Introduction

The separation of long-lived trivalent minor actinides (An(III), mainly Am(III) and Cm(III)) from lanthanides (Ln(III)) is a key step in nuclear fuel cycle, either for transmutation of minor actinides, or for the volume reduction of α radioactive waste. Many researchers have reported that the ligands containing soft donor atoms such as nitrogen and sulfur are most promising to be used for separation of An(III) from Ln(III) [1–12]. In all those studies, 152Eu and 241Am were chosen as the representative radiotracers of Ln(III) and An(III), and their γ activities were measured by a NaI(Tl) scintillation detector when only one radiotracer was used [1–9] or a germanium detector (Ge(Li) or HPGe) when radiotracers mixture was used [7–12]. It is well known that a germanium detector is very good for the detection of mixed γ-emitters, because of its high energy resolution. However, it is still necessary to provide other options, especially in one of the following cases: (1) when a laboratory has no germanium detectors, but has liquid scintillation counting (LSC) analyzer with the function of pulse shape analysis (PSA); (2) when a germanium detector is not equipped with automatic sample changer, which now is common for many laboratories; and (3) when the γ activity of a sample is so low that the counting will be too time-consuming. In this study, we try to determine 152Eu and 241Am simultaneously using LSC instead of a germanium detector, based on the following considerations: (1) 152Eu and 241Am can be discriminated with the technique of PSA which now is commonly equipped for LSC; (2) the counting efficiencies of LSC are reported as 82.6 % for 152Eu [13] and nearly 100 % for 241Am [14–17] in low quenched conditions, which are much higher than those of germanium detectors; and (3) nowadays almost every LSC has already equipped with automatic sample changer, which can make overnight and weekend hours as productive counting hours and lead to significant increase in the production of radioactive measurement work.

Experimental

Equipment

An ultra-low background liquid scintillation analyzer (Quantulus 1220) from Perkin Elmer has been used for the measurements. It is provided with a function of PSA which discriminates α from β radiations and directs them separately into α- or β-multi-channel analyzers (MCA). The discrimination results vary with the PSA parameter, which can be set between 1 and 256. Quenching can be monitored with the aid of the external standard’s Compton electron spectrum end point (SQP(E)). The SQP(E) is defined mathematically as the channel number of the external standard spectrum, above which 1 % of total intensity of the spectrum is found. The external standard spectrum is derived from the subtraction of the two spectra obtained from a two-step process: two successive measurements (counting time 1:1) of the sample with or without the external standard in the counting chamber.

Materials

Cocktail Ultima Gold AB (Perkin Elmer) and 20 mL polyethylene vials (Perkin Elmer) were employed for LSC measurement. 241Am in 0.5 mol L−1 HNO3 (radiopurity >99.9 %) was provided by China Institute of Atomic Energy. 152Eu in 0.5 mol L−1 HCl was purchased from Eckert & Ziegler, with specific activity of 3.7 × 107 Bq mL−1 and radioactive impurities of 154Eu (0.979 %) and 153Gd (8.21 %) on November 1, 2011. For the convenience of description, in the next text we use 152Eu to refer pure 152Eu only, and Eu to stand for the mixture of 152Eu, 154Eu, and 153Gd. Because both 154Eu and 153Gd are not α emitters, their radiations, i.e., β particles from 154Eu and mono-energy electrons from 154Eu and 153Gd will be directed into β-MCA together with those of 152Eu, as long as a proper PSA is set. If the total count rates of 152Eu, 154Eu, and 153Gd are assigned to Eu, the difference between the misclassification ratios of α/β discrimination for the pair of 241Am and Eu and those for the pair of 241Am and 152Eu, the count rate of which is equal to that of Eu, will be neglected. This means the results from Eu and 241Am can be also applied to simultaneously determine 152Eu and 241Am.

The quenching agent employed for this study was the simulated solution (referred as SimS) which reflects the quenching effect of acid and salt and represents the main composition of Chinese high level liquid waste. SimS was a mixture of 1.0 mol L−1 HNO3 and metallic ions, the concentrations of which were 18.3, 6.0, 5.7, 2.9 and 1.5 g L−1 for Na, Fe, Al, Ni, and Nd.

