Measurement of ¹⁶⁰Tb and ¹⁶¹Tb in nuclear forensics samples

Abstract

¹⁶⁰Tb and ¹⁶¹Tb are important radionuclides to measure when analysing a Nuclear Forensics sample. An analytical method for the measurement of both ¹⁶⁰Tb and ¹⁶¹Tb was developed in this study. Terbium was separated and purified using exchange resin and TrisKem LN Resin. The purified fraction containing ¹⁶⁰Tb and ¹⁶¹Tb was measured by gamma spectrometry and liquid scintillation counting. The counting efficiencies of ¹⁶⁰Tb and ¹⁶¹Tb were determined using the CIEMAT/NIST efficiency tracing method. The LSC count rate ratio, ${{R_{{{}^{160}{\text{Tb}}}} } \mathord{\left/ {\vphantom {{R_{{{}^{160}{\text{Tb}}}} } {R_{{{}^{161}{\text{Tb}}}} }}} \right. \kern-0pt} {R_{{{}^{161}{\text{Tb}}}} }}$, on the reference date was determined by sequential counting and calculated using a custom script based on their half-lives.

Introduction

Terbium is one of the lanthanides which are located in group 3 of the periodic table and conventionally known as rare earth elements (REE). The lanthanides typically appear in oxidation state +III and are present in aqueous solution as Ln³⁺ ions except for cerium; the chemical behaviour of the lanthanides is therefore very similar [1]. The lanthanide elements include several fission products, and the half-lives for some of these are relatively short. Yttrium is also +III in solution and behaves as the lanthanides; it is therefore known as a pseudo-lanthanide.

¹⁶¹Tb is a fission product. It is a high energy beta emitter, which decays 100% by β⁻ decay to stable ¹⁶¹Dy with an endpoint energy of 593.0 keV [2]. Its main beta and gamma emissions are shown in Table 1. The determination of ¹⁶¹Tb activity is challenging due to its very low fission yield [3], relatively short half-life of 6.89 (2) days [2], low energy gamma emissions in the X-ray region of the spectrum, and difficult separation from other lanthanides and yttrium which have similar chemical properties.

Table 1 Main beta and gamma emissions of ¹⁶⁰Tb and ¹⁶¹Tb [2]

The radiochemical separation and measurement of ¹⁶¹Tb was investigated in previous studies [4, 5]. A lanthanide intra-group separation method was developed using LN extraction chromatography resin from Eichrom or TrisKem [6]. The lanthanide sorption and elution behaviour is dependent on the nitrate concentration, therefore a gradient elution by nitric acid was used to separate neighbouring lanthanide elements. The method was then modified to achieve higher chemical recovery, better lanthanide separation and a pure terbium fraction, while keeping the separation time reasonable (about 6 h) [7]. The purified ¹⁶¹Tb was measured by gamma spectrometry and liquid scintillation counting (LSC) [8]. The CIEMAT/NIST efficiency tracing (CNET) method was used to determine the counting efficiency of ¹⁶¹Tb because a ¹⁶¹Tb certified standard solution was unavailable for the efficiency calibration.

¹⁶⁰Tb is the activation product of stable nuclide ¹⁵⁹Tb. It decays 100% by β⁻ decay to stable ¹⁶⁰Dy with a half-life of 72.3 (2) days (Table 1) [2]. Its endpoint energy is 1748.3 keV, which is higher than that of ¹⁶¹Tb. ¹⁶⁰Tb has a few gamma emissions in the high energy region, so the activity of ¹⁶⁰Tb can be measured by gamma spectrometry. However, if a sample contains both ¹⁶⁰Tb and ¹⁶¹Tb, the measurement of their individual activity is difficult either by gamma spectrometry, due to the low energy emission of ¹⁶¹Tb, or by LSC because these two radionuclides cannot be chemically separated and their beta spectra overlap.

