Cosmic muons are highly energetic and penetrative particles and these figures are used for imaging of large and dense objects such as spent nuclear fuels in casks and special nuclear materials in cargo. Cosmic muon intensity depends on the incident angle (zenith angle). The low intensity of cosmic muon requires a long measurement time to acquire statistically meaningful counts. Therefore, high-energy particle simulations e.g., GEANT4, are often used to guide measurement studies. However, the measurable cosmic muon count rate changes upon detector geometry and configuration. Here we develop an effective solid angle model to estimate experimental results more accurately than the simple cosine-squared model. We show that the cosine-squared model has a large error at high zenith angles, whereas our model provides improved estimations at all zenith angles. We anticipate our model will enhance the ability to estimate actual measurable cosmic muon count rates in muon imaging applications by reducing the gap between simulation and measurement results. This will increase the value of modeling results and improve the quality of experiments and applications in muon detection and imaging.
A New Semi-Empirical Model for Cosmic Ray Muon Flux Estimation
宇宙射线μ子已经成为一种非传统的高能辐射探测器，用于监测密集和大型物体。μ子是地球上最丰富的宇宙辐射，然而，它们在海平面上的通量约为10，000 min^-1 m ^-2，远小于感应辐射的通量。此外，宇宙射线μ子通量不仅取决于各种自然条件（例如，天顶距、高度或太阳活动），而且还取决于探测器的几何特征。由于低μ子通量通常导致长测量时间，因此可测量μ子计数的准确估计对于μ子应用是重要的。在这里，我们提出了一个简单而通用的半经验模型，以提高精度μ子通量估计在所有天顶距通过将探测器的几何参数，我们称之为有效立体角模型。为了证明的功能，我们的模型进行了比较，i）余弦平方，ii）PARMA模型，和iii）蒙特卡罗模拟，和iv）测量。我们的研究结果表明，μ子计数率估计能力显着提高，导致平均C/E从0.7增加到0.95。通过选择适当的强度关联，该模型可以很容易地扩展到不同高度和地下水平的μ子通量估计。
Cosmic-ray muon flux at Canfranc Underground Laboratory
在Canfranc地下实验室（LSC）的两个地下位置，使用专用的μ子监测器测量了高能宇宙μ子的剩余通量和角分布。该仪器由三层快速闪烁探测器模块组成，作为352个独立像素运行。该监测器的通量定义区域为1 m ${}^{2}$，覆盖所有方位角和最高达$80^\circ$的天顶角。在LAB 2400的A厅中测得的积分μ子通量为$(5.26 \pm 0.21) \times 10^{-3}$ m ${}^{-2}$ s ${}^{-1}$，在LAB 2500中测得的积分μ子通量为$(4.29 \pm 0.17) \times 10^{-3}$ m ${}^{-2}$ s ${}^{-1}$。这种角度依赖性与周围山脉的已知轮廓和岩石密度是一致的。特别是，有一个明显的最大通量来自Rioseta山谷的方向。
