Dependence of the energy resolution of a scintillating crystal on the readout integration time

The possibilty of performing high-rate calorimetry with a slow scintillating crystal is studied. In this experimental situation, to avoid pulse pile-up, it can be necessary to base the energy measurement on only a fraction of the emitted light, thus spoiling the energy resolution. This effect was experimentally studied with a BGO crystal and a photomultiplier followed by an integrator, by measuring the maximum amplitude of the signals. The experimental data show that the energy resolution is exclusively due to the statistical fluctuations of the number of photoelectrons contributing to the maximum amplitude. When such number is small its fluctuations are even smaller than those predicted by Poisson statistics. These results were confirmed by a Monte Carlo simulation which allows to estimate, in a general case, the energy resolution, given the total number of photoelectrons, the scintillation time and the integration time