In this study, the measurement of ¹⁶⁰Tb was investigated as the additional work of previous studies. A LSC method was developed for the measurement of both purified ¹⁶⁰Tb and ¹⁶¹Tb using a 1220 Quantulus™ liquid scintillation (LS) spectrometer (PerkinElmer™, Waltham, MA USA). The CNET method was used to determine the counting efficiencies of ¹⁶⁰Tb and ¹⁶¹Tb because of the unavailability of certified solutions. The ratio of ¹⁶⁰Tb and ¹⁶¹Tb in the sample was determined by sequential counting and calculated using a custom script in GNUPlot. The method was validated during the analysis of an irradiated sample. The results of LSC method were compared with the results obtained by gamma spectrometry.

Experimental

Sample preparation

A sample from a Nuclear Forensics exercise was used in the experiments. The sample contained uranium and some stable elements, and was irradiated with neutrons on 21 July 2015 22:11 (GMT). The sample therefore contained both mixed fission and activation products. The sample was left for a few days and then dissolved by nitric acid digestion. The final solution was diluted to give an acid concentration of 3 mol L⁻¹. AWE received a portion of this solution, which contained approximately 1 × 10¹⁴ fission products estimated from gamma measurement. Four replicates were prepared and each of them contained from 0.5 to 1 × 10¹³ fission products (approximately 0.05–0.1 g of solution).

Stable carriers of samarium, europium, terbium and yttrium, at 500 µg each were added to the sample. The sample was initially separated by anion exchange chromatography using Bio-Rad (Watford, UK) AG1 × 8 anion exchange resin (part number: 1401451). This was followed by a series of precipitation reactions to separate the lanthanide fraction, containing cerium, neodymium, samarium, europium, terbium (and yttrium), from other elements. Yttrium behaves as a lanthanide in solution and it is therefore processed alongside the lanthanides. The lanthanide fraction was evaporated to dryness, dissolved in 0.01 mol L⁻¹ nitric acid, and intra-group separated using 1.56 g of TrisKem (Bruz, France) 50–100 µm LN Resin (part number: LN-B200-S) in a 20 cm Econo-Column (internal diameter: 0.7 cm) (part number: 737-4721) from Bio-Rad. Lanthanides were eluted from the column in order of increasing atomic number by increasing nitric acid concentration from 0.01 to 8 mol L⁻¹. The cerium/neodymium, samarium, europium, terbium and yttrium fractions were collected individually at different specific nitric acid concentrations. For the collected terbium fraction, an additional separation using 0.78 g of resin in a 10 cm Bio-Rad Econo-Column (part number: 737-4711) was used for a final purification [7, 8].

The radiochemically purified samarium, europium, terbium and yttrium fractions were dissolved in 2.1 mL of 0.1 mol L⁻¹ nitric acid. An aliquot of 0.1 mL sample solution was diluted to 10 mL with 0.1 mol L⁻¹ nitric acid and measured by inductively coupled plasma–optical emission spectrometry (ICP-OES) using an iCAP™ 6500 ICP-OES Analyzer (Thermo Fisher Scientific, Waltham, MA USA) [7, 8]. Mixed calibration solutions ranging from 0.1 to 20 µg/g in 2% nitric acid were prepared from 1000 µg/mL single element standards. A calibration curve was obtained by using five calibration solutions at different concentrations. The measured amount of stable carriers, samarium, europium, terbium and yttrium, in their individual purified fraction was compared to the amount added to calculate chemical recovery for each element. The remainder of the 2 mL solution was transferred into a 20 mL plastic LS vial (part number: 6008117, PerkinElmer™) for gamma spectrometry measurement. A XPE205 balance from Mettler Toledo (Leicester, UK) was used to weigh the sample solutions. The chemical recoveries for the collected cerium/neodymium fraction were not determined because they were not a concern in the radiochemical analysis. The cerium and neodymium radionuclides in a fission sample can be measured by gamma spectrometry directly without separation due to their high activity concentrations.

