Introduction

Extinct radionuclides play an essential role in the description and in the reconstruction of recent galactic events, providing as well essential timescale constraints1,2,3,4. Even though such radionuclides became extinct soon after the formation of the Solar System, it is possible from the analysis of the abundances of their stable decay products to reconstruct the nucleosynthetic processes that occurred millions (or even billions) of years ago, e.g. in5,6,7,8,9. Over the past two decades, there has been a strong effort in the description of the mechanism responsible for the synthesis of p-nuclei. The latter is a group of proton-rich isotopes between 74Se and 196Hg that cannot be produced by either slow neutron-capture (s-process) or rapid neutron-capture (r-process) reactions10,11. Instead, they are produced in a network of photodisintegration and charged particle reactions called p-process12. Interestingly, the extinct 154Dy (Iα = 100% at Eα = 2.87 MeV)13 is one of the nuclides involved in such p-process reaction networks. Through the nuclear reactions 154Dy(α, γ)158Er14, 154Dy(γ, α)150Gd, and 154Dy(γ, 2n)152Dy15, this exotic radionuclide contributes to the synthesis of 142Nd, 146Sm, 150Gd, 152Gd, and 158Dy – all nuclides shielded from s- and r-nucleosynthetic processes by their respective isobars. As stated in16,17, knowledge on the reaction rates of nuclear reactions such as 154Dy(α, γ) and 154Dy(n,γ), respectively, is useful to test and improve the models used in the prediction of astrophysical p-process reaction rates. These models18,19, that correlate the observed isotopic abundances to specific nuclear reaction paths, depend on the cross section reactions, which in turn strongly depend on the half-lives of all the nuclides involved. Furthermore, due to the pure α-decay series of 154Dy (i.e., 154Dy → 150Gd → 146Sm → 142Nd), nucleosynthesis computations aimed to explain the processes that led to the natural isotopic abundances of 146Sm and 142Nd need to take into account the contribution of the decay of its α-unstable progenitors. Therefore, a precise half-life value of 154Dy is required as an input parameter20,21.

Besides significant applications in cosmo and geoscience, a precise value for the half-life of 154Dy is also required for safety evaluation of spallation target facilities, such as Accelerator Driven Systems and/or Spallation Neutron Source Facilities, that utilize targets made of heavy metals – e.g., lead, tantalum, tungsten22. During the spallation process, exotic α-emitting radionuclides like 154Dy are produced23. Recent theoretical calculations24 estimated the contribution of 154Dy, 146Sm, and 148Gd to the overall radiotoxicity of spallation targets to be similar to that of Po radionuclides. In that work, uncertainties on the adopted half-life values were not taken into account. Therefore, precise nuclear data for the production and decay of 154Dy are thus needed in order to estimate operational mode and maintenance of such facilities, as well for the decommissioning of the irradiated material.

Despite its relevance, since the discovery of 154Dy in 196125 an accurate half-life value for this exotic radionuclide is still not available. Instead, a plethora of half-life values can be found in literature, summarized in Table 1.

