# Pulse-Shape Discrimination of SiPM Array-Coupled CLYC Detector Using Convolutional Neural Network
## 3 Pulse-Shape Discrimination  
### Time Window Optimization of Charge Comparison  
Figure 4 depicts the normalized pulse form created by neutrons and gamma rays in the CLYC scintillator. The \(\gamma\) and neutron signals in Figure 4 were extracted from the \({}^{137}\)Csy peak and the \({}^{252}\)Cf source thermal neutron peak, respectively. The equivalent energy of the gamma signal was 637.98 keV (energy resolution: 8%@662 keV), and the equivalent energy of the neutron signal was 3266.58 keV. After normalization, the equivalent energy of the gamma signal was 1270.23 keV, the neutron signal was 1262.67 keV, and there was no significant difference in electron equivalents. There is an observable, but unclear, difference between the two waveforms. Due to the large parasitic capacitance of the SiPM array, the difference in pulse shape appears on the rising edge instead of the falling edge due to the integration of the parasitic capacitance on the signal. Moreover, the single signal as illustrated in Figure 4, rather than the average signal, is more disturbed by noise, resulting in a faster reduction in neutrons on the falling edge of the signal. The charge comparison method can discriminate unknown signals based on the difference between different signals. The more obvious the initial difference between neutron and gamma signals, the better the \(PSD\) performance. The selection of the prompt and total window is shown in Figure 4. There are many possible combinations of window widths. Under this condition, choosing  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Response Spectrum/nm** & **Peak Wavelength/nm** \\ \hline SenSL Micro]series & 200–900 & 420 \\ \hline \hline \end{tabular}
\end{table}
Table 2: SiPMs’ main properties.  
Figure 3: The simulated energy spectrum of \({}^{252}\)Cf neutron source moderated by PE.  
Figure 2: Thermal neutron signal acquisition.  
the best window combination can produce the best discrimination performance. We then discriminated the signal by the \(PSD\) parameter, which is calculated as  
\[PSD=\frac{Q_{t}-Q_{p}}{Q_{t}}. \tag{1}\]  
Here, \(Q_{t}\) is the total window charge integral and \(Q_{p}\) is the prompt window charge integral. The figure of merit (\(FoM\)) was introduced to evaluate the \(PSD\)'s performance and is defined as  
\[FoM=\frac{|P_{\gamma}-P_{n}|}{FWHM_{\gamma}+FWHM_{n}}, \tag{2}\]  
where \(\mid P_{\gamma}-P_{n}\mid\) represents the distance between the \(\gamma\) peak and the neutron peak, and \(FWHM_{\gamma}\) and \(FWHM_{n}\) are the half-height widths of the \(\gamma\) and neutron peaks, respectively.  
This study set the prompt window range to \([0,1\;\mathrm{s}]\) and the total window range to \([0,2\;\mathrm{s}]\) to produce the best combination of prompt and total windows, wherein the value of the total window should be greater than that of the prompt window, traversed in steps of \(10\;\mathrm{ns}\). After the traversal was completed, a two-dimensional distribution map of the \(PSD\)\(FoM\) value changing with the prompt and total window could be drawn. In Figure 5, it can be seen that the \(FoM\) value is more sensitive to changes in the prompt window. The optimal prompt and total window size under this experimental condition are [140 ns, 530 ns].  
Figure 4: The pulse shape and time window of neutron and \(\gamma\) in CLYC.  
Figure 5: Two-dimensional histogram of \(PSD\)\(FoM\) value changing with prompt window and total window.