Uncertainty propagation in nuclear forensics

Radionuclide metrology: confidence in radioactivity measurements

Radionuclides, whether naturally occurring or artificially produced, are readily detected through their particle and photon emissions following nuclear decay. Radioanalytical techniques use the radiation as a looking glass into the composition of materials, thus providing valuable information to various scientific disciplines. Absolute quantification of the measurand often relies on accurate knowledge of nuclear decay data and detector calibrations traceable to the SI units. Behind the scenes of the radioanalytical world, there is a small community of radionuclide metrologists who provide the vital tools to convert detection rates into activity values. They perform highly accurate primary standardisations of activity to establish the SI-derived unit becquerel for the most relevant radionuclides, and demonstrate international equivalence of their standards through key comparisons. The trustworthiness of their metrological work crucially depends on painstaking scrutiny of their methods and the elaboration of comprehensive uncertainty budgets. Through meticulous methodology, rigorous data analysis, performance of reference measurements, technological innovation, education and training, and organisation of proficiency tests, they help the user community to achieve confidence in measurements for policy support, science, and trade. The author dedicates the George Hevesy Medal Award 2020 to the current and previous generations of radionuclide metrologists who have devoted their professional lives to this noble endeavour.

Derivation of an uncertainty propagation factor for half-life determinations

An analytical equation is derived for the uncertainty propagation factor for a half-life determination from a least-squares fit to equidistant activity measurements performed with identical relative uncertainties. The obtained formula applies to a purely random statistical uncertainty component. It is equivalent to the solution published by Parker in Nucl. Instr. Meth. A 286, 502. A more general equation for weighted least-squares fitting is derived and presented in a compact manner. It is used as a benchmark to verify the applicability of Parker's solution to non-equidistant data with unequal uncertainties.

Isolation and purification of protactinium-231

Protactinium-231 is one of the lesser known actinides, yet the measurement of this radionuclide is central to dating studies in both paleoclimate and nuclear forensics measurements; furthermore, it is important as the immediate parent nuclide of the ²²⁷Ac decay chain. In this paper, we present the preparatory work for an upcoming CCRI(II) supplementary comparison of this radionuclide. The material used in this work was of poorly known provenance, and it was necessary to carry out a chemical purification of this material prior to use. A new extraction chromatography resin, TK 400, which has been developed for the separation of ²³¹Pa, was tested at NPL. The aims of the work were achieved; the recovery of ²³¹Pa was ~85%, the decay products were recovered in good yield (~95%) and stable element impurities were removed.

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

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.

High-Resolution Inductively Coupled Plasma Optical Emission Spectrometry for (234)U/(238)Pu Age Dating of Plutonium Materials and Comparison to Sector Field Inductively Coupled Plasma Mass Spectrometry

Employing a commercial high-resolution inductively coupled plasma optical emission spectrometry (HR-ICP-OES) instrument, an innovative analytical procedure for the accurate determination of the production age of various Pu materials (Pu powder, cardiac pacemaker battery, (242)Cm heat source, etc.) was developed and validated. This undertaking was based on the fact that the α decay of (238)Pu present in the investigated samples produced (234)U and both mother and daughter could be identified unequivocally using HR-ICP-OES. Benefiting from the high spectral resolution of the instrument (<5 pm) and the isotope shift of the emission lines of both nuclides, (234)U and (238)Pu were selectively and directly determined in the dissolved samples, i.e., without a chemical separation of the two analytes from each other. Exact emission wavelengths as well as emission spectra of (234)U centered around λ = 411.590 nm and λ = 424.408 nm are reported here for the first time. Emission spectra of the isotopic standard reference material IRMM-199, comprising about one-third each of (233)U, (235)U, and (238)U, confirmed the presence of (234)U in the investigated samples. For the assessment of the (234)U/(238)Pu amount ratio, the emission signals of (234)U and (238)Pu were quantified at λ = 424.408 nm and λ = 402.148 nm, respectively. The age of the investigated samples (range: 26.7-44.4 years) was subsequently calculated using the (234)U/(238)Pu chronometer. HR-ICP-OES results were crossed-validated through sector field inductively coupled plasma mass spectrometry (SF-ICPMS) analysis of the (234)U/(238)Pu amount ratio of all samples applying isotope dilution combined with chromatographic separation of U and Pu. Available information on the assumed ages of the analyzed samples was consistent with the ages obtained via the HR-ICP-OES approach. Being based on a different physical detection principle, HR-ICP-OES provides an alternative strategy to the well-established mass spectrometric approach and thus effectively adds to the quality assurance of (234)U/(238)Pu age dates.

Remeasurement of (234)U Half-Life

The half-life of (234)U has been measured using a novel approach. In this method, a uranium material was chemically purified from its thorium decay product at a well-known time. The ingrowth of the (230)Th daughter product in the material was followed by measuring the accumulated (230)Th daughter product relative to its parent (234)U nuclide using inductively coupled plasma mass spectrometry. Then, the (234)U decay constant and the respective half-life could be calculated using the radioactive decay equations based on the n((230)Th)/n((234)U) amount ratio. The obtained (234)U half-life is 244 900 ± 670 years (k = 1), which is in good agreement with the previously reported results in the literature with comparable uncertainty. The main advantages of the proposed method are that it does not require the assumption of secular equilibrium between (234)U and (238)U. Moreover, the calculation is independent from the (238)U half-life value and its uncertainty. The suggested methodology can also be applied for the remeasurement of the half-lives of several other long-lived radionuclides.

Conversion electron spectrometry of Pu isotopes with a silicon drift detector

An electron spectrometry set-up was built at IRMM consisting of a vacuum chamber with a moveable source holder and windowless Peltier-cooled silicon drift detector (SDD). The SDD is well suited for measuring low-energy x rays and electrons emitted from thin radioactive sources with low self-absorption. The attainable energy resolution is better than 0.5keV for electrons of 30keV. It has been used to measure the conversion electron spectra of three plutonium isotopes, i.e. (238)Pu, (239)Pu, (240)Pu, as well as (241)Am (being a decay product of (241)Pu). The obtained mixed x-ray and electron spectra are compared with spectra obtained with a close-geometry set-up using another SDD in STUK and spectra measured with a Si(Li) detector at IRMM. The potential of conversion electron spectrometry for isotopic analysis of mixed plutonium samples is investigated. With respect to the (240)Pu/(239)Pu isotopic ratio, the conversion electron peaks of both isotopes are more clearly separated than their largely overlapping peaks in alpha spectra.

Validation of reference materials for uranium radiochronometry in the frame of nuclear forensic investigations

The results of a joint effort by expert nuclear forensic laboratories in the area of age dating of uranium, i.e. the elapsed time since the last chemical purification of the material are presented and discussed. Completely separated uranium materials of known production date were distributed among the laboratories, and the samples were dated according to routine laboratory procedures by the measurement of the (230)Th/(234)U ratio. The measurement results were in good agreement with the known production date showing that the concept for preparing uranium age dating reference material based on complete separation is valid. Detailed knowledge of the laboratory procedures used for uranium age dating allows the identification of possible improvements in the current protocols and the development of improved practice in the future. The availability of age dating reference materials as well as the evolvement of the age dating best-practice protocol will increase the relevance and applicability of age dating as part of the tool-kit available for nuclear forensic investigations.

Synthesis, characterization and application of a modified acrylamide–styrene sulfonate resin and a composite for sorption of some rare earth elements

A new composite was successfully prepared by irradiation polymerization. The composite has higher uptake and capacity for lanthanides than polymers.