Method

All the samples were measured with α/β discrimination. The optimum PSA parameter and misclassification ratio at the optimum were determined by the generation of crossover plot. In order to obtain the optimum PSA parameter at different quench levels, eight runs of measurement were carried out. Four vials (six vials for the first run, see Quenching effect and α/β discrimination), each containing 10 μL 241Am or Eu solution mixed with 10 mL cocktail, were quenched with SimS, by adding 100 μL aliquots at first, and then 200 μL each time from the third run to the eighth run. After each addition, the vials were counted for 10 min at a series of preset PSA parameters.

With the known optimum PSA parameters, six unmixed samples (each sampling volume of which was 10 μL, Table 1) and five mixed samples (Table 2) were counted for 60 min. Afterwards, we repeated the addition of SimS and measurement as described above.

Table 1 Six unmixed solutions with different specific activities
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Table 2 Five mixed samples with different activities
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All reported uncertainties correspond to ± 1σ. The relative standard deviation of counting rate for any single counting is calculated from (rt)−1/2 × 100 %, where r is the count rate, and t is the counting time which is considered as a constant. For all multiple independent measurements, the standard deviation of mean value is calculated with the STDEV.S function of Excel 2010 (Microsoft), as shown in Table 3; Figs. 1 and 4. In addition, error propagation is in consideration for the derived quantities such as the misclassification ratio.

Table 3 Effects of anticoincidence shield on background and count rates of Eu
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Fig. 1
figure 1

The effect of counting time on SQP(E)s for Eu or 241Am samples with different count rates

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Fig. 2
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Misclassification versus PSA for Eu and 241Am in 10 mL cocktail and 0 μL SimS

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Results and discussion

Anticoincidence shield and background

Quantulus 1220 is equipped with anticoincidence shield (or called guard detector). As shown in Table 3, when the anticoincidence shield is inactive, the average background is 23.19 cpm in β-MCA and 1.93 cpm in α-MCA; while when the anticoincidence shield is active, the average backgrounds reduce to 5.31 cpm in β-MCA and 0.67 cpm in α-MCA. The anticoincidence shield not only reduces the backgrounds, but also has different influences on the count rates of different radionuclides [18]. The influences of anticoincidence shield on the count rates can be neglected for α-emitters, β-emitters and β/γ emitters without β/γ cascade radiations. However, remarkable decreases of count rates are observed when anticoincidence shield is applied for β/γ emitters with β/γ cascade radiations. As for 152Eu, there are some decay branches with β/γ cascade radiations [13, 19], therefore three Eu samples were measured to check the influences of anticoincidence shield. When the anticoincidence shield is set from inactive to active, the count rates in β-MCA + α-MCA of the three Eu samples decrease with almost the same ratio, which is 0.766 ± 0.002 (counts with guard active divided by counts with guard inactive). Even though the counting efficiencies of Eu decrease 23.4 %, in order to improve the figure of merit, we still chose to set the anticoincidence shield as active in most cases.

The error of SQP(E) from statistical fluctuations

As the most important factor responsible for reduction in counting efficiency of a given sample/cocktail mixture, quenching must be considered for LSC. For Quantulus 1220, quenching is quantified with the parameter SQP(E); when quenching increases in the sample, the SQP(E) decreases. In the case of low level counting, for which Quantulus 1220 is designed specifically, the influence of statistical fluctuations in the two-step process (refer to Equipment) on the SQP(E) can be ignored; but for high level counting, the influence should be in consideration [20].

We tested a series of Eu or 241Am samples which were prepared with different count rates but to almost the same extent of quenching. Since the statistical fluctuations will decrease with the increase of counting time, the counting time in the two-step process was set ranging from 1 + 1 min (default) to 40 + 40 min (Fig. 1). Error bars in Fig. 1 were derived from three repeated measurements for all six samples. Figure 1 shows that the influence of the statistical fluctuations varies with the count rate of the sample. When the count rate is less than 1.5 × 105 cpm, the SQP(E) is approaching to 898.7 ± 1.0 with the increase of the counting time, and the difference between the SQP(E) obtained within 10 + 10 min and that within 40 + 40 min can be ignored; but when the count rate is close to 1 × 106 cpm, the SQP(E) is significantly higher (for Eu) or lower (for 241Am) than 898.7 ± 1.0, which implies the SQP(E) may has large uncertainty if the count rate of the sample is too high and the default counting time (1 + 1 min) is applied. As a result, in this study most samples were prepared deliberately with count rates less than 1.5 × 105 cpm, and the counting time in the two-step process was set as 10 + 10 min.