Radiochemical purity check and measurement of ¹⁶⁰Tb and ¹⁶¹Tb by gamma spectrometry

The LS vial containing 2 mL of purified terbium was counted for 250,000 s on a broad energy high-purity germanium detector (BEGe) (Canberra BE3825, Meriden, CT USA). The detector was calibrated using a mixed radionuclide standard from the National Physical Laboratory (Teddington, UK). Apex and Genie2000™ software (version 4.1 and 3.4, Canberra Industries Inc, Meriden, CT USA) was used for the spectrum acquisition and analysis [9, 10]. The nuclear data of ¹⁶⁰Tb and ¹⁶¹Tb were obtained using the NuDat from the National Nuclear Data Center (NNDC) at Brookhaven National Laboratory (BNL) [2]. The ¹⁶⁰Tb and ¹⁶¹Tb in the sample were quantified using 966.1 keV as the key peak for ¹⁶⁰Tb and 48.9 keV for ¹⁶¹Tb. The sample was also verified to be free from interferences, primarily the other lanthanides, prior to LSC.

Measurement of ¹⁶⁰Tb and ¹⁶¹Tb by CNET LSC

After the radiochemical purity had been checked by gamma spectrometry, Ultima Gold™ cocktail (part number: 6013321, PerkinElmer™), 15 mL, was added to the purified terbium fraction in the 20 mL plastic LS vial. The sample was dark-adapted for at least 12 h and then measured on a 1220 Quantulus™ Liquid Scintillation Spectrometer for 5 h every 3 days for 4 weeks. A total of 10 measurements were collected. The instrument was configured as “Special setup”, which switched off the guard detectors, PSA/PAC options were disabled, and a full counting window was used.

The CNET method was used in the determination of ¹⁶⁰Tb and ¹⁶¹Tb counting efficiencies because there are no ¹⁶⁰Tb and ¹⁶¹Tb certified standard solutions available commercially for instrument calibration. A certified ³H standard solution from Eckert and Ziegler (Braunschweig, Germany) was used as the tracer radionuclide. The relative standard uncertainty of the activity concentration of this solution was 0.8%. Six standard LS sources were prepared by adding 0.1 mL of ³H tracer, 1.9 mL of 0.1 mol L⁻¹ nitric acid, and 15 mL of Ultima Gold™ cocktail. Nitromethane was used as the quenching agent. A Mettler XPE205 balance was used to weigh the added ³H tracer containing solution. Each standard vial contained about 125 Bq of ³H. Six blanks containing the same components except the tracer were prepared for background determination. The ³H standards were counted on the Quantulus™ instrument for 15 min each.

Calculations in the LSC method

Computer program CN2005, developed by E. Günther at the Physikalisch-Technische Bundesanstalt (PTB), was used for the calculation of ¹⁶⁰Tb and ¹⁶¹Tb counting efficiencies by the CNET method as a function of the free parameter [11, 12]. The atomic data used in the input file for this program were generated using the computer program ATOMIC DATA [13].

The total LSC count rate of ¹⁶⁰Tb and ¹⁶¹Tb on the count date can be expressed as:

$$R_{\text{Tc}} = R_{{{}^{160}{\text{Tb}}}} \times D_{{{}^{160}{\text{Tb}}}} + R_{{{}^{161}{\text{Tb}}}} \times D_{{{}^{161}{\text{Tb}}}} ,$$

(1)

where, R _Tc is the total net count rate in counts per second, $R_{{{}^{160}{\text{Tb}}}}$ and $R_{{{}^{161}{\text{Tb}}}}$ are the count rates of ¹⁶⁰Tb and ¹⁶¹Tb on the reference date, and $D_{{{}^{160}{\text{Tb}}}}$ and $D_{{{}^{161}{\text{Tb}}}}$ are their decay factors.

The net count rate ratio, ${{R_{{{}^{160}{\text{Tb}}}} } \mathord{\left/ {\vphantom {{R_{{{}^{160}{\text{Tb}}}} } {R_{{{}^{161}{\text{Tb}}}} }}} \right. \kern-0pt} {R_{{{}^{161}{\text{Tb}}}} }}$, on the reference date was calculated by sequential counting because the two radionuclides decayed at different speeds due to their different half-lives. A custom script in GNUPlot was used to calculate this ratio. The total net count rates of ¹⁶⁰Tb and ¹⁶¹Tb obtained from the 10 LSC measurements, half-lives of these two radionuclides, and the sample reference date were used in the calculation.

