High precision half-life measurement of the extinct radio-lanthanide Dysprosium-154

Sixty years after the discovery of 154Dy, the half-life of this pure alpha-emitter was re-measured. 154Dy was radiochemically separated from proton-irradiated tantalum samples. Sector field- and multicollector-inductively coupled plasma mass spectrometry were used to determine the amount of 154Dy retrieved. The disintegration rate of the radio-lanthanide was measured by means of α-spectrometry. The half-life value was determined as (1.40 ± 0.08)∙106 y, with an uncertainty reduced by a factor of ~ 10 compared to the currently adopted value of (3.0 ± 1.5)∙106 y. This precise half-life value is useful for the the correct testing and evaluation of p-process nucleosynthetic models using 154Dy as a seed nucleus or as a reaction product, as well as for the safe disposal of irradiated target material from accelerator driven facilities. As a first application of the half-life value determined in this work, the excitation functions for the production of 154Dy in proton-irradiated Ta, Pb, and W targets were re-evaluated, which are now in agreement with theoretical calculations.

The nowadays-accepted half-life value for 154 Dy, i.e., t 1/2 = 3.0 My is associated with a 50% uncertainty and derives from the revision made in 28 of the works of MacFarlane 25 and Gōnō 27 . The half-life value in 29 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 154 Dy 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 154 Dy, performed in the framework of ERAWAST. 154 Dy material was obtained by reprocessing Ta samples irradiated with protons and spallation neutrons during the SINQ Target Irradiation Program (STIP) at PSI 32 . 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 154 Dy 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 154 Dy 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 electrodeposition 33,34 . Following the Guide to the expression of uncertainty in measurement -GUM recommendations 35,36 , a realistic and complete uncertainty budget for the measured t 1/2 is given as well.

Experimental techniques and methodology
Separation and purification of the 154 Dy sample. The Dy fraction containing 154 Dy 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 in 37 . Successively, a series of ion-exchange separation processes allowed us to obtain a purified Dy fraction in 1 M HNO 3 . During the separation process, the γ-emitter 159 Dy (t 1/2 = (144.4 ± 0.2) d, I γ = 2.29% at E γ = 58 keV 38 ) was added as an internal radio-tracer. The separation method for the retrieval of the Dy fraction is reported in detail in 39 . A scheme of the chemical separation steps is reported in Fig. 1.
The homogeneous Dy fraction (in 1 M HNO 3 ) 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). www.nature.com/scientificreports/ 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 154 Dy in the Dy master solution was calculated from the amount of 161 Dy (deduced by SF-ICP-MS) and from the 154 Dy/ 161 Dy isotope ratio in solution (determined by MC-ICP-MS). 161 Dy 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 161 Dy concentration in the Dy master solution. In this procedure, several dilutions of a Dy-ESI reference standard solution (Elemental scientific nat Dy 10 mg•l -1 ± 2% k = 2 in 2% HNO 3 , 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 nat Re 10 mg•l −1 ± 2% k = 2 in 2% HNO 3 , 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 HNO 3 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 161 Dy content in the Dy master solution was obtained by correlating the backgroundcorrected and Re-normalized 161 Dy signal to the external calibration line.

MC-ICP-MS measurements. Dy isotopic ratio analysis was conducted on the Nu Instruments Plasma 3 Multi-Collector 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 10 11 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 HNO 3 solution. To the diluted Dy aliquot, nat Er 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 HNO 3 solution used in the preparation of the analytes. Online recorded 170 Er/ 166 Er 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 154 Dy 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 154 Dy atoms plated. The deposition yield was determined by monitoring the activity of the γ-tracer 159 Dy added during the separation process (see "Separation and purification of the 154Dy sample" Section). Specifically, the activity of 159 Dy in the Dy aliquote before molecular plating was measured, and compared to the activity of the 159 Dy plated on the deposition foil. Since isotopes of the same element behave chemically identically, the yield of deposited 159 Dy is thus equal to the yield of deposited 154 Dy. For a reliable deduction of the deposition yield, both 159 Dy 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 159 Dy before electrodeposition), and Position B (used to quantify the activity of 159 Dy 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 133 Ba (t 1/2 = 10.54 y, I γ = 32.9% at E γ = 80.99 keV 40  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 N 2 gas flow. To ensure a complete transfer of the Dy aliquot, the HDPE vial was rinsed with 10 ml 1 M HNO 3 , transferring the washing www.nature.com/scientificreports/ solution to the PEEK vial, and evaporating the liquid to dryness. This process was repeated 5 times. Then, 400 μl of 1 M HNO 3 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 159 Dy at 58 keV due to the presence of Dy(NO 3 ) 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 HNO 3 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 159 Dy 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 N 2 gas flow. To ensure a complete transfer of the Dy, the PEEK vial was rinsed with 5 ml 1 M HNO 3 , the washing solution was transferred to the HDPE vial, and the liquid was evaporated to dryness at 70 °C under a N 2 flow. This process was repeated 5 times. The dried Dy was then dissolved in 6 M HNO 3 to promote the formation of nitrate species and again evaporated to dryness at 70 °C under a N 2 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) H 2 O 2 + 4.5 ml conc. HCl + 1.5 ml conc. HNO 3 . The solution was evaporated to dryness at 80 °C under a N 2 flow, and the residual solid was re-dissolved in a mixture of 2 ml conc. HNO 3 , 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 N 2 flow), dissolved in 1 M HNO 3 , and re-evaporated to dryness (70 °C in N 2 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 in 42 . Before electrodeposition, a cleaning procedure (stepwise rinsing in 1 M HNO 3 , 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 159 Dy 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 159 Dy deposited on the graphite foil was conducted for 2.16•10 6 s (i.e., 25 days).