The sampling volume of each sample in Fig. 1 is 10 μL. The SQP(E)s of the four samples with count rates less than 1.5 × 105 cpm are 898.7 ± 1.0, which are almost the same as those of blank samples listed in Table 3. This verifies that 10 μL Eu or 241Am has little influence on the SQP(E).

Quenching effect and α/β discrimination

The six samples used in Fig. 1 were also measured to obtain the optimum PSA parameter when the quenching agent SimS was absent. The results are shown in Fig. 2. The misclassification ratio is defined as: for α emitters, count rates in β-MCA divided by count rates in α-MCA + β-MCA; for β emitters, count rates in α-MCA (here the counting window is only the region of interest (ROI) for the α peak) divided by count rates in α-MCA + β-MCA. The large uncertainties, two of which are too large to be completely displayed in Fig. 3, are come from the low misclassified count rates of the sample “Eu: 1.26 E + 4 cpm” at PSA = 160–180, which are very close to the background in the corresponding ROI.

Fig. 3
figure 3

Changes in optimum PSA (A) and misclassification ratio (B) over a range of SQP(E) for the pair of Eu and 241Am

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The optimum PSA is chosen at the crossover point where the misclassification ratio of α event equals that of β event. When the count rate is less than 1.5 × 105 cpm, the crossover point is at almost the same place; but when the count rate is close to 1 × 106 cpm, the crossover point is at an obviously higher place, meaning a higher misclassification ratio. In order to avoid too high misclassification ratios and inaccurate SQP(E)s as described in The error of SQP(E) from statistical fluctuations, it is advisable to prepare LSC samples less than 1.5 × 105 cpm.

In order to study the effect of quenching on α/β discrimination, the four vials, count rates of which were less than 1.5 × 105 cpm, were added with quenching agent SimS and measured by LSC step by step. For each quench level, the results are similar to those in Fig. 2. The crossover point is at almost the same place for the two Eu samples and the two 241Am samples, meaning the count rates of Eu and 241Am, if they are less than 1.5 × 105 cpm, have little effect on the optimum PSA and the misclassification ratio. Therefore, the average of optimum PSAs and misclassification ratios at each quench level are shown in Fig. 3. As expected, with the volume of SimS (V SimS ) increasing from 0 to 1,300 μL (accordingly the SQP(E) is getting from 899 to 688), the optimum PSA decreases from 121 to 44, and the misclassification ratio increases from 0.0017 to 0.029.

Fig. 4
figure 4

Effects of SQP(E) on the counting efficiencies of Eu or 241Am

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Counting efficiency

Both quench level and α/β discrimination have important effect on the counting efficiency. With the known optimum PSA parameters as shown in Fig. 3, six unmixed samples (each sampling volume of which was 10 μL, Table 1) were counted to obtain counting efficiencies of Eu and 241Am at different quench levels. Figure 4 shows the average counting efficiencies of three Eu samples and three 241Am samples with two data processing methods. “Method A + B” means the counts both in β-MCA and α-MCA are summed to make the total counts for pure α or β emitters; while “Method A/B” means only counts in β-MCA are accepted to make the counts for Eu or those in α-MCA for 241Am. When the SQP(E) is getting from 899 to 688, the counting efficiencies of 241Am (with Method A + B) keep at nearly a constant of 100 %, which is in good agreement with reported results [14–17]. But for the other three cases as shown in Fig. 4, the counting efficiencies decrease with increase of quench level.

The counting efficiencies shown in Fig. 4 were calculated from the specific activities of the six unmixed samples listed in Table 1. The specific activities of Am-H, Am-M, and Am-L are very easy to be determined by measuring 10 μL each sample with LSC [14–17]. As for Eu-H, Eu-M, and Eu-L, we prepared a diluted Eu sample (referred as Eu-ref), which had the same quench level as the six unmixed samples listed in Table 1, to obtain the apparent counting efficiency of Eu as follows.

The preparation of Eu-ref includes two steps: (1) diluting 100 μL original Eu solution with 10 mL 0.5 mol L−1 HNO3 to make 10.1 mL stock solution; (2) taking 10 μL stock solution into a vial and adding 10 mL cocktail to make the LSC sample, Eu-ref. Eu-ref was measured using LSC with the anticoincidence shield inactive, and the count rate was 181,656 ± 135 cpm on May 5, 2012. The activity of Eu-ref can be figured out with the consideration of dilution factor and half-life correction, based on the above preparation process and the following data: (1) on November 1, 2011, the specific activity of 152Eu was 3.7 × 107 Bq mL−1; and the radioactive impurities were 0.979 % 154Eu and 8.21 % 153Gd; (2) the half-lives of 152Eu, 154Eu, and 153Gd are 13.522 years [19], 8.601 years [21], and 240.4 days [22]. The total activity of Eu-ref on May 5, 2012 was calculated as 3,801 Bq, including 3,569 Bq 152Eu; and the radioactive impurities were 0.997 % 154Eu and 5.10 % 153Gd.