The activity concentrations of ¹⁶⁰Tb and ¹⁶¹Tb can then be calculated by Eqs. (2) and (3):

$$A_{{{}^{160}{\text{Tb}}}} = \frac{{R_{\text{Tc}} }}{{D_{{{}^{160}{\text{Tb}}}} + \frac{{R_{{{}^{161}{\text{Tb}}}} }}{{R_{{{}^{160}{\text{Tb}}}} }} \times D_{{{}^{161}{\text{Tb}}}} }} \times \frac{{m_{\text{T}} }}{{\varepsilon_{{{}^{160}{\text{Tb}}}} Ym_{\text{S}} m_{\text{C}} }},$$

(2)

$$A_{{{}^{161}{\text{Tb}}}} = \frac{{R_{\text{Tc}} }}{{D_{{{}^{161}{\text{Tb}}}} + \frac{{R_{{{}^{160}{\text{Tb}}}} }}{{R_{{{}^{161}{\text{Tb}}}} }}\times D_{{{}^{160}{\text{Tb}}}} }} \times \frac{{m_{\text{T}} }}{{\varepsilon_{{{}^{161}{\text{Tb}}}} Ym_{\text{S}} m_{\text{C}} }},$$

(3)

where, $A_{{{}^{160}{\text{Tb}}}}$ and $A_{{{}^{161}{\text{Tb}}}}$ are the activity concentrations of ¹⁶⁰Tb and ¹⁶¹Tb, $\varepsilon_{{{}^{160}{\text{Tb}}}}$ and $\varepsilon_{{{}^{161}{\text{Tb}}}}$ are their counting efficiencies, Y is the terbium chemical recovery, m _S is the sample mass taken for analysis, m _T is the total mass of final solution after separation, and m _C is the mass of counted solution which is taken from the final solution after separation.

The uncertainty associated with the result was assessed based on the uncertainty evaluation method provided by United Kingdom Accreditation Service (UKAS, 2007) [14]. The uncertainty components were identified based on the equation which was used to calculate the result. The major components of the uncertainty came from the counting statistics (u _c), the ¹⁶⁰Tb and ¹⁶¹Tb counting efficiency determination (u _ε ), the count rate ratio calculation (u _R), the LSC drift (u _LSC), the chemical recovery measurement by ICP-OES (u _Y), the solution weighing (u _w), and the decay corrections for ¹⁶⁰Tb and ¹⁶¹Tb half-lives (u _t1/2). Each uncertainty component was assessed individually, and then propagated according to the ISO Guide to the expression of uncertainty in measurement provided by UKAS [14]. The total relative standard uncertainty (u _total) for the final result was calculated as:

$$u_{\text{total}} = \sqrt {\left( {u_{\text{c}}^{2} + u_{\varepsilon }^{2} + u_{\text{R}}^{2} + u_{\text{LSC}}^{2} + u_{\text{Y}}^{2} + u_{\text{w}}^{2} + u_{{{\text{t}}1/2}}^{2} } \right)} .$$

(4)

The detection limit was determined following Currie (1968) [15]:

$$L_{\text{D}} = 2.71 + 4.653\sqrt B ,$$

(5)

where L _D is the detection limit in counts and B is the number of blank counts. For this to be valid, the blank and sample counting times should be equal. The L _D was then expressed as minimum detectable concentration (MDC) in Bq g⁻¹, by correcting for the counting time, counting efficiency, and sample mass measured.

Results and discussion

Lanthanide separation

The elution of the elements in the lanthanide series with increasing nitric acid concentration is presented in Table 2 with the chemical recoveries for the four replicates, which were calculated from the ICP-OES measurements. Lanthanide intra-group separation is challenging due to their similar chemical behaviour. The use of TrisKem LN extraction resin has significantly improved their chemical recoveries compared to the conventional cation exchange method using the 2-hydroxy-2-methylpropionic acid (α-hydroxyisobutyric acid, α-HIBA) gradient elution [16]. The chemical recoveries for all the lanthanide elements were 51–83% except for cerium and neodymium, which are shown as N/A in Table 2, because they were not measured. The ICP-OES measurements showed that there were no other measurable lanthanides, of which samarium and europium were of the highest concern, present in the purified terbium fraction.