Table 1 Half-life values for 154Dy available from literature.
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The nowadays-accepted half-life value for 154Dy, i.e., t1/2 = 3.0 My is associated with a 50% uncertainty and derives from the revision made in28 of the works of MacFarlane25 and Gōnō27. The half-life value in29 was calculated by applying a cluster model for the ground state α-decay of even-even nuclei. In most cases, little is known about the experimental procedure or about the effects taken into account in the calculation of the relative uncertainties, rendering a re-evaluation of the mentioned works difficult. It is important to mention that 154Dy is an extinct nuclide that can be obtained only from nuclear fusion reactions, as a by-product of spallation reactions, or by the reprocessing of nuclear waste. Therefore, the limited availability of suitable sample material, together with inherent complications in performing accurate activity measurements with long-lived nuclides, represent the main reasons for such a lack of reliable nuclear data. To overcome those difficulties, the initiative “Exotic Radionuclides from Accelerator Waste for Science and Technology – ERAWAST” was launched in 2006 at Paul Scherrer Institute (PSI)30,31. This long-term project aims, among others, to improve the existing nuclear databases, with a special focus on the re-determination of uncertain decay data. For this purpose, the necessary exotic radionuclides are obtained by reprocessing radioactive waste already available at the PSI site. In this work, we report on a high-precision half-life measurement of 154Dy, performed in the framework of ERAWAST. 154Dy material was obtained by reprocessing Ta samples irradiated with protons and spallation neutrons during the SINQ Target Irradiation Program (STIP) at PSI32. For the estimation of half-lives in the order of millions of years, we applied the so-called direct method. This consists of the determination of the number of radioactive atoms in a specific sample, combined with the measurement of its radioactivity. Here, the number of atoms of 154Dy was determined using sector field inductively-coupled plasma mass spectrometry (SF-ICP-MS) in combination with multicollector inductively-coupled plasma mass spectrometry (MC-ICP-MS). The radioactivity of 154Dy in the sample was measured by means of α-spectroscopy. Thin and homogeneous radioactive sources, necessary to obtain high-resolution α-spectra, were prepared using the molecular plating technique—also referred to as electrodeposition33,34. Following the Guide to the expression of uncertainty in measurement – GUM recommendations35,36, a realistic and complete uncertainty budget for the measured t1/2 is given as well.

Experimental techniques and methodology

Separation and purification of the 154Dy sample

The Dy fraction containing 154Dy was obtained from the reprocessing of four Ta samples from the STIP-II project. The procedure for the dissolution of the Ta samples is described in detail in37. Successively, a series of ion-exchange separation processes allowed us to obtain a purified Dy fraction in 1 M HNO3. During the separation process, the γ-emitter 159Dy (t1/2 = (144.4 ± 0.2) d, Iγ = 2.29% at Eγ = 58 keV38) was added as an internal radio-tracer. The separation method for the retrieval of the Dy fraction is reported in detail in39. A scheme of the chemical separation steps is reported in Fig. 1.

Figure 1
figure 1

Separation scheme adopted for the retrieval of a pure Dy fraction (in 1 M HNO3) containing the exotic radio-lanthanide 154Dy. The so-obtained Dy fraction is suitable for mass spectrometric analysis without further processing. The scheme was made with the Microsoft PowerPoint 2016 software.

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The homogeneous Dy fraction (in 1 M HNO3) was collected in a scintillation vial (HDPE material, capacity: 20 ml). The total mass of the collected Dy solution – from now onwards referred to as “Dy master solution” – was determined gravimetrically (averaged value of five consecutive weightings: (5.02657 ± 0.00001) g, see Table S1). All the gravimetric steps were performed on a certified Mettler-Toledo XP56 balance (10–6 g scale interval), in a room with controlled temperature within 20–23 °C. Systematic uncertainties inherent to the weighing process are below 0.055%. This bias derives from the buoyancy difference between the calibration weight of the balance and the weighed solution, and therefore can be considereded negligible for differences in weight of the same solution and for mixed samples where the relative amount of each individually weighed part counts.

Mass spectrometric analysis

The concentration of 154Dy in the Dy master solution was calculated from the amount of 161Dy (deduced by SF-ICP-MS) and from the 154Dy/161Dy isotope ratio in solution (determined by MC-ICP-MS). 161Dy was chosen as reference nuclide due to the absence of isobaric interferences for mass 161. All gravimetric additions were done on a Mettler-Toledo XP56 balance.

