Pommé S, Collins SM, Harms A, Jerome SM. Fundamental uncertainty equations for nuclear dating applied to the
140Ba-
140La and
227Th-
223Ra chronometers.
JOURNAL OF ENVIRONMENTAL RADIOACTIVITY 2016;
162-163:358-370. [PMID:
27348041 DOI:
10.1016/j.jenvrad.2016.06.013]
[Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2016] [Revised: 06/14/2016] [Accepted: 06/15/2016] [Indexed: 06/06/2023]
Abstract
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.
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