Covariances between Signals of Photodetectors of a Scintillation Spectrometer

Abstract

An accurate mathematical description of the processes occurring in a scintillation spectrometer with several photodetectors registering primary particles allows obtaining correct formulas for the mean value and amplitude dispersion at the output of the photodetectors, as well as an expression for the covariance between photodetector signals. In contrast to the formulas available in the literature, the formula obtained in this work for the energy resolution of a scintillation spectrometer with one photodetector contains information on the relation between the corresponding processes occurring in the detector upon the registration of particles with the characteristics of the scintillation crystal and the scintillator-photodetector interface and the characteristics of the photodetector and the electronics of the spectrometer. It is shown that the fluctuations of the light output and the Fano factor for the scintillation crystal material can be determined using the relative covariance between photodetector signals.