SF-ICP-MS measurements

SF-ICP-MS analyses were conducted using a Thermo Scientific Element 2 spectrometer, applying the medium mass resolution setting in order to minimize potential effects of molecular interferences. The plasma was operated at 1350 W. All analytes were introduced into a cyclonic PFA spray chamber using an ELEMENTAL SCIENTIFIC PFA-ST nebulizer and a peripump set, with a sample consumption of ca. 130 µl∙min−1. An external linear calibration was used to establish the 161Dy concentration in the Dy master solution. In this procedure, several dilutions of a Dy-ESI reference standard solution (Elemental scientific natDy 10 mg∙l-1 ± 2% k = 2 in 2% HNO3, density: 1.00885 g∙ml−1) were repeatedly analyzed (before, in-between, and after the replicate analysis of the sample solution). In all the Dy dilutions used for the external calibration, a Re-ESI reference standard solution (Elemental scientific natRe 10 mg∙l−1 ± 2% k = 2 in 2% HNO3, density: 1.00885 g∙ml−1) was added as an internal reference. This allowed for cancelling potential temporal drift in instrumental signal response or plasma instability. The series of dilutions used for the external calibration scheme is presented in Tables S2–S3. An aliquot of the Dy master solution (averaged value of 5 consecutive weightings: (0.030000 ± 0.000001) g, see Table S4) was used for mass-spectrometry analysis. To this Dy aliquot, the same Re-ESI standard solution used in the preparation of calibration standards were added as an internal reference. The Dy aliquot was then diluted with a 0.28 M HNO3 solution, to a total weight of (13.909720 ± 0.000005) g (averaged value of 5 consecutive weightings – see Table S4). Instrumental background signals (including potential imperfect washout between analytes) were subtracted by repeated analysis of the same acid used to prepare the external standards and the sample analytes. Each of these “blank” measurements preceded the standard and the sample analyses. The 161Dy content in the Dy master solution was obtained by correlating the background-corrected and Re-normalized 161Dy signal to the external calibration line.

MC-ICP-MS measurements

Dy isotopic ratio analysis was conducted on the Nu Instruments Plasma 3 MultiCollector Inductively Coupled Plasma Mass Spectrometer (MC-ICP-MS) equipped with an inductively coupled Ar-plasma ion source, 16 Faraday cups, 3 Daly detectors, and 3 secondary electron multipliers. These instrumentational characteristics allow for the simultaneous measurement of up to 22 ion beams. Analytes were introduced into the system using an Elemental Scientific Apex HF desolvating nebulizer and a self-aspiring Elemental Scientific PFA-ST Microflow at a consumption rate of ca. 50 µl∙min−1. The plasma was operated at 1350 W forward power. Ion beams of masses 149 (Sm), 152 (Sm, Gd), 154–164 (Sm, Gd, Tb, Dy), 166–167 (Er), and 170 (Er, Yb) were collected simultaneously in Faraday cups connected to amplifier systems with a 1011 Ω resistors in their feedback loop. To assess potential isobaric interferences of Yb, mass 172 was monitored using a Daly ion counting detector. An aliquot of the Dy master solution was diluted by a factor of ca. 500 by addition of a pure 0.28 M HNO3 solution. To the diluted Dy aliquot, natEr was added, allowing for an empirical semi-external mass discrimination correction. Successively, six analyses of the so-prepared Dy sample were bracketed by 10 analyses of mixed Er-Dy solution standards. Each analysis consisted of 60 ten-second-long integrations of the ion beam intensities. Instrumental background signals were removed using interspersed analysis of the Dy sample and of the 0.28 M HNO3 solution used in the preparation of the analytes. Online recorded 170Er/166Er values of the admixed Er were used to determine the magnitude of instrumental mass discrimination during the analysis of the Dy sample.

