# Neutron and Gamma Pulse Shape Discrimination by Robust Determination of the Decay Shape
## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multirow{2}{*}{**Data Window**} & \multirow{2}{*}{\begin{tabular}{c} **PD\({}_{\gamma}\) after LS** \\ **Computation** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **PD\({}_{\alpha}\) after LS** \\ **Computation** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **PD\({}_{\gamma}\) after RE** \\ **Computation** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **PD\({}_{\alpha}\) after RE** \\ **Computation** \\ \end{tabular} } \\ \hline \(\tau\) & All decaying parts & 0.9123 & 0.6173 & 0.9174 & 0.9320 \\ \(\delta A\) & All decaying parts & 0.9517 & 0.9932 & 0.9268 & 0.9921 \\ \(\tau\delta A\) & All decaying parts & 0.9297 & 0.9926 & 0.9830 & 0.9968 \\ \hline \(\tau\) & 36 ns after the peak & 0.8061 & 0.9762 & 0.9701 & 0.9864 \\ \(\delta A\) & 36 ns after the peak & 0.8769 & 0.9926 & 0.9489 & 0.9077 \\ \(\tau\delta A\) & 36 ns after the peak & 0.8946 & 0.9950 & 0.9479 & 0.9956 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: PD rates for gamma (\(\gamma\)) and neutron (n) for the different parameters computed, data windows and the two computation strategies: least squares (LS) and robust estimation (RE). Figure 16: Scatter plot for \(\tau\delta A\) by robust estimation and data from all the decaying parts. A clear separation between neutron and gamma-ray pulses can be seen. As said, the amplitudes in the dataset were said to be normalized between 0 and 1. However, this is clearly not the case of the pulses having \(\delta A\) values in Area I, since they have several values with negative amplitudes. Similarly, two example pulses are shown in Figures 19 and 20 for \(\delta A\) values around 0.025 (Area II, right of the main gamma peak), pulse numbers 3371 and 5624 in the dataset. Figure 17: Amplitude of a first example pulse in Area I (peak to the left of the main gamma peak). Some amplitudes have negative values. Pulse amplitudes are unitless. Figure 18: Amplitude of a second example pulse in Area I (peak to the left of the main gamma peak). Some amplitudes have negative values. Pulse amplitudes are unitless. Now, apart from a few values with negative amplitude, the most evident problem is that the supposedly normalized amplitudes surpass the value of 1. Also, in the very final part of the pulse, the amplitude seems to grow rather than decrease. All these abnormalities could have been caused by undesired pulse reflections coming from cables and electronic components or by calibration issues. In any case, this cannot be known at this stage. The Matlab computing codes, working along with the library and datasets given in [11], give the results for all decaying parts by least squares (S1) and robust estimation  
Figure 19: Amplitude of a first example pulse in Area II (peak to the right of the main gamma peak). The maximum amplitude exceeds 1. Pulse amplitudes are unitless. Figure 20: Amplitude of a second example pulse in Area II (peak to the right of the main gamma peak). The maximum amplitude exceeds 1. Pulse amplitudes are unitless. (S2), and for the time window by least squares (S3) and robust estimation (S4) and are provided in the Supplementary Materials.