Derivation of an uncertainty propagation factor for half-life determinations

Half-life determination of the ground state decay of 167Tm and 168Tm

Precise determination of half-lives of 167Tm and 168Tm are important for their application in nuclear medicine diagnostics, nuclear forensics, and other nuclear data measurements. We produced 167Tm and 168Tm sources using an α-particle beam bombarded 165Ho target and a series purification steps. A series of 173 measurements was performed over a period of 44 days using a high-purity germanium (HPGe) detector to track the count rate change as a function of time by following the 207.8 keV and 531.5 keV γ-lines to determine the radioactive decay half-life of 167Tm. The measurement of half-life of 168Tm ground state has been performed using the same HPGe γ-ray spectrometer to observe γ-lines at 198.3 keV, 816.0 keV, 184.3 keV, 741.4 keV and 914.9 keV. Weighted least-squares fits of exponential decay curves were performed for the dataset of each γ-ray emission, with final determined half-lives of 9.250(15) d and 93.41(12) d for 167Tm and 168Tm, respectively. The uncertainty budgets are presented and discussed in detail. Our result of 167Tm half-life is consistent with the Evaluated Nuclear Structure Data File (ENSDF) recommended half-life of 9.25(2) d. The outcome of 168Tm half-life determination is longer than the ENSDF recommended half-life of 93.1(2) d. Further independent measurements would be ideal to resolve the discrepancy.

Liquid scintillation efficiencies, gamma-ray emission intensities, and half-life for Gd-153

Gadolinium-153 was standardized for activity by live-timed anticoincidence counting and an ampoule was submitted to the international reference system (SIR). Absolute emission intensities for the main γ rays were determined with calibrated high-purity germanium (HPGe) and lithium-drifted silicon (Si(Li)) detectors. A revised decay scheme is indicated, with no probability of direct electron capture to the 153Eu ground state. Triple-to-double coincidence ratio (TDCR) efficiency curves indicate that the revised decay scheme is consistent with experiment. Half-life measurements agree with a previous NIST determination and show no sensitivity to chemical environment.

Determination of the Terbium-152 half-life from mass-separated samples from CERN-ISOLDE and assessment of the radionuclide purity

Terbium-152 is one of four terbium radioisotopes that together form a potential theranostic toolbox for the personalised treatment of tumours. As 152 Tb decay by positron emission it can be utilised for diagnostics by positron emission tomography. For use in radiopharmaceuticals and for activity measurements by an activity calibrator a high radionuclide purity of the material and an accurate and precise knowledge of the half-life is required. Mass-separation and radiochemical purification provide a production route of high purity 152Tb. In the current work, two mass-separated samples from the CERN-ISOLDE facility have been assayed at the National Physical Laboratory to investigate the radionuclide purity. These samples have been used to perform four measurements of the half-life by three independent techniques: high-purity germanium gamma-ray spectrometry, ionisation chamber measurements and liquid scintillation counting. From the four measurement campaigns a half-life of 17.8784(95) h has been determined. The reported half-life shows a significant difference to the currently evaluated half-life (ζ-score = 3.77), with a relative difference of 2.2 % and an order of magnitude improvement in the precision. This work also shows that under controlled conditions the combination of mass-separation and radiochemical separation can provide high-purity 152Tb.

Determination of the half-life of 161Tb

¹⁶¹Tb has potential applications in targeted radionuclide therapy and nuclear forensic science. However, the half-lives of ¹⁶¹Tb in previous studies show a discrepancy. In this study, ¹⁶¹Tb samples were produced by irradiating ¹⁶⁰Gd₂O₃ with thermal neutron flux. A series of procedures were applied to extract a pure ¹⁶¹Tb solution and three solid samples were prepared. The half-life of ¹⁶¹Tb has been measured with a high-purity germanium (HPGe) detector. The time-dependency of the ¹⁶¹Tb activity was followed by assessing the count rate of their characteristic gamma-ray emissions at 48.9 keV and 74.6 keV over a period of 33-43 days. The experiment and uncertainty budget are discussed in detail. Different uncertainty propagation equations were applied for random uncertainties, medium-frequency deviations and potential systematic errors. The result for the ¹⁶¹Tb half-life of 6.967 (11) d was determined by the weighted mean of half-lives from three samples, which confirms that the half-life is longer than the of the current evaluated half-life of 6.89 (2) d. From all available quoted experimental values, a recommended half-life of 6.934 (14) d was determined by the power-moderated method (PMM). Based on recent four published half-life values, a half-life of ¹⁶¹Tb of 6.9582 (33) d was determined by the PMM analysis.

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.

Measurement of the 145Sm half-life

The half-life of ¹⁴⁵Sm has been measured by means of the reference source method with a HPGe detector. The long-lived radionuclide ⁴⁴Ti was mixed into the source for reference. The time-dependency of the ¹⁴⁵Sm/⁴⁴Ti activity ratio was followed by assessing the count-rate ratio of their characteristic gamma-ray emissions at 61.2 keV (¹⁴⁵Sm) and 67.9/78.3 keV (⁴⁴Ti) in spectra recorded over periods of typically one day. In total, 220 measurements were performed over a period of 384 days or about one half-life period. The experiment and ensuing uncertainty budget are discussed in detail. Different error propagation is applied for random uncertainties, autocorrelated structures in the fit residuals, and potential systematic errors. The result for the ¹⁴⁵Sm half-life, 345 (16) d, is compatible with the scarce literature values, however the experimental details of the old measurements were barely documented.