Preparation of the 154Dy α-source for activity measurements

For the preparation of a thin radioactive source with the molecular plating technique, an aliquot of the Dy master solution (averaged value of 5 consecutive weightings: (2.77410 ± 0.00001) g – see Table S11) was used. The estimation of the deposition efficiency (also referred to as deposition yield) was necessary to determine the effective number of 154Dy atoms plated. The deposition yield was determined by monitoring the activity of the γ-tracer 159Dy added during the separation process (see “Separation and purification of the 154Dy sample” Section). Specifically, the activity of 159Dy in the Dy aliquote before molecular plating was measured, and compared to the activity of the 159Dy plated on the deposition foil. Since isotopes of the same element behave chemically identically, the yield of deposited 159Dy is thus equal to the yield of deposited 154Dy. For a reliable deduction of the deposition yield, both 159Dy γ-activity measurements had to be performed in equal geometries. This was achieved by using a custom-made holder made of two interchangeable parts (see Fig. 2), that allowed for performing γ-spectrometry measurements in two geometrically equivalent positions, namely Position A (used to quantify the activity of 159Dy before electrodeposition), and Position B (used to quantify the activity of 159Dy after electrodeposition), at a sample/detector endcap distance of 1.8 cm. Technical drawings in scale of the holder are given in the Supporting Information, Figure S2. A correction factor, that allows to convert the count rate of a volumetric sample measured in Position A to the count rate of an electrodeposited sample measured in Position B, was deduced by performing γ-spectroscopy measurements in both positions with a calibrated source of 133Ba (t1/2 = 10.54 y, Iγ = 32.9% at Eγ = 80.99 keV40) in 1 M HNO3. For Position A, a known amount of the 133Ba liquid source was put into a polyether ether ketone (PEEK) vial, evaporated to dryness under a N2 flow at T = 70 °C, and dissolved in 400 μl of 1 M HNO3. For Position B, a known amount of the calibrated 133Ba liquid source was drop-deposited onto a graphite foil (thickness: 75 μm, purity: 99.8%, Flexible Graphite, GoodFellow). The liquid was evaporated by heating the graphite foil at T = 70 °C, resulting in a point-like drop source of about 2.5 mm diameter. Further details are given in Section 2 of the Supporting Information.

Figure 2
figure 2

Schematic drawing of the custom-made holder, made of two interchangeable parts (namely, “Holder part 1” and “Holder part 2”), used to quantify the activity of 159Dy via γ-spectrometry. (a) 2D front section and 3D view of Position A, used to measure the γ-activity of 159Dy contained in the vial before molecular plating. (b) 2D front section and 3D view of Position B, used to quantify the γ-activity of 159Dy deposited on a graphite support after molecular plating. Both positions are geometrically equivalent. The acronym PEEK stands for polyether ether ketone. The drawing was made with the Microsoft PowerPoint 2016 software.

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All γ-spectroscopy measurements were performed with a BEGe™ (Broad Energy Germanium γ-detector, Mirion Technologies (Canberra), Inc.; crystal dimensions diameter: 61 mm, thickness: 25 mm). Data acquisition and analysis were done using the Genie™ 2000 Gamma Acquisition & Analysis Software. Energy calibration was done using a 152Eu (t1/2 = 13.53 y, Iγ = 28.41% at Eγ = 121.78 keV41) point-source (Physikalisch-Technische Bundesanstalt – PTB). The energy resolution FWHM (Full Width at Half Maximum) was 0.54 keV at 58 keV.

γ-activity measurements before molecular plating (Position A)

For the γ-spectrometry measurement in Position A, the Dy aliquot was transferred from the HDPE vial to a custom-made PEEK vial (internal diameter: 20 mm, thickness at the bottom: 1 mm), and evaporated to dryness at 70 °C under a N2 gas flow. To ensure a complete transfer of the Dy aliquot, the HDPE vial was rinsed with 10 ml 1 M HNO3, transferring the washing solution to the PEEK vial, and evaporating the liquid to dryness. This process was repeated 5 times. Then, 400 μl of 1 M HNO3 were added in order to dissolve the dried Dy solid. The added volume corresponded to the minimum volume that would entirely cover the bottom of the PEEK vial. This step was necessary to avoid attenuation of the γ-rays of 159Dy at 58 keV due to the presence of Dy(NO3)3 crystals, as well as to ensure a specific geometry equivalent to the one of the electrodeposited radioactive source. The PEEK vial containing the Dy dissolved in 1 M HNO3 was placed in the custom-made holder. A graphite foil (thickness: 75 μm, purity: 99.8%, Flexible Graphite, GoodFellow) was inserted between the bottom of the PEEK vial and the detector endcap, as shown in Fig. 2a. The γ-measurement of the 159Dy contained in the PEEK vial was performed for 540 s.

