The performance of scintillation detectors for x rays and gamma rays is limited fundamentally by the statistics of the scintillation light and the resulting photoelectrons. This paper presents a new experimental approach to studying these statistics by observing correlations in the signals from two photodetectors. It is shown that the Fano factors (ratios of variance to mean), both for the number the photoelectrons produced on the photocathode of the photomultiplier and for the underlying number of scintillation photons, can be deduced from these correlations. For LaBr3(Ce) and 662 keV gamma rays, the photopeak signals obtained by photomultipliers on opposite faces of a thin sample are negatively correlated, and the Fano factor for the photoelectrons is significantly less than one. The inferred Fano factor for the optical photons is very small, indistinguishable from zero within experimental error.
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