Table 2 Elution of lanthanides and yttrium from LN chromatography column and their chemical recoveries

The uncertainty for the determination of chemical recovery by ICP-OES was 4.3% (k = 1) overall. The main components came from the instrument calibration. The detailed uncertainty budget is given in Table 3.

Table 3 Uncertainty budget for the determination of chemical recovery by ICP-OES

Gamma spectrometry

The gamma spectrum of the purified terbium for Replicate 1 obtained on the BEGe detector is shown in Fig. 1, with the main gamma emissions of ¹⁶⁰Tb and ¹⁶¹Tb. Peaks within the spectrum are from ¹⁶⁰Tb, ¹⁶¹Tb, and some naturally occurring radionuclides in the detector background. The measurement needs to be conducted as early as possible because of the relatively short half-life of ¹⁶¹Tb and the complication of its measurement.

Fig. 1

Gamma spectrum of purified ¹⁶⁰Tb and ¹⁶¹Tb for Replicate 1

The most abundant gamma rays for ¹⁶¹Tb are in the X-ray region of the spectrum with emission probabilities of 6–24% and the energies are very similar, complicating the measurement. The presence of any interfering radionuclide could also cause a raised background, which increases the difficulty of spectrum analysis. The peak at 48.9 keV was used as the key peak for ¹⁶¹Tb and a total of 42,346 counts were collected in 250,000 s. The measurement of ¹⁶⁰Tb is less challenging because there are a few peaks with reasonable abundance in the gamma spectrum. The peak at 966.1 keV was chosen as the key peak and a total of 7841 counts were collected.

An in-house code RIMMER [17,18,19] was used for the calculation of cascade summing corrections. A cascade summing factor of 0.884 was applied to the peak area. The counting efficiencies for the BEGe detector used were 4.7% for the ¹⁶⁰Tb 996.1 keV peak and 27.3% for the ¹⁶¹Tb 48.9 keV peak.

The activity concentrations of ¹⁶⁰Tb and ¹⁶¹Tb in the sample are shown in Table 4. The results were decay corrected to the reference date 21 July 2015 22:11 (GMT). The results for the four replicates are very consistent. The MDCs for the measurements are also given in Table 4. The MDC for ¹⁶¹Tb is generally high due to its short half-life and the complicated background in the X-ray region of the spectrum. Replicate 4 has the lowest sample mass and chemical recovery, which results in the least activity in the counting source and the highest MDC. LSC has much higher counting efficiency than gamma spectrometry due to its high energy beta emission; for a sample containing a small amount of ¹⁶¹Tb, LSC is therefore preferred for the activity concentration measurement as long as the radiochemical separation/purification is successful.

Table 4 ¹⁶⁰Tb and ¹⁶¹Tb results obtained by gamma spectrometry

The total relative uncertainty of activity concentration was approximately 7–8% (k = 1). The major components of the uncertainty are presented in Table 5, in which the largest values were from detector efficiency calibration, emission probabilities, cascade summing correction, and the chemical recovery determination.

Table 5 Uncertainty budget for the measurement of ¹⁶⁰Tb and ¹⁶¹Tb by the BEGe gamma method

The gamma-ray spectrum also confirmed the radiochemical purity of the terbium source. It was free from any other lanthanide radionuclides, such as ¹⁵³Sm and ¹⁵⁶Eu, which could interfere with the measurement by LSC. The minimum detectable activities (not chemical recovery and decay corrected) in the sample were 0.016, 0.224, 0.059 and 0.063 Bq for ¹⁵³Sm, ¹⁵⁶Eu, ¹⁶⁰Tb and ¹⁶¹Tb, respectively.