Molecular plating

After the γ-spectroscopy measurements, the Dy solution was transferred from the PEEK vial to a HDPE vial and evaporated to dryness at 70 °C under a N2 gas flow. To ensure a complete transfer of the Dy, the PEEK vial was rinsed with 5 ml 1 M HNO3, the washing solution was transferred to the HDPE vial, and the liquid was evaporated to dryness at 70 °C under a N2 flow. This process was repeated 5 times. The dried Dy was then dissolved in 6 M HNO3 to promote the formation of nitrate species and again evaporated to dryness at 70 °C under a N2 flow. Any organic species that might derive from the separation process described in “Separation and purification of the 154Dy sample” Section was digested by the addition of modified aqua regia, i.e., 1.5 ml 30% (w/w) H2O2 + 4.5 ml conc. HCl + 1.5 ml conc. HNO3. The solution was evaporated to dryness at 80 °C under a N2 flow, and the residual solid was re-dissolved in a mixture of 2 ml conc. HNO3, 6 ml conc. HCl, and 2 ml conc. HF for the destruction and removal of any silica compound that might derive from the ion exchange resins used in the separation of the Dy fraction from the Ta matrix. The solution was then evaporated to dryness (80 °C under a N2 flow), dissolved in 1 M HNO3, and re-evaporated to dryness (70 °C in N2 flow). Finally, the electroplating solution was obtained by adding a 50:50 methanol (MeOH) / isopropanol (iPrOH) mixture to the dried solid residue, for a total volume of 10 ml. The liquid was then transferred to the electrodeposition cell made of polytetrafluoroethylene (PTFE). A description of the molecular plating setup can be found in42. Before electrodeposition, a cleaning procedure (stepwise rinsing in 1 M HNO3, MilliQ water, and iPrOH) was applied to the PTFE cell and to the spiral Pt wire (anode). The cathode, made of a copper block, was cleaned with 0.1 M citric acid, washed with MilliQ water, and rinsed with iPrOH. The graphite deposition foil (thickness: 75 μm, diameter of deposition area: 20 mm, GoodFellow Cambridge Ltd.) was cleaned with iPrOH before molecular plating. For a constant deposition temperature, the setup was implemented with a Peltier cooler at the cathode, maintaining the graphite foil at 15 °C during the entire plating procedure. The distance between the two electrodes was approximately 10 mm. The electrodeposition of Dy on the graphite foil was achieved in 8 h by applying a constant voltage of 550 V.

γ-activity measurements after molecular plating (Position B)

The activity of the 159Dy contained in the Dy deposited on the graphite foil was measured by placing the foil in Position B (see Fig. 2b). In between the graphite foil and the BEGe™ detector endcap, a PEEK disk (thickness = 1.0 mm, identical to the bottom of the PEEK vial) was inserted, as shown in Fig. 2b. The γ-spectrometry measurement of the 159Dy deposited on the graphite foil was conducted for 2.16∙106 s (i.e., 25 days).

154Dy α-activity measurement

The graphite foil with the electrodeposited Dy was then transferred to an α-chamber for the measurement of the α-activity of 154Dy. α-spectrometry was performed using the Alpha Analyst Integrated Alpha Spectrometer (model A-450-21AM, Canberra) equipped with a silicon semiconductor detector (Passivated Implanted Planar Silicon – PIPS. Detector sensitive area: 450 mm2; energy resolution FWHM: 21 keV). Data acquisition and analysis were done using the Genie™ 2000 Alpha Analysis Software. Energy calibration of the detector was performed with an α-source of 148Gd (t1/2 = 74.6 y, Iα = 100% at Eα = 3.182 MeV43), and a mixed 239Pu (t1/2 = 2.41 y, Iα = 70.77% at Eα = 5.157 MeV44), 241Am (t1/2 = 432.8 y, Iα = 84.8% at Eα = 5.486 MeV45), and 244Cm (t1/2 = 18.1 y, Iα = 76.90% at Eα = 5.805 MeV46) α-source. For all measurements, the sample-detector distance (SDD) was 10.4 mm. The efficiency calibration of the detector was performed with a certified 241Am standard source (PTB, calibration reference n° PTB-6.11-2016-1769, A = (539 ± 11) Bq @01.11.2016 00:00:00 MEZ, uncertainty with k = 2), having the same diameter (20 mm) as the Dy deposition area on the graphite foil. Geometrical differences between the 241Am standard source and the Dy electrodeposited sample were further minimized by using holders with the same SDD for both samples. The activity of the 154Dy electrodeposited sample was measured at a defined solid angle. The α-spectrometry measurement of the electrodeposited Dy layer was conducted for 5∙105 s (i.e., 5.8 days).

