Xiao-gui
Feng
,
Qian-ge
He
,
Jian-chen
Wang
and
Jing
Chen
*
Institute of Nuclear and New Energy Technology, Tsinghua University, P.O. Box 1021, 102201 Beijing, PR China. E-mail: jingxia@tsinghua.edu.cn; Fax: +86-10-62771740; Tel: +86-10-89796064
First published on 15th October 2013
In the application of liquid scintillation counting (LSC), the α/β discrimination is carried out with the function of pulse shape analysis (PSA), which requires the setting of the optimum PSA level. The optimum PSA is usually determined by the generation of cross-over plots (referred as Conventional Method), whereby a pair of pure α and β emitters is essential. However, in some cases, a pure α or β emitter is not available. In order to deal with this problem, we have developed a new approach (referred as Present Method) to set the optimum PSA by measuring the sample itself of mixed α/β emitters. The results from Present Method are in good agreement with those from Conventional Method when a pair of pure α and β emitters is available. Besides the obvious advantage that Present Method can be applied no matter whether a pure α emitter or a pure β emitter is available or not, Present Method has another important advantage that it is not necessary to prepare the quench curves for the measurement of samples with different quench levels. Therefore, Present Method is a general method for optimizing the parameter of α/β discrimination in LSC. In addition, the application of Present Method can be broadened by combining the method with α spectrometry.
Alpha spectrometer (Alpha Analyst 7200) with passivated implanted planar silicon (PIPS) detectors of 300 mm2 active area was produced by Canberra Industries, Inc.
The quenching agent employed in this study was the simulated solution (referred as SimS) which reflects the quenching effect of acid and salt. 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, representing the main composition of Chinese high level liquid waste.
For Conventional Method, the optimum PSA is determined by the generation of cross-over plot, whereby the percentage misclassification is defined as eqn (1)–(4). In eqn (1)–(4), “C” stands for count rate, and “E” the percentage misclassification; the subscript “A” stands for α emitter, “B” β emitter, “α” α-MCA, and “β” β-MCA; the superscript “PK” stands for the peak area of α emitter in this study (Fig. 1). For example, CAα denotes the count rate of the α emitter on the α-MCA; CAβ denotes the count rate of the α emitter on the β-MCA; and EA denotes the percentage of α particles misclassified into the β-MCA when an α emitter is measured. The region of interest for any “C” usually refers to the whole spectrum, except that with the superscript “PK”, which refers to the peak area of α emitter in α-MCA only. As shown in Fig. 1 and eqn (4), the count rate in α-MCA outside the PK area is still assigned to β emitter, because this portion of count rate will not interfere with the count rate of α emitter.
CA = CAα + CAβ | (1) |
CB = CBα + CBβ | (2) |
![]() | (3) |
![]() | (4) |
![]() | ||
Fig. 1 An example of LSC spectra. A: 241Am, B: 90Sr/90Y, in 10 mL Ultima Gold AB + 0.3 mL SimS, PSA = 80. |
For Present Method, the optimum PSA is obtained according to the following steps: (1) summarizing the count rates of any pair of α and β emitters within the PK area at a series of PSAs as eqn (5), which gives the value of Cα; (2) graphing the relation between Cα and PSA, which will always have an inflection point related to the optimum PSA; (3) fitting the data near the inflection point with the function y = ax3 + bx2 + cx + d, from which the value of optimum PSA can be simply obtained as −b/(3a) when the second derivative of the function, y′′, is equal to zero; (4) calculating the Cα at the optimum PSA with the function y = ax3 + bx2 + cx + d, while the relative error of Cα, Eα, is defined as eqn (6).
Cα = CPKAα + CPKBα | (5) |
![]() | (6) |
The above statements focus on how to obtain Cα. The count rate of β emitter can be easily obtained from the difference between (CA + CB) and Cα.
Group | Pair ID | α emitter | β emitter | Cocktail |
---|---|---|---|---|
1 | G1P1 | 1375 Bq 241Am | 1281 Bq 90Sr/90Y | 10 mL Ultima Gold AB |
G1P2 | 1416 Bq 137Cs | |||
G1P3 | 12692 Bq 90Sr/90Y | |||
G1P4 | 13805 Bq 137Cs | |||
2 | G2P1 | 1441 Bq 241Am | 1277 Bq 90Sr/90Y | 10 mL OptiPhase Hisafe 3 |
G2P2 | 1421 Bq 137Cs | |||
G2P3 | 12542 Bq 90Sr/90Y | |||
G2P4 | 13666 Bq 137Cs |
The experimental data for each pair of α and β emitters can be processed with both Conventional Method and Present Method. Due to the difference of the cocktail, the PK areas for the two groups have a little difference, which are channels 710–820 for the first group and channels 680–790 for the second group. Considering that the figures for the two groups are very similar to each other, we only present the figures for the first group as examples (Fig. 2–4). Fig. 2 shows the cross-over plots for Conventional Method, from which four optimum PSAs are obtained as shown by the corresponding cross-over points (between 120 and 140). Fig. 3 and 4 show the data process for Present Method. Fig. 3 shows that Cα changes monotonically with the increase of the PSA, and there is always an inflection point near the Cα of 8 × 10000 cpm. For clarity, the data near the inflection point are redrawn in Fig. 4. By fitting the data displayed in Fig. 4 with the function y = ax3 + bx2 + cx + d, the parameters (a, b, c, d) related to the function are obtained as listed in Table 2, from which three parameters at the optimum are derived: x = PSA parameter, y = count rate (cpm) and y′ = the derivative of y. All the absolute value of y′ at the optimum PSA is very small relative to y, which implies the error of y resulting from the uncertainty of PSA near the optimum (e.g., the uncertainty of PSA is 5) can usually be ignored. From this point of view, the optimum PSAs obtained from Present Method are in good agreement with those from Conventional Method. This result can also be confirmed by the small measurement error listed in the last column of Table 2 (less than 3%).
![]() | ||
Fig. 4 The enlargement of Fig. 3 near the optimum PSA. |
Pair ID | a | b | c | d | R 2 | Parameters at the optimum | E α (%) | ||
---|---|---|---|---|---|---|---|---|---|
x | y | y′ | |||||||
G1P1 | −0.1449 | 55.787 | −7130.3 | 382![]() |
0.9904 | 128.3 | 80![]() |
29.1 | −2.54 |
G1P2 | −0.1432 | 55.052 | −7022.4 | 377![]() |
0.9901 | 128.1 | 80![]() |
32.4 | −2.44 |
G1P3 | −0.2427 | 98.466 | −13![]() |
678![]() |
0.9970 | 135.2 | 81![]() |
22.2 | −1.45 |
G1P4 | −0.1466 | 56.684 | −7292.6 | 393![]() |
0.9932 | 128.9 | 81![]() |
13.2 | −1.00 |
G2P1 | −0.1313 | 44.299 | −4947.8 | 268![]() |
0.9988 | 112.5 | 85![]() |
34.2 | −0.67 |
G2P2 | −0.1295 | 43.557 | −4847.7 | 264![]() |
0.9987 | 112.1 | 85![]() |
35.7 | −0.71 |
G2P3 | −0.1938 | 69.716 | −8369.9 | 422![]() |
0.9985 | 119.9 | 87![]() |
−10.2 | 0.70 |
G2P4 | −0.1530 | 53.201 | −6170.4 | 325![]() |
0.9998 | 115.9 | 87![]() |
−4.1 | 0.95 |
The above result is also supported by the data for the second group. The parameters for Present Method are listed in the second half of Table 2. And the four optimum PSAs obtained from Conventional Method are between 110 and 130 (as mentioned above, the cross-over plots are omitted).
Run no. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|
Volume of SimS (μL) | 0 | 100 | 300 | 500 | 700 | 900 | 1100 | 1300 |
PK area (channels) | 725–825 | 690–795 | 630–760 | 600–735 | 575–715 | 490–690 | 475–680 | 475–680 |
Fig. 5 shows that the trend of the optimum PSA vs. SQP(E) from Present Method is the same as that from Conventional Method. With the volume of SimS added in each vial increasing from 0 to 1300 μL, the SQP(E) decreases, resulting in the decrease of the optimum PSA. Fig. 6 shows the percentage misclassification for Conventional Method and the relative error of Cα for Present Method at the optimum. Even though the general trend is the same, the line for Present Method is obviously positioned below that for Conventional Method. This is resulting from the different definition of EA, EB and Eα. From eqn (1)–(6), we can obtain eqn (7):
![]() | (7) |
Eqn (7) shows the relation between Eