# Neutron and Gamma Pulse Shape Discrimination by Robust Determination of the Decay Shape
## 3 Results and Discussion
Since the biggest difference between the results obtained by standard least squares and robust estimation occurs for the determination of the characteristic decay time (\(\tau\)), one may suspect that this estimation is particularly difficult to obtain by least squares using a time window starting exactly at the peak, that is, using all the data points in the pulse with times equal or higher to the time where the maximum amplitude is found. If it is used for the determination of \(\tau\) and \(\delta A\), only a time window starting a few \(\tau\) times after the peak, in a similar strategy to the time window for the computation of the \(Q_{s}\) value (Figure 1), the values estimated for the characteristic decay time (\(\tau\)) by least squares improve indeed, with their results now being much similar than those obtained by robust estimation. The values obtained for \(\tau\) by least squares and robust estimation for a time window starting at \(3\tau_{approx}\) (that is 36 ns) after each pulse peak are shown in Figures 10 and 11, respectively. They have FOM values of 0.6897 and 0.7614, respectively. Figure 8: Discrimination by tau*deltaA (\(\tau\delta A\)) values obtained by least squares. Gamma and neutron contributions are separated with a FOM value of 0.9265. \(\tau\delta A\) values in ns. Figure 7: Discrimination by deltaA (\(\delta A\)) values obtained by robust estimation. The separation between gamma and neutron contributions is clearly observable (FOM value of 0.9525). \(\delta A\) values are unitless. Figure 11: Discrimination by tau (\(\tau\)) values obtained by robust estimation with a time window set at 36 ns (3_Tapprx_), which gives an FOM value of 0.7614. The FOM previously evaluated with the same method but without a time window was 0.6128 (see Figure 5). \(\tau\) values in ns. Figure 10: Discrimination by tau (\(\tau\)) values obtained by least squares with a time window here chosen to be 3_Tapprx_, thus 36 ns. Evaluation of FOM gives 0.6897. As a reminder, the same method with no time window resulted in an FOM of 0.4064, with no clear separation between gamma-rays and neutrons (see Figure 4). \(\tau\) values in ns. Figure 9: Discrimination by tau*deltaA (\(\tau\delta A\)) values obtained by robust estimation. Gamma and neutron contributions are clearly separated with a FOM value of 1.0353. \(\tau\delta A\) values in ns. The discrimination by the \(\delta A\) values obtained with the time window are shown in Figures 12 and 13, with the FOM values having worsened slightly for least squares (0.9089) and improved slightly for robust estimation (0.9973). In these latter figures, Figures 12 and 13, the existence of other peaks apart from the main gamma peak (around 0.02) and the main neutron peak (around 0.04) became evident: those to the left and the right sides of the main gamma peak with respective peaks of around 0.015 and 0.025. These peaks were already present, though not so clearly visible in the previous Figures 6 and 7. The discussion of this phenomenon is deferred until the end of the section so as not to interfere with the current presentation of results since, as it will be shown, it is not caused by the method proposed. Finally, the discrimination capabilities of \(\tau\delta A\) after the estimation of \(\tau\) and \(\delta A\) with the time window by least squares (Figure 14, FOM value of 0.9876) and robust estimation (Figure 15, FOM value of 0.9896) are similar; only slightly worse than the best results obtained without the time window, that is, those for \(\tau\delta A\) by robust estimation. Figure 12: Discrimination by deltaA (\(\delta A\)) values obtained by least squares with a time window of 36 ns (\(3\tau_{approx}\)). The FOM value is 0.9089. The previous computation with no setup of a time window gave an FOM value of 0.9521 (see Figure 6). \(\delta A\) values are unitless. Figure 3:0 Discrimination by deltaA (\(\delta A\)) values obtained by robust estimation with a time window of 36 ns, which gives an FOM value of 0.9973.