The apparent counting efficiency of Eu by LSC is 181,656 ÷ 60 ÷ 3,801 × 100 % = 79.7 %, the uncertainty of which is about 3.5 %, mainly from the original Eu solution specific activity (3 %) and volume measurement (1 %, three times). With the consideration of the uncertainty and the differences between this study and [13], including quench level, LSC setting, and radioactive impurities, it is acceptable that the apparent counting efficiency of 79.7 % is a little less than 82.6 % [13].

The apparent counting efficiency of 79.7 % is obtained with the anticoincidence shield inactive and the quench level of Eu-ref close to those of blank samples. If the anticoincidence shield is set from inactive to active, the apparent counting efficiency will reduce to 79.7 × 0.766 % = 61.1 %. When SimS is absent, the three Eu samples have the same quench level as Eu-ref, therefore their average counting efficiency is the same as 61.1 % (Fig. 4). From this counting efficiency and the count rates of the three Eu samples when SimS is absent, the specific activities of Eu-H, Eu-M and Eu-L can be figured out, which is listed in Table 1.

Measurement of mixed samples

All the above experimental results are obtained from unmixed samples. In order to check the feasibility of this study, we also prepared five mixed samples with different ratios of 152Eu to 241Am (Table 2). The five samples were measured at different quench levels by gradually adding SimS as described in Method. For the convenience of comparison, all the results are expressed as relative error Err (Tables 4, 5, 6, 7), which is calculated from Eq. (1):

$$ Err = \frac{{\frac{r}{60 \cdot Eff} - A}}{A} \times 100\,\% $$
(1)

where r is the count rate in the ROI of 152Eu in β-MCA or of 241Am in α-MCA (cpm); A is the radioactivity of Eu or 241Am listed in Table 2 (Bq); and Eff is the counting efficiency obtained by linear interpolation at the corresponding SQP(E) on the dashed line as shown in Fig. 4.

Table 4 Relative errors for five mixed samples with no overlap correction
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Table 5 Relative errors for minor nuclide in four mixed samples with linear correction
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Table 6 Relative errors for Eu in MIX1 with linear correction and subtraction of A Am/Eu
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Table 7 Relative errors for 241Am in MIX5 with parabolic correction
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Listed in Table 4 are relative errors for the five mixed samples with no overlap correction, just by simple integration between the limits of ROIs. Both the errors for 241Am in MIX1, MIX2, and MIX3 and those for Eu in MIX3, MIX4, and MIX5 are less than 5 %, indicating that no overlap correction is needed if the count rates of 241Am and Eu are in the same order of magnitude, or the count rate of interested nuclide is major in the mixture. On the contrary, if the count rate of interested nuclide is minor in the mixture, i.e., the Eu in MIX1 and MIX2 or the 241Am in MIX4, and MIX5, the errors are getting larger and larger with the increase of quench level or the count rates of uninterested nuclides. On the other hand, the interference of 241Am on Eu is greater than that of Eu on 241Am. Except for Eu of MIX2 in the absence of SimS, all the errors of Eu in MIX1 and MIX2 are greater than 5 %. While the errors of 241Am in MIX4 and MIX5 are less than 5 % in much wider range: SQP(E) > 802 (V SimS  < 500 μL) for MIX4 and SQP(E) > 871 (V SimS  < 100 μL) for MIX5. This means: if the count rate of 241Am is one order of magnitude higher than that of Eu, overlap correction is usually needed for Eu; while if the highest count rate of Eu is not two orders of magnitude higher than that of 241Am, overlap correction is not needed when the SQP(E) is greater than 871 (V SimS  < 100μL).

