Evaluation of Thermal Neutron Scattering Data for H in ZrHx Based on Deterministic Method
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摘要: ZrHx由于具有较高的H含量和较好的慢化特性，在核技术中得到了广泛的应用，然而，ZrHx中H的热中子散射数据的产生大多采用了直接数值模拟的方法，并未经过基于实验数据的评价。本文提出了一种与半经验声子模型相关的ZrHx中H的热中子散射数据的快速确定论评价方法，通过采用广义最小二乘法将计算机模拟的热散射数据与实验数据进行调整来完成，实验数据采用总截面测量值和反应堆基准题的有效增殖系数（keff），结果表明，经过调整后ZrHx中H声子态密度光学项的能量区间发生高能区偏移，所得到的总截面值与实验数据吻合较好，调整之后的2个TRIGA反应堆临界基准题的keff计算精度得到了改进。Abstract: ZrHx has been widely used in nuclear technology because of its high H content and good moderating property. However, the thermal neutron scattering data generation of H in ZrHx mostly uses direct numerical simulation method, which has not been evaluated with experimental data. In this paper, a fast determinstic evaluation method of thermal neutron scattering data of H in ZrHx is presented, which is related to semi-empirical phonon model. It is completed by adjusting the thermal scattering data simulated by computer with the experimental data by using generalized least square method. The experimental data are based on the total cross-section measurements and the effective multiplication coefficient (keff) of the benchmark reactor. The results show that the optical range of the H phonon density in the modified ZrHx is shifted to high energy region, and the total cross-section values are in good agreement with the experimental data. The accuracy of keff calculation for the two TRIGA reactors after adjustment has been improved.
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图 1 基于总截面测量值的GLS调整前后声子态密度的对比
Figure 1. Comparison of the Phonon Density of State before and after GLS Adjustment Based on Total Cross-section Measurement
图 2 基于总截面测量值的GLS迭代10次前后的总截面对比
1 b=10−28m2
Figure 2. Comparison of Total Cross-section before and after 10-Iteration GLS Based on Total Cross-section Measurement
图 3 基于总截面测量值的GLS迭代10次内的χ2变化
Figure 3. χ2 Change of GLS within 10 Iterations Based on Total Cross-section Measurements
图 4 基于基准题keff实验数据调整前后的声子态密度对比
Figure 4. Comparison of Phonon Density of State before and after Adjustment Based on Benchmark keff Experimental Data
图 5 基于基准题keff实验数据的GLS迭代10次内的χ2变化
Figure 5. χ2 Change of GLS within 10 Iterations Based on Benchmark keff Experimental Data
表 1 ZrHx中H的PP声子模型各参数取值范围
Table 1. Range of Parameters of the PP Phonon Model of H in ZrHx
参数 b p/MeV $ {T_{{\text{DH}}}} $/MeV F/MeV 取值范围 [1/361,1/91] [127,147] [16,24] [25,31] 
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表 2 基于总截面测量值的GLS调整前后的各参数方差
Table 2. Variance of Parameters before and after GLS Adjustment Based on Total Cross-section Measurement
参数 调整前 调整后 先验值 先验方差/% 后验值 后验方差/% b 0.00688 59.70 0.00987991 26.74 TDH 0.020 20.00 0.02072131 18.95 p 0.137 7.30 0.14431658 0.42 σ 0.028 10.70 0.03080419 5.15
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表 3 基于总截面测量值的GLS调整前后的各参数协方差系数百分比 %
Table 3. Percentage of Covariance Coefficient of Parameters before and after GLS Adjustment Based on Total Cross-section Measurement
参数 调整前 调整后 b 100 0 0 0 100 7 −56 −57 TDH 0 100 0 0 7 100 13 9 p 0 0 100 0 −56 13 100 55 σ 0 0 0 100 −57 9 55 100
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表 4 GLS调整前后总截面计算值与实验值的平方偏差
Table 4. Square Deviation between Calculated and Experimental Total Cross-Section before and after GLS Adjustment
参数 CF 模型 DG 模型 GLS初始值 GLS迭代10次的结果 χ2 3.15×101 3.75×101 3.42×101 7.91
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表 5 基于总截面测量值调整前后的基准题keff计算值对比
Table 5. Comparison of Calculated Values of Benchmark keff Based on Total Cross-section Measurement before and after Adjustment
基准题结果 初始结果（误差/pcm） 基于总截面测量值GLS
调整后的基准题keff（误差/pcm）1.00060 1.00243（183） 1.00189（129） 1.00460 1.00719（259） 1.00701（241）
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表 6 基于基准题keff实验数据调整前后的声子态密度参数方差
Table 6. Variance of Parameters before and after Adjustment Based on Benchmark keff Experimental Data
参数 调整前 调整后 先验值 先验方差/% 后验值 后验方差/% b 0.00688 59.70 0.00707 2.36 TDH 0.02000 20.00 0.02055 2.05 p 0.13700 7.30 0.13874 1.89 σ 0.02800 10.70 0.02876 2.12
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表 7 基于基准题keff实验数据调整前后的声子态密度参数的协方差相关系数百分比 %
Table 7. Percentage of Covariance Coefficient of Phonon Density of State Parameters before and after Adjustment Based on Benchmark keff Experimental Data
参数 调整前 调整后 b 100 0 0 0 100 −36 −20 −15 TDH 0 100 0 0 −36 100 −27 −6 p 0 0 100 0 −20 −27 100 −25 σ 0 0 0 100 −15 −6 −25 100
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表 8 基于基准题keff实验数据调整前后的keff计算值对比
Table 8. Comparison of keff Calculation Value before and after Adjustment Based on Benchmark keff Experimental Data
调整前 误差/pcm 调整后 误差/pcm 1.00189 129 1.00157 97 1.00701 241 1.00617 157
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