Results and discussion

Mass spectrometry analysis

The 161Dy content in the Dy sample for SF-ICP-MS analysis, resulting from the average of six analyses (see Table S5), was deduced to be (0.01203 ± 0.00046) nmol∙g-1. In the data analysis for the external standards, the accepted natural isotope composition of Dy given in47 was used. Possible isobaric interferences from Sm and Gd on the 154Dy ion-beam were considered negligible, since the ratios of the signals 149Sm/154total (where 154total stands for the bulk signal on mass 154 without element distinction), 152(Sm,Gd)/154total, 155Gd/154total, and 157Gd/154total are all below 10−3. Therefore, a correction of the 154total/161Dy value for isobaric interferences from Sm and Gd – assuming natural isotope compositions of the interfering species – would result to a 0.02% lower value. Therefore, no isobaric correction was undertaken. Likewise, potential interferences from Yb on mass 170 were insignificant since the signal ratios 172Yb/170total (where 170total stands for the bulk signal on mass 170 without element distinction) were below 10−5. The signal ratio 170Yb/170total was in the order of 10−6. The relation between the exponential mass discrimination factors for Er and Dy48 was established from the analyses of the natural Er-Dy solution standards, considering the natural isotopic abundances reported in47,49 and the nuclide masses listed in50. This (linear) relation, together with the exponential mass discrimination factors for Er, allowed for accurate mass discrimination corrections of the 154Dy/161Dy ratio in the Dy master solution. As a final result from the average of six analyses (see Table S6), the 154Dy/161Dy ratio was determined as (0.277317 ± 0.000085). The concentration of 154Dy in the Dy master solution was assessed as 1.547 nmol∙g−1, with an uncertainty of 3.82% (k = 1). The latter includes the uncertainty on the concentration of the Dy standard used for SF-ICP-MS.

Estimation of the molecular plating efficiency

From the comparison of the 133Ba measurements in Position A and Position B, a geometry conversion factor of (1.045 ± 0.015) was deduced (see Section 2 of the Supporting Information). From the knowledge of the 154Dy concentration in the master solution, it follows that the amount of 154Dy contained in the aliquot (mass: (2.77410 ± 0.00001) g, see Table S11) used for the preparation of the thin radioactive α-source corresponds to (4.291 ± 0.163) nmols. The count rate of the 159Dy tracer before electrodeposition contained in the PEEK vial was quantified to be (2.7870 ± 0.0232) counts∙s−1 @13.08.2020, whereas the count rate of the 159Dy tracer electrodeposited on the graphite foil amounted to (0.0047 ± 0.0002) counts∙s−1 @30.03.2021. Parameters used for the estimation of the count rates are given in Table 2. The corresponding γ-spectra are included in Section 2 of the Supporting Information. Considering the decay of 159Dy in the time elapsed between the measurement in Position A and the measurement in Position B (i.e., 229.16 days), and the geometry conversion factor, a deposition yield of (0.53 ± 0.02)% was calculated. The reported deposition yield includes the 0.14% uncertainty on the half-life of the 159Dy tracer38. Taking into account the uncertainties deriving from (SF-MC)-ICP-MS and from the 159Dy activity measurements, (0.0226 ± 0.0009) nmols of 154Dy were electrodeposited on the graphite foil, equivalent to (1.361 ± 0.052)∙1013 atoms of 154Dy.

Table 2 Count rate (in counts∙s-1) at 58 keV corresponding to the γ-measurements of 159Dy in Position A and Position B.
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154Dy α-activity measurement

As shown in Fig. 3, a slight contamination of 148Gd was visible in the α-spectrum. Thus, a deconvolution method based on a combination of51 and52 for a precise peak-shape fitting in the (1.1–3.5) MeV energy range (see Section 3 of the Supporting Information for further details), was applied. The fitting residuals, given as well in Fig. 3, are consistent with the measured counting statistics. The activities of 154Dy and 148Gd, together with the one of the 241Am standard source used for efficiency calibration, are given in Table 3.

