On the Statistics of Luminescent Counter Systems

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Abstract
The method of generating functions is employed to analyze the composite statistical variations which arise in a counting system that consists of a source, a luminescent crystal, and a photo-multiplier tube. The methods are applied to several photo-type assemblies and indicate that the techniques can be used to treat any problem of this type in a simple way. It is found that once the crystal has accepted energy, the effectiveness of the assembly is measured by the number of photo-electrons ejected from the photo-cathode of the multiplier. This quantity, which depends upon the luminescent efficiency of the crystal, the geometry of the crystal-multiplier arrangement and the efficiency of the photo-cathode, should be at least 5 for faithful counting of particles absorbed in the crystal. The number of photoelectrons must be much larger than 5 for good statistics if the current from the multiplier is measured. The results of Schiff and Evans for the statistical variations in the voltage of a condensor which is charged with the pulses from the multiplier are generalized to cover the case in which the size of pulses varies.