# Mountain Muon Tomography Using a Liquid Scintillator Detector
## 3 Results and Discussion
### Internal Imaging of the Mountain Using Simulated Data
#### 3.2.2 Scenario 2: The Detector Is Placed outside the Mountain  
We place the detector on the surface of a ravine of the mountain to reduce the flux attenuation due to the mountain, thereby increasing the event rate. The mountain height is set to 1 km. Figure 8 shows the shape and location of the density variation region. Compared with Scenario 1, in which the detector is placed inside the mountain, the imaging here is more difficult, mainly for the following two reasons. Firstly, the distance from the detector to the center of the density variation region increases such that the muon flux from the region decreases. Secondly, the zenith angle of the region viewed by the detector increases and further reduces the flux due to the angular dependence of cosmic-ray muons: the greater the zenith angle, the lower the flux. Therefore, we up-shift the region's position, thereby reducing the zenith angle; however, the location is closer to the mountain top. Hence, the horizontal size of the region must be reduced, and, therefore, we increase its height to 0.4 km to compensate. To make the region completely wrapped by the mountain, we set its shape as a circular truncated cone. To balance the contradiction between the distance and the zenith angle, we place the detector in a position with a horizontal distance of 1.5 km and a vertical distance of 0.6 km from the density variation region's center, and the region is located in the northeast of the detector. Compared with the case in which the detector is placed inside the mountain, due to the lack of mountain shielding, a large number of muons from the sky can reach the detector directly without attenuation. Such muons have a high event rate and do not carry information about the internal structure of the mountain. Their reconstructed directions will deviate from the actual path to the mountain direction by a considerable proportion, which increases the background rate. Installing an anti-coincidence detector (for example, a plastic scintillator) facing the sky will contribute to solving this problem. For the inner liquid scintillator detector, the time window of about 20 us after the muon event is not available due to electronic system restoration and other reasons. When  
Figure 8: The mountain (grey) with an artificially embedded density variation region (cyan) and its shape and location. The height and diameter of the detector are enlarged 100 times for display convenience. The horizontal distance from the detector to the center of the region is 1.5 km. there is a signal in the anti-coincidence detector, we open an anti-coincidence time window, set its width to 20 us, and mark the signal within it. Such signals, while not useful for direct mountain imaging, are useful for event rate calibration, thus indirectly contributing to the technique. The fraction of the dead time (i.e., the period that a detector stops functioning) in the detection is  
\[\eta_{\text{dead}}=230\text{ Hz}\times 20\text{ }\upmu\text{s}\times 100\% \approx 0.5\%, \tag{12}\]  
which is so small that we can ignore its contributions to this study. For the sake of simplicity, we assume that the muons coming directly from the sky are within the detection range of the anti-coincidence detector, so their contribution is not considered. We ignore the non-uniformity of the detection efficiency caused by the anti-coincidence detector because it has little effect on the mountain center (in which we are more interested). Through the method described in Section 2.4, we obtain the ratio radar image of the density variation, as shown in Figure 9.  
Figure 9: The ratio radar images of the density variation region, assuming a six-month data acquisition period with the detector placed outside the mountain. The radial dimension is the cos\(\theta_{\text{zen}}\); the innermost point and the outermost circle correspond to the vertical (cos\(\theta_{\text{zen}}=1\)) and horizontal (cos\(\theta_{\text{zen}}=0\)) direction of muon momentum, respectively.