对涂硼正比计数管的热中子响应函数计算公式进行了理论推导.在圆柱形几何结构下,热中子在垂直柱面径向入射和任意角度入射两种情况时的响应函数得到了一种普适性的响应函数表达式,并选取正比管典型尺寸(内径10 mm,涂层厚度3 μm)进行蒙特卡罗模拟,对理论推导公式进行模拟验证,理论计算结果与模拟结果基本一致.研究表明,在垂直柱面任意角度入射的情况下,热中子的响应率随入射方向与圆柱中心距离y的增加呈规律性分布,即先增加后迅速降低,有一个峰值.在本文尺寸下,正向峰值在9 900～1 000μm之间,而反向峰值在9 700～9 800 μm之间,反向较正向数值上偏小.此外,对理论计算值与模拟值、理论值与实验值的偏差进行了分析,并给出了解释.%The thermal neutron response functions for boron-lined proportional counters are derived theoretically and simulation of responsivity is conducted with Monte-Carlo-based toolkit-Geant4. The results of theoretical calculation are coincident with the simulational ones. In the present study, it is found that responsivity varies along with the increase of the distance between incident direction and counter's central line and there is a responsivity peak in the case of vertical injection. The deductive expression is a simpler and effective method compared with Monte-Carlo simulation and the results are reliable. This is helpful for proportional counter design.
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