Should the Poisson statistical density function be used in the mesurement of short-lived isotopes?

Abstract

The conditions under which the Poisson statistical density function adequately describes the counting of a radioactive isotope are examined and found that for counting processes where λt≳1, where λ is the decay constant and t the counting period, one of the fundamental properties, namely the condition of stationarity, is violated rendering application of Poisson statistics invalid. The Ruark-Devol statistical density function, a binomial, is instead shown to be satisfactory since it is capable of describing radioactive disintegration where the only fundamental property is independence and its use is recommended in both activation analysis and medical imaging when the half-life of the isotope of interest is short compared to the period of observation. It is pointed out that no satisfactory expression incorporating the distortion produced by dead-time on the statistical density function has yet been derived but the practical implications of the adoption of the Ruark-Devol function are discussed with respect to standard deviation and precision of the measurement. It is shown how the application of the Poisson statistical density function, under conditions of tλ≳1, is not only invalid but also overestimates the standard deviation significantly.