CNET LSC

The LSC counting efficiencies were determined using the CNET method for ¹⁶⁰Tb and ¹⁶¹Tb because of the unavailability of their certified standard solutions. Ionisation quenching parameter of k _B = 0.0075 cm/MeV was used when calculating the counting efficiencies using program CN2005. The calculated ¹⁶⁰Tb and ¹⁶¹Tb LSC efficiencies ($\varepsilon_{{{}^{160}{\text{Tb}}}}$ and $\varepsilon_{{{}^{161}{\text{Tb}}}}$) versus ³H LSC efficiency $\left( {\varepsilon_{{{}^{3}{\text{H}}}} } \right)$ are plotted in Fig. 2, which shows that the counting efficiencies for both terbium radionuclides are close to 100% due to their high beta energies.

Fig. 2

Predicted ¹⁶⁰Tb and ¹⁶¹Tb efficiencies versus ³H efficiency

For the activity measurement by LSC, it is important to know the ¹⁶⁰Tb and ¹⁶¹Tb activity ratio in the sample because they cannot be either chemically separated or distinguished in the LSC spectrum. This ratio can be determined using sequential counting due to their different half-lives. The four replicates were sequentially counted every 3 days and a total of 10 measurements were collected for each replicate.

The 10 LSC spectra for the purified ¹⁶⁰Tb and ¹⁶¹Tb in Replicate 1 are shown in Fig. 3. The background spectrum had been subtracted. The net counts decreased from the 1st count to the 10th count. The decrease became less significant after the 6th count due to the decay of ¹⁶¹Tb. The SQP(E) values for the measurements were in the range of 861–865. The $\varepsilon_{{{}^{3}{\text{H}}}}$ was (0.4479 ± 0.0039) cps Bq⁻¹ calculated from the experimentally determined quench curve. The calculated $\varepsilon_{{{}^{160}{\text{Tb}}}}$ was (0.9950 ± 0.0050) cps Bq⁻¹ and $\varepsilon_{{{}^{161}{\text{Tb}}}}$ was (0.9916 ± 0.0050) cps Bq⁻¹ using the CNET method. All the spectra were smooth, which suggested the purified terbium was free from any observable alpha or low energy beta interference. Therefore the purity of the terbium fraction was proved by the absence of other lanthanides in the ICP-OES, the clean gamma spectrum and LSC spectrum.

Fig. 3

LSC spectra of purified ¹⁶⁰Tb and ¹⁶¹Tb for Replicate 1

The LSC total net count rates for all of the four replicates are given in Table 6 and plotted vs. time elapsed in Fig. 4. The count rate ratios, ${{R_{{{}^{160}{\text{Tb}}}} } \mathord{\left/ {\vphantom {{R_{{{}^{160}{\text{Tb}}}} } {R_{{{}^{161}{\text{Tb}}}} }}} \right. \kern-0pt} {R_{{{}^{161}{\text{Tb}}}} }}$, on the reference date were calculated using a custom script in GNUPlot and are also presented in Table 6. The ratios are in very good agreement for all the replicates. Figure 5 shows the calculated individual net count rate of ¹⁶⁰Tb and ¹⁶¹Tb vs. time elapsed using the obtained ratio for Replicate 1, together with the combined fit and the total net count rates obtained experimentally.

Table 6 LSC total net count rates and calculated count rate ratios of ¹⁶⁰Tb and ¹⁶¹Tb on reference date for Replicates 1–4

Fig. 4

LSC total net count rates for Replicates 1–4

Fig. 5

Calculated LSC net count rates of ¹⁶⁰Tb and ¹⁶¹Tb for Replicate 1

The activity concentrations of ¹⁶⁰Tb and ¹⁶¹Tb on the reference date and their standard uncertainties are presented in Table 7. They agree very well with the results from gamma measurement, which were (35.16 ± 2.35) Bq g⁻¹ (k = 1) for ¹⁶⁰Tb and (289.9 ± 22.6) Bq g⁻¹ (k = 1) for ¹⁶¹Tb. The results obtained from LSC method have lower uncertainties. The MDCs reported in Table 7 for LSC are much lower than those obtained by gamma spectrometry, especially for ¹⁶¹Tb, due to the higher counting efficiencies and the less complication of LSC.

