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

摘要

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 Ba-140-La-140 chronometry, which is particularly useful for dating a nuclear explosion through measurement of the produced activity ratio of La-140 and Ba-140 in a finite time interval. They were also applied to the Th-227-Ra-223 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. (C) 2016 The Author(s). Published by Elsevier Ltd.