For the minor Eu and 241Am, the errors of which are greater than 5 %, we made overlap correction between the lower and upper limits of the 241Am ROI with a linear interpolation at first (Table 5). Table 5 shows after linear correction the errors are significantly less than those listed in Table 4. When the highest count rate of major nuclide is not one order of magnitude higher than that of minor nuclide, all the errors are less than 5 %. However, for Eu in MIX1, all the errors remain at (16.9 ± 0.8 %) no matter how many SimS are included. This is mainly because the Compton electrons continuum resulting from the 59.54 keV γ radiations of 241Am (between channels 50 and 400, and close to the horizontal axis as shown in Fig. 5) are overlapped with the spectrum of Eu, which can be subtracted by Eq. (2):

$$ A_{Am/Eu} = \frac{{A_{Am} \cdot R_{mis} \cdot \left( {1 - k_{ROI} } \right)}}{{Eff_{Eu} }} $$
(2)

where A Am/Eu is the part which should be subtracted from the Eu radioactivity (Bq), A Am is the 241Am radioactivity of the sample (Bq), R mis is the misclassification ratio as shown in Fig. 3, k ROI is the ratio of counts in the 241Am ROI to counts in all channels of β-MCA, and Eff Eu is the counting efficiency of Eu as shown by the dashed line in Fig. 4. Because the quench level has little effect on A Am/Eu , the least quenched 10 μL Am-H sample (V SimS  = 0 μL) is used to calculate A Am/Eu in this study. For Eu in MIX1, A Am  = 1,190 Bq, R mis  = 0.0017, k ROI  = 0.196, Eff Eu  = 61.1 %, therefore A Am/Eu  = 2.66 Bq. With the subtraction of 2.66 Bq from the Eu radioactivity, the errors of Eu in MIX1 are reduced to less than 5 % as listed in Table 6.

Fig. 5
figure 5

LSC spectra of MIX1 and 10 μL Am-H in β-MCA at different quench levels 1 MIX1/100 μL SimS, 2 10 μL Am-H/100 μL SimS, 3 MIX1/1,300 μL SimS, 4 10 μL Am-H/1,300 μL SimS

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As for 241Am in MIX5, the low error range (<5 %) is extended from SQP(E) > 871 (V SimS  < 100 μL) to SQP(E) > 802 (V SimS  < 500 μL). When the SQP(E) is lower than 802 (V SimS  > 500 μL), the errors are still greater than 5 %, which needs more complex correction.

Figure 6 shows the effect of the misclassified Eu on the count rate of 241Am at different quench levels. When the quench level is low, for example, V SimS  = 100 μL, a linear interpolation or even no correction can give sufficient accuracy. While when the quench level is high, for example, V SimS  = 1,300 μL, the continuum of Eu under the 241Am peak is like a parabola, which means parabolic correction is necessary. Take line 3 in Fig. 6 as an example to show how to make the parabolic correction. Together with the lower and upper limits of the 241Am ROI (channels 460 and 650), one more channel is chosen from 30 to 50 channels at the right of the upper limit (channel 700) to obtain a fitted quadratic polynomial, which is used to calculate the continuum of Eu between the channels 460–650. By subtracting the count rate of the Eu continuum from overall count rate in the ROI, the net count rate of 241Am is obtained, which is used in Eq. (1) to calculate the relative error. The errors in Table 7 are obtained after parabolic correction, which are lower than those in Table 5, with the biggest one of 5.5 %.

Fig. 6
figure 6

LSC spectra of MIX5 and 10 μL Eu-H in α-MCA at different quench levels 1 MIX5/100 μL SimS, 2 10 μL Eu-H/100 μL SimS, 3 MIX5/1,300 μL SimS, 4 10 μL Eu-H/1,300 μL SimS

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Generally speaking, if the count rate ratio of 241Am to Eu is ranging from 100:1 to 1:100, both 241Am and Eu can be simultaneously determined by LSC with the errors less than 5 % with or without overlap correction. The interferences of 241Am on Eu are divided into two parts: inside and outside the 241Am ROI. If the count rate ratio of 241Am to Eu is less than 10:1, the latter interference can be neglected; otherwise, both interferences should be eliminated.

Conclusions

Based on the counting efficiencies of Eu or 241Am at different quench levels, which obtained from unmixed Eu or 241Am samples, the radioactivities of Eu and 241Am in mixed samples can be simultaneously determined by LSC with the errors less than 5 %, as long as the count rate ratio of 241Am to Eu is within the range of 100:1 to 1:100. If the quench level increases, obvious overlap will be found in the LSC spectrum. Depending on the shape of the spectrum, linear or parabolic correction can be used to decrease the errors. In addition, the interferences of 241Am on Eu are divided into two parts: inside and outside the 241Am ROI. Only if the count rate ratio of 241Am to Eu is more than 10:1, should the latter interference be in consideration.