Table 7 ¹⁶⁰Tb and ¹⁶¹Tb results obtained by CNET LSC

For this study, 10 LSC measurements were taken over 4 weeks. Table 6 and Fig. 4 show that the decreases in count rate were very small for the last few measurements and they became less significant for the count rate ratio calculation. The count rate ratio for Replicate 1 was calculated again using from 3 to 9 measurements. The re-calculated ratios and their discrepancies from the ratio obtained using 10 measurements are presented in Table 8. It has been shown that comparable data, within 1% of the ratio from 10 measurements, can be obtained from eight measurements. Therefore eight measurements should be sufficient for the ratio calculation, and the total measurement period can be reduced to approximately 20 days. For interim results the measurement can be quoted from five measurements, which takes 12 days. Such lowering of numbers of measurements depends on the ratio of ${{R_{{{}^{160}{\text{Tb}}}} } \mathord{\left/ {\vphantom {{R_{{{}^{160}{\text{Tb}}}} } {R_{{{}^{161}{\text{Tb}}}} }}} \right. \kern-0pt} {R_{{{}^{161}{\text{Tb}}}} }}$ and gives rise to a slightly high uncertainty. Discrepancies of up to 2.5% have been observed.

Table 8 Re-calculated count rate ratios of ¹⁶⁰Tb and ¹⁶¹Tb on reference date for Replicate 1

The detailed uncertainty budget for the CNET LSC method is given in Table 9. The largest uncertainty component came from the chemical recovery determination by ICP-OES, which was 4.3% overall. The ¹⁶⁰Tb and ¹⁶¹Tb counting efficiency uncertainties were attributed to the uncertainties from nuclear and atomic data, polynomial fitting, and the ³H efficiency measurement, which were used in the CNET calculation. The uncertainty on the count rate ratio calculation was approximately 1%, and other associated main uncertainties involved counting statistics, LSC drift, sample weight and decay corrections. This uncertainty budget assumes there is a reasonable amount of both ¹⁶⁰Tb and ¹⁶¹Tb in the sample and ¹⁶¹Tb has not significantly decayed, otherwise the uncertainty for the minor nuclide will be increased due to the interference from the major nuclide.

Table 9 Uncertainty budget for the measurement of ¹⁶⁰Tb and ¹⁶¹Tb by the CNET LSC method

LSC measurement takes longer time compared to gamma spectrometry, but it benefits from lower uncertainty and much better detection limits. It also has the advantage of being able to measure multiple samples in the three day window as each measurement is 5 h. A purity check could be completed by counting multiple samples at the same time.

Conclusions

The analysis of ¹⁶⁰Tb and ¹⁶¹Tb in a Nuclear Forensics sample containing mixed fission and activation products was performed by radiochemical separation of terbium followed by gamma spectrometry and Quantulus™ LSC. A BEGe gamma detector was used for the radioactivity measurement and radiochemical purity verification. The LSC counting efficiencies were determined by the CNET method using the computer program CN2005. Because ¹⁶⁰Tb and ¹⁶¹Tb cannot be chemically separated and their LSC spectra overlap, the LSC count rate ratio, ${{R_{{{}^{160}{\text{Tb}}}} } \mathord{\left/ {\vphantom {{R_{{{}^{160}{\text{Tb}}}} } {R_{{{}^{161}{\text{Tb}}}} }}} \right. \kern-0pt} {R_{{{}^{161}{\text{Tb}}}} }}$, on the reference date was determined by sequential counting and calculated using a custom script in GNUPlot.

The results obtained using CNET LSC are in very good agreement with the results using BEGe detection. The analysis by gamma spectrometry is challenging if the sample contains low levels of ¹⁶¹Tb because the measurement of ¹⁶¹Tb is difficult. The CNET LSC method gives a complementary independent technique to gamma spectrometry. It takes approximately 12–20 days, but it does provide lower uncertainty and much better detection limit.