# Neutron and Gamma Pulse Shape Discrimination by Robust Determination of the Decay Shape
###### Abstract  
Neutron/gamma pulse shape discrimination (PSD) is essential in applications such as radiation source analysis, nuclear material detection, detection of pollutants in the soil and cultural heritage. Neutrons are accompanied by gamma-ray photons due to the interaction with the environment so neutron detectors require some techniques to differentiate them. There are several methods enabling such differentiation. In the current submission, a robust estimation of the decay shape is proposed as a new alternative. To do so, a robust estimator computed by a global optimization method is used. After presenting the theoretical background and explaining the required computations to be realized, the proposed method is tested in a publicly available large dataset. Evaluations of the figure of merit and the positive discrimination rate values are used to assess the degree of improvement attained. A computing code for the method, which is easily adaptable by users to their own datasets, is also provided. neutron and gamma discrimination; pulse shape discrimination; robust estimation; global optimization +
Footnote †: journal: _Sci._  
0000-0001-999-2276-2800][PERSON] 0000-0001-9999-2276-2800][PERSON] 0000-0002-0002-0002-0002-0002-0002-0002-0002-0002-0002-0002-  
Another simple method for PSD makes use of the determination of the slope for the falling edge region [13]. It is easy to compute the slope of the straight line connecting two points (one upper threshold and one lower threshold) but it is less evident how to properly select these threshold points for them to be representative of the neutron or gamma process taking place in order to maximize the discrimination capabilities. Since the decay observed is not linear but exponential, the approach proposed in the present paper is the determination of the exponential decay shape after the maximum amplitude for each scintillation pulse and its corresponding characterization so that it can be used for neutron and gamma discrimination. Some reasons prevent a simple computational process, however. First, the functional relationship between pulse amplitude and time is not exactly exponential, due to interactions with the observing environment. Second, it is quite common that some outlying values appear in the pulse registration. Lastly, even if the functional model was exactly exponential, the need to linearize the function before a standard adjustment might have a significantly adverse impact on the results of the estimation process. For all these reasons, namely, the inexact functional relationship, the noise in the observational process and lack of linearity, the standard least-squares (LS) estimator may be quite adversely influenced and produce a clearly unacceptable solution. In fact, it will be shown in the application that it provides suboptimal results. By contrast, robust estimation (RE) techniques were devised in the last decades to attain a solution for the adjustment problem that is minimally affected by the appearance of outliers in the data or systematic effects either in the data or in the model (inexactness of the functional model) while producing a solution close to the LS solution in the case of the correct functional model and the inexistence of outliers and systematic errors in the data. For a general reference on RE, the reader may consult [14]. Many robust estimators have been proposed, some showing better performance than others in coping with undesired errors of different sizes and distributions. Among them, the minimum L\({}_{1}\)-norm has been extensively used [15; 16; 17]. Regarding the question of how to compute the solution once the robust estimator has been selected, the so-called iteratively reweighted least squares (IRLS) scheme is the normal procedure followed due to the simplicity of recasting the RE technique in an iterative procedure based on the familiar LS scheme.