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Fundamental uncertainty equations for nuclear dating applied to the 140Ba-140La and 227Th-223Ra chronometers

Pommé, S., Collins, S.M., Harms, A., Jerome, S.M.
Journal of environmental radioactivity 2016 v.162-163 pp. 358-370
equations, half life, radionuclides, uncertainty
Basic equations for age dating through activity ratio measurements are presented and applied to nuclear chronometers based on parent-daughter decay. Uncertainty propagation formulae are derived which relate the relative uncertainty on the half-lives and measured activity ratios with the relative uncertainty on the calculated time of a nuclear event. Particular attention is paid to the case of relatively short-lived radionuclides for which the change in decay rate during the measurement is non-negligible. Mathematical solutions are presented to correct the perceived activity ratio and adapt the uncertainty propagation formulae to complete the uncertainty budget. The formulae have been applied to 140Ba-140La chronometry, which is particularly useful for dating a nuclear explosion through measurement of the produced activity ratio of 140La and 140Ba in a finite time interval. They were also applied to the 227Th-223Ra parent-daughter pair produced for therapeutic use. The impact of inaccuracies in the nuclear decay data on the performance of these nuclear chronometers is shown and discussed.