Theoretical Approach to the Energy Resolution of a Scintillation Spectrometer with Several Photodetectors

The exact mathematical description of processes at registration of incident particles by a scintillation spectrometer with several photodetectors allows receiving correct formulae for the mean value and the variance of the amplitude at the output of photodetectors, and for the covariance between signals of photodetectors. It was shown that using the relative covariance of signals allows the experimental determination of the covariance in the light yield and the Fano factor in a scintillator. The important advantage of the proposed method is its independence on the gains and the noises of photodetectors electronics