Results and discussion
Mass spectrometry analysis. The 161 Dy 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 in 47 was used. Possible isobaric interferences from Sm and Gd on the 154 Dy ion-beam were considered negligible, since the ratios of the signals 149 Sm/ 154 total (where 154 total stands for the bulk signal on mass 154 without element distinction), 152 (Sm,Gd)/ 154 total, 155 Gd/ 154 total, and 157 Gd/ 154 total are all below 10 −3 . Therefore, a correction of the 154 total/ 161 Dy 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 172 Yb/ 170 total (where 170 total stands for the bulk signal on mass 170 without element distinction) were below 10 −5 . The signal ratio 170 Yb/ 170 total was in the order of 10 −6 . The relation between the exponential mass discrimination factors for Er and Dy 48 was established from the analyses of the natural Er-Dy solution standards, considering the natural www.nature.com/scientificreports/ isotopic abundances reported in 47,49 and the nuclide masses listed in 50 . This (linear) relation, together with the exponential mass discrimination factors for Er, allowed for accurate mass discrimination corrections of the 154 Dy/ 161 Dy ratio in the Dy master solution. As a final result from the average of six analyses (see Table S6), the 154 Dy/ 161 Dy ratio was determined as (0.277317 ± 0.000085). The concentration of 154 Dy 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 133 Ba 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 154 Dy concentration in the master solution, it follows that the amount of 154 Dy 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 159 Dy 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 159 Dy 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 159 Dy 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 159 Dy tracer 38 . Taking into account the uncertainties deriving from (SF-MC)-ICP-MS and from the 159 Dy activity measurements, (0.0226 ± 0.0009) nmols of 154 Dy were electrodeposited on the graphite foil, equivalent to (1.361 ± 0.052)•10 13 atoms of 154 Dy.
154 Dy α-activity measurement. As shown in Fig. 3, a slight contamination of 148 Gd was visible in the α-spectrum. Thus, a deconvolution method based on a combination of 51 and 52 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 154 Dy and 148 Gd, together with the one of the 241 Am standard source used for efficiency calibration, are given in Table 3.

Dy half-life. A reliable half-life value is obtained by applying the following equation:
where N is the number of atoms of 154 Dy-i.e., (1.361 ± 0.052)•10 13 , and A is their activity-i.e., (0.2126 ± 0.0040) Bq. Here, the half-life value for 154 Dy 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.
Re-evaluation of the production cross-sections of 154 Dy from proton irradiated Pb, Ta, and W targets. The production cross-sections of 154 Dy in proton-irradiated Ta, Pb, and W targets previously reported in 37,53,54 were re-evaluated applying Eq. 2: where σ* is the re-calculated cross section, σ is the experimental cross section from literature, t * 1/2 is the halflife value of 154 Dy determined in this work, and t 1/2 is the currently adopted half-life value for 154 Dy. As shown in Fig. 4, a significant decrease in the uncertainty of the experimental excitation functions for 154 Dy was achieved, with the new results being in agreement with theoretical calculations obtained using INCL + + and ABLA 07 codes [55][56][57] . For the sake of completeness, the comparison with the cross-section results derived using t 1/2 = (3.0 ± 1.5) My is depicted as well.    Table 3. Activity (A, in Bq) of the 154 Dy electrodeposited on the graphite foil, together with the activity of the 148 Gd impurity. a Activity of the source at the date of the efficiency calibration (20.07.2021), calculated using (432.6 ± 0.6) y as the half-life of 241 Am, as reported in 45 . The activity of the 241 Am standard source used for efficiency calibration is indicated as well. For each measurement, the real time (t real , in seconds) and the life time (t life , in seconds) is reported. The energy range considered for the calculation of the count rate (in counts•s -1 ) of each α-peak is given as well.   www.nature.com/scientificreports/