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The ionization produced by individual fast charged particles is frequently used as a measure of their initial energy; fluctuation effects set a theoretical limit to the accuracy of this method. Formulas are derived here to estimate the statistical fluctuations of the number of ions produced by constant amounts of radiation energy. The variance of the number of ionizations is found to be two or three times smaller than if this number were governed by a Poisson distribution. An improved understanding is gained of the statistical treatment of fluctuation phenomena.
U. Fano (1947) studied this question.