A review of the statistical foundations of the classical pulse shape discrimination techniques in scintillation applications

Pulse shape discrimination (PSD) is an intrinsic property of organic, as well as of some inorganic, liquid and solid scintillators, identified at a very early stage of their development as one of their most distinguishing properties. Usually it is adopted either for n/γ or for α/β discrimination. The two classical methods extensively adopted over the past four decades for practical PSD implementations are the rise time technique, also called zero crossing method because of its more popular realization, and the charge method, which are both sub-optimal with respect to the optimum method described in a seminal paper by Gatti and De Martini. The aim of this work is to review thoroughly the features and the statistical foundations of the two sub-optimal approaches, as well as those of the Gatti´s methodology, showing how in all the three cases the respective discrimination capabilities can be quantitatively predicted on the basis of the knowledge of the average time profile of the signals produced in the scintillator by the particles to be identified. The work is completed with a detailed comparison of the discrimination performances that each of these methods can achieve. The calculations are carried out with reference to the statistical properties of the detected photoelectrons, on the assumption that they reflect the original statistics of the photons emitted in the scintillator, hence neglecting any possible influence of the detecting phototube.