Measuring radioactive half-lives via statistical sampling in practice

¹ Chemical Medical and Environmental Science Division, National Physical Laboratory - Hampton Road, Teddington, Middlesex, TW11 0LW, UK
² Department of Physics, University of Surrey - Guildford, Surrey, GU2 7XH, UK
³ Data Science Division, National Physical Laboratory - Hampton Road, Teddington, Middlesex, TW11 0LW, UK
⁴ Department of Physics and Engineering Science, Coastal Carolina University - Conway, 29528-6054, SC, USA
⁵ Ionizing Radiation Metrology Department, National Institute for Standards - Tersa Street El-Haram El-Giza, P.O. Box 136 Giza, El-Giza, Egypt
⁶ Department of Nuclear Engineering, Khalifa University - Abu Dhabi, P.O. Box 127788, United Arab Emirates

Received: 27 October 2017
Accepted: 18 December 2017

Abstract

The statistical sampling method for the measurement of radioactive decay half-lives exhibits intriguing features such as that the half-life is approximately the median of a distribution closely resembling a Cauchy distribution. Whilst initial theoretical considerations suggested that in certain cases the method could have significant advantages, accurate measurements by statistical sampling have proven difficult, for they require an exercise in non-standard statistical analysis. As a consequence, no half-life measurement using this method has yet been reported and no comparison with traditional methods has ever been made. We used a Monte Carlo approach to address these analysis difficulties, and present the first experimental measurement of a radioisotope half-life (²¹¹Pb) by statistical sampling in good agreement with the literature recommended value. Our work also focused on the comparison between statistical sampling and exponential regression analysis, and concluded that exponential regression achieves generally the highest accuracy.