Figure 3
figure 3

(a) α-spectra (black line) of the electrodeposited Dy on a graphite foil (SDD = 10.4 mm, counting time = 5∙105 s or 5.8 days). The histogram bin size is 5.925 keV. The presence of 148Gd, contained in traces in the Dy separated fraction (isotope ratio 154Dy:148Gd ≈ 28,000:1), is clearly visible. The model (navy line) that comprises the fit of the 154Dy peak (red line), the 148Gd peak (green line), as well as the electronic low energy noise, is shown. In addition, the background (light grey line) recorded during a period of 10 days (8.64∙105 s) is superimposed. (b) Fitting residuals. The residuals (orange line) are consistent with the Poisson counting statistics of the spectrum (1σ uncertainty, blue line).

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Table 3 Activity (A, in Bq) of the 154Dy electrodeposited on the graphite foil, together with the activity of the 148Gd impurity.
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154Dy half-life

A reliable half-life value is obtained by applying the following equation:

$$ t_{1/2} = \ln 2 \cdot \frac{N}{A} $$
(1)

where N is the number of atoms of 154Dy—i.e., (1.361 ± 0.052)∙1013, and A is their activity—i.e., (0.2126 ± 0.0040) Bq. Here, the half-life value for 154Dy was determined as (1.40 ± 0.08) My, with an estimated total uncertainty of 5.6%. All the uncertainties (see the uncertainty budget in Table 4) were combined under the assumption that they are completely uncorrelated. For the half-life calculation, 1 year was considered to be equal to 365.242198 days.

Table 4 Uncertainties budget (with k = 1) for the 154Dy half-life measurement.
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Re-evaluation of the production cross-sections of 154Dy from proton irradiated Pb, Ta, and W targets

The production cross-sections of 154Dy in proton-irradiated Ta, Pb, and W targets previously reported in37,53,54 were re-evaluated applying Eq. 2:

$$ \sigma^{*} = \sigma \cdot \frac{{t_{1/2}^{*} }}{{t_{1/2} }} $$
(2)

where σ* is the re-calculated cross section, σ is the experimental cross section from literature, t*1/2 is the half-life value of 154Dy determined in this work, and t1/2 is the currently adopted half-life value for 154Dy. As shown in Fig. 4, a significant decrease in the uncertainty of the experimental excitation functions for 154Dy was achieved, with the new results being in agreement with theoretical calculations obtained using INCL +  + and ABLA 07 codes55,56,57. For the sake of completeness, the comparison with the cross-section results derived using t1/2 = (3.0 ± 1.5) My is depicted as well.

Figure 4
figure 4

Excitation functions for the production of 154Dy in proton irradiated Ta (a), Pb (b), and W (c) targets. Solid lines: theoretical values obtained with INCL +  + and ABLA 07 codes; filled dots: experimental values using t1/2 = (1.40 ± 0.08) My; open squares: experimental values using t1/2 = (3.0 ± 1.5) My.

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Conclusions

By applying state-of-the-art radiochemical separation techniques, in conjunction with high precision activity measurements, the half-life of the pure α-emitting radio-lanthanide 154Dy was determined as (1.40 ± 0.08) My. This result is in very good agreement with the half-life value deduced by MacFarlane et al.25. Compared to the currently adopted value of (3.0 ± 1.5) My, the new measurement drastically reduced the uncertainty by a factor of ~ 10. The increased accuracy of the half-life of 154Dy can be exploited in, e.g., the development of a novel dating tool that uses the 154Dy/142Nd radiometric pair as chronometer. As a first application of the updated decay data for 154Dy, the experimental cross sections for the Ta(p,x)154Dy, Pb(p,x)154Dy, and W(p,x)154Dy nuclear reactions were re-evaluated. The resulting cross-sections are now in better agreement with the theoretical values obtained with INCL +  + and ABLA 07 codes. Since the shorter half-life value measured in this work implies a greater decay rate for 154Dy at a given time t, a re-evaluation of the toxicity of spallation targets that contain 154Dy as by-product is required.

For future calculations or derivations using the half-life of 154Dy, it is recommended to adopt the value deduced in this work.