube detectors planted in two orthogonal coordinate for tracking muon trajectory. Five materials are selected to be distinguished in the experiment, they being C, Al, Fe, Pb, and W. The scattering angles formed by muons passing through these materials are measured respectively, and their radiation lengths are measured and identified in pairs. In order to evaluate material discrimination accuracy, we plot the ROC curve between each pair of materials. The result reveals that Al-Fe and Fe-Pb can be effectively identified at a 95% confidence level, under 1400 valid muon events. Considering that the difference in material density also influences discrimination accuracy, we simulate several other materials identified by Pb. It is concluded that this method can identify the materials with radiation length greater than 0.7 cm. Compared with the discrimination method of unknowing muon energy, this method improves the accuracy of Pb-W discrimination by 18.5%.

#### 作者及机构信息

###### 通信作者: 汤秀章, tangxz@ciae.ac.cn
• 基金项目: 国家财政部稳定支持研究(批准号: WDJC-2019-05)资助的课题.

#### Authors and contacts

###### Corresponding author: Tang Xiu-Zhang, tangxz@ciae.ac.cn
• Funds: Project supported by the Fund for Stable Support Research in Ministry of Finance, China (Grant No. WDJC-2019-05)

#### 施引文献

• 图 1  三种不同厚度铅块及散射成像结果

Fig. 1.  Lead cube with different thickness and the image of scattering tomography.

图 2  权重标定实验的Geant4模型

Fig. 2.  Geant4 model for weight calibration experiment.

图 3  (a) 缪子穿过不同厚度铅块的散射角分布(点)与拟合曲线(线); (b) 10 cm铅块的实验结果与模拟结果对比

Fig. 3.  (a) Measured scattering angle distributions of lead cubes under different thicknesses (dot) and fitting curve (line); (b) the comparison between experiments and simulations of 10 cm Pb.

图 4  测量五种材料的散射角及散射成像结果

Fig. 4.  Measurement of scattering angles for the different materials and the image of scattering tomography.

图 5  缪子穿过不同材料的散射角分布(点)与拟合曲线(线)

Fig. 5.  Measured scattering angle distribution of different materials (dot) and fitting curve (line).

图 6  材料鉴别实验ROC曲线

Fig. 6.  ROC curve of material distinguishment experiment.

图 7  两种方法鉴别铅-钨的ROC曲线对比

Fig. 7.  ROC curves of the lead-tungsten distinguishment performed by different method.

图 8  径迹测量误差与各材料辐射长度误差的关系

Fig. 8.  Relationship between measurement error and the radiation length error of different materials.

图 9  不同径迹测量误差下鉴别ROC曲线　(a) C-Al; (b) Pb-W

Fig. 9.  ROC curve of distinguishment under the different measurement error: (a) C-Al; (b) Pb-W.

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• 被引次数: 0
##### 出版历程
• 收稿日期:  2022-08-18
• 修回日期:  2022-10-14
• 上网日期:  2022-10-19
• 刊出日期:  2023-01-20

## 基于缪子离散能量的材料鉴别实验研究

• 中国原子能科学研究院, 北京　102413
• ###### 通信作者: 汤秀章, tangxz@ciae.ac.cn
基金项目: 国家财政部稳定支持研究(批准号: WDJC-2019-05)资助的课题.

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