# Neutron and Gamma Pulse Shape Discrimination by Robust Determination of the Decay Shape
## 3 Results and Discussion
The same method without any use of a time window gave an FOM of 0.9525 (see Figure 7). \(\delta A\) values are unitless. The results obtained above are summarized in the following table of FOM values for the different approaches, Figure 3:1 Those clearly improving the separation ability of the classical charge comparison method (FOM value 0.9405) come from \(\tau\delta A\) computed by robust estimation (FOM value 1.0356), with moderate improvements over the charge comparison FOM for the \(\tau\delta A\) obtained with the data window by least squares and robust estimation, and \(\delta A\) with the data window and robust estimation. \begin{table}
\begin{tabular}{c c c c} \hline
**Parameters** & **Data Window** & **FOM Value after LS Computation** & **FOM Value after RE Computation** \\ \hline \(\tau\) & All decaying parts & 0.4064 & 0.6128 \\ \(\delta A\) & All decaying parts & 0.9521 & 0.9525 \\ \(\tau\delta A\) & All decaying parts & 0.9265 & 1.0356 \\ \hline \(\tau\) & 36 ns after the peak & 0.6897 & 0.7614 \\ \(\delta A\) & 36 ns after the peak & 0.9089 & 0.9973 \\ \(\tau\delta A\) & 36 ns after the peak & 0.9876 & 0.9896 \\ \hline \end{tabular}
\end{table} 
Table 1: FOM values for the different parameters computed, data windows and the two computation strategies: least squares (LS) and robust estimation (RE). Figure 14: Discrimination by tau*deltaA (\(\tau\delta A\)) values obtained by least squares with a time window of 36 ns, which gives an FOM value of 0.9876, instead of 0.9265 with no setup of time window (see Figure 8). \(\tau\delta A\) values in ns. Figure 15: Discrimination by tau*deltaA (\(\tau\delta A\)) values obtained by robust estimation with a time window of 36 ns. The FOM value is 0.9896, whereas it is 1.0356 with no time window (see Figure 9). \(\tau\delta A\) values in ns. As a note of caution, it is highlighted the fact that the resulting uncertainties in \(\tau\) and \(\delta A\) are around 0.01 and 0.05 times the respective values obtained in the adjustment, so, even if the FOM values above are given with four decimal places, differences of one percent or less in FOM values are not statistically significant. The scatter plot for the best solution in terms of FOM value, that is, for the discrimination by \(\tau\delta A\) with data from all the decaying parts by means of robust estimation, is given in Figure 16.  
The positive discrimination (PD) rates for gamma and neutron are also given for the different methods in Table 2. They account for the number of gamma (or neutron) pulses that were correctly classified according to the CL in Equation (16). As can be seen, the best approaches according to Table 1 are, in general, also delivering the best results in terms of PD rates. In particular, the best FOM resulted for \(\tau\delta A\), determined by robust estimation from data for all decaying parts, which also gave the best PD rates: 0.9830 and 0.9968 for gamma and neutron, respectively. Now, it is time to discuss the origin of the two abnormal peaks in the \(\delta A\) plots, namely, those to the left and the right sides of the main gamma peak with respective peaks of around 0.015 and 0.025 (unitless), see Figures 12 and 13. It could be thought that they come from artifacts of the algorithm. However, a close inspection of the pulses whose \(\delta A\) values result around 0.015, say Area I, and those whose \(\delta A\) values result around 0.025, say Area II, reveals that the problem is coming from the dataset. Figures 17 and 18 show two sample pulses having \(\delta A\) values around 0.015 (Area I, left of the main gamma peak), pulse numbers 98 and 348 in the dataset.