Abstract

To obtain the characteristic information of unknown radionuclides by analyzing the γ-energy spectrum of a low-resolution detector, and to improve the accuracy and validity of the analysis of overlapping and weak peaks in the γ-energy spectrum, in this paper we analyze the γ-energy spectrum of NaI(Tl) detectors based on the Boosted-Gold algorithm. A simulation model of NaI(TI) detector is established by using MCNPX, and a detector response matrix with dimension 201 × 200 is obtained. The γ-energy spectrum unfolding program is developed based on the Boosted-Gold algorithm. The detector response spectra of the γ radioactive sources <sup>22</sup>Na, <sup>133</sup>Ba, and <sup>152</sup>Eu are measured. Three groups of low-resolution γ spectra are constructed with different γ-ray energy, different energy differences (<inline-formula><tex-math id="M2">\begin{document}$ \Delta E $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20212429_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20212429_M2.png"/></alternatives></inline-formula>) and different relative intensities by simulation. Combining the response matrix and the unfolding procedures, the measured and simulated γ energy spectra are unfolded. The unfolding results are analyzed with the nuclide standard characteristics information from the IAEA database. The results show that the maximum unfolding error of the characteristic energy of the measured γ-energy spectrum is 2.17% (0.276 MeV for <sup>133</sup>Ba source) by the Boosted-Gold algorithm, and the maximum deviation between the unfolded intensity and the standard intensity is 0.197 (1.408 MeV for <sup>152</sup>Eu source). For the simulated γ energy spectrum, the characteristic energy of nuclide can be accurately analyzed, and the deviation between unfolded intensity and standard intensity maintains 0.01. When the enhancement factor <i>p </i>≤ 14, the Boosted-Gold algorithm is beneficial to the quantitative analysis of γ-radionuclides. For the relative intensity of γ-rays greater than 10%, this algorithm has better analysis accuracy.

Highlights

  • The results show that the maximum

  • (School of Nuclear Science and Technology, University of South China, Hengyang 421001, China)

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Summary

H T y i xi k n

其中 n 为构成响应矩阵的响应函数个数,将满足收敛条件解 x 的各分量 xi 进行如 (7)式的幂指数非线性增强,并将其作为迭代初值再一次进入(6)式迭代计算,最终得 到满足收敛条件的解. 图 1 Boosted-Gold 算法计算过程 Fig. 1 The calculation process of Boosted-Gold Algorithm. 如图 1 所示,算法迭代过程如下: a) 首先.给定初值 x(0)、迭代次数 k 以及迭代终止判定条件 φ. 3.1 实验系统及γ能谱测量 γ 能谱测量实验系统主要由 FJ374 型 NaI(TI)闪烁体探测器(40mm×40mm)、 BH1283N 型高压电源、BH1218 型线性放大器(FH0001A 型机箱)、ADC 多道脉 冲幅度分析器以及 PC 搭建,如图 2 所示.实验中 γ 源到探测器探头的距离为 1.5 cm, 高压电源电压为 420 V,主放放大倍数为 20,测量时间 120 min,输出信号由 4096 道 ADC 多道脉冲幅度分析器进行数据采集并在 PC 端显示;最后对标准 γ 源 22Na、 60Co、133Ba、137Cs 和 152Eu 脉冲响应谱进行了测量,并在相同实验条件下测量了环 境本底用于后续数据处理. 探测器的能量刻度和分辨率刻度是 γ 能谱分析的依据,也为 NaI(TI)探测器蒙 特卡罗建模提供准确参数.能量刻度函数由γ射线的全能峰峰位与对应的特征能 量线性拟合获得.为了准确获得标准 γ 源 22Na、60Co、133Ba、137Cs 全能峰的峰位 以及半高宽(FWHM),首先根据实测自然本底对实验能谱进行了本底计数扣除;然 后采用 Savitzky-Golay 方法对谱数据进行了 3 点平滑滤波,消除探测器对 γ 射线响 应统计过程中统计涨落的影响;最后采用一阶导数寻峰方法,获得所测 γ 源全能峰 峰位及半高宽信息;能量刻度如图 3 所示: 1.332MeV. 其中,a、b、c 为待定展宽参数.Eγ 为全能峰对应的入射 γ 射线特征能量,单位为 MeV; 根据实测标准 γ 源特征能量及对应全能峰半高宽信息进行非线性待参拟合,获得 (8)式待定参数 a=0.01607,b=0.02729,c=1.28065.如图 4 所示: 6.5. 图 4 能量(Eγ)与半高宽(FWHM)对应关系 Fig. The correspondence between energy (Eγ) and half-maximum width (FWHM). 将每个入射单能 γ 射线响应函数作为构建响应矩阵一个列向量,共由 200 个 单能 γ 射线的响应函数列向量构成;模拟过程采用 F8 计数卡进行计数抽样为 200 道,抽样能量范围为 0-2 MeV;各单能 γ 射线能量随步长 0.01MeV,覆盖能量区间为 0.01MeV 至 2MeV;采用公式(10)对模拟响应函数进行展宽 ,最终得到维度为 201×200 的响应矩阵.结果如图 6 所示: 非

Boosted-Gold算法反演低分辨率γ能谱的准确性
Boosted-Gold算法反演低分辨率γ能谱的准确性和有效性
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