title: Fundamental uncertainty equations for nuclear dating applied to the140Ba-140La and227Th-223Ra chronometers.
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 to140Ba-140La chronometry, which is particularly useful for dating a nuclear explosion through measurement of the produced activity ratio of140La and140Ba in a finite time interval. They were also applied to the227Th-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.
authors.affiliation: European Commission, Joint Research Centre, Retieseweg 111, B-2440 Geel, Belgium. Electronic address: stefaan.pomme@ec.europa.eu.
authors.forename: S
authors.initials: S
authors.lastname: Pommé
authors.affiliation: National Physical Laboratory, Hampton Road, Teddington, Middlesex TW11 OLW, UK.
authors.forename: S M
authors.initials: SM
authors.lastname: Collins
authors.affiliation: National Physical Laboratory, Hampton Road, Teddington, Middlesex TW11 OLW, UK.
authors.forename: A
authors.initials: A
authors.lastname: Harms
authors.affiliation: National Physical Laboratory, Hampton Road, Teddington, Middlesex TW11 OLW, UK.
authors.forename: S M
authors.initials: SM
authors.lastname: Jerome
mesh_terms: D001464:Barium / Q000032:analysis*; D007811:Lanthanum / Q000032:analysis*; D011851:Radioactivity; D011868:Radioisotopes / Q000032:analysis; D011883:Radium / Q000032:analysis; D013910:Thorium / Q000032:analysis*; D035501:Uncertainty
chemical_list: D011868:Radioisotopes; D001464:Barium; D013910:Thorium; D007811:Lanthanum; D011883:Radium
keywords: CTBT; Dosimetry; Geochronology; Non-proliferation; Nuclear chronometry; Nuclear medicine; Uncertainty