基于数值解析方法的γ能谱无源效率刻度方法研究

Sourceless efficiency calibration method forγspectrum based on numerical analysis

以理论分析和数值计算为基础,建立了一种基于数值解析的无源效率刻度方法。构建了φ3.8 cm×3.8 cm的LaBr_(3)(Ce)和NaI(Tl)探测器几何模型,分析了γ射线与探测器的作用路径、源与探测器相对位置和峰总比等因素,并提出非同轴点源本征效率计算公式。据此,将点源效率的数值计算拓展至面源和体源效率计算,以辛普森算法为基础对数值积分进行求解,并利用数值解析公式计算各向同性的^(137)Cs点源、面源和体源探测效率,与蒙特卡罗模拟结果相比相对偏差不超过3.5%;对不同位置处点源和不同尺寸面源、体源效率进行计算,与蒙特卡罗模拟结果相比相对偏差不超过4%。结果表明,基于数值解析的无源效率刻度方法具有快速的优势,可代替实验测量或者蒙特卡罗(Monte Carlo,MC)软件仿真效率刻度方法。该方法能推广至不同形状核辐射探测器效率刻度,为探测器效率刻度提供了新的途径。

[Background]Efficiency calibration is an important prerequisite forγ-spectroscopy measurement,and its accuracy directly affects the reliability of measurement results.The commonly used efficiency calibration methods are active efficiency calibration based on experimental measurement and passive efficiency calibration based on Monte Carlo(MC)simulations.[Purpose]This study aims to propose a sourceless efficiency calibration method forγspectrum based on numerical analysis.[Methods]Based on theoretical analysis and numerical calculation,a passive efficiency calibration method based on numerical analysis was established,and applied to a constructed geometric model for typical cylindrical LaBr_(3)(Ce)and NaI(Tl)detector with a diameter and length of 3.8 cm.Theγ-ray path trajectory inside the detector,relative position of the source and detector,and peak-to-total ratio were comprehensively analyzed.Efficiency formulas for radioactive point,surface,and volume radioactive sources were formulated.Then,a numerical integration program based on Simpson's algorithm was implemented in MATLAB to solve the numerical analytical formula,and applied to the calculation of detection efficiencies of the 3.8 cm cylindrical LaBr_(3)(Ce)and NaI(Tl)detectors for isotropic 137Cs point,surface,and volume sources.The calculation was performed again by changing the position of the point source and the size of the surface and volume sources.Simultaneously,the Monte Carlo(MC)simulation software MCNP5 was employed to establish the physical model of the detector,and the F8 pulse amplitude card was used to calculate the detection efficiency of the detector for specific energyγ-rays.Finally,detection efficiency obtained by numerical calculation was compared with that of MC simulation to verify the efficiency of proposed sourceless efficiency calibration method forγspectrum.[Results]Compared with the MC simulation results,the maximum error of numerical calculation does not exceed 3.5%,and the maximum relative errors of the point source efficiency,surface source efficiency and volume source efficiency are 3.26%,3.33%and 3.36%,repectively,which proves the reliability and accuracy of the numerical analysis method in calculating the detection efficiency.[Conclusions]The passive efficiency calibration method proposed in this study is accurate and fast,avoids complicated MC simulation software,which tends to be difficult to understand and operate.Additionally,this work can be extended to the efficiency calibration of nuclear radiation detectors with different shapes,providing a new pathway for the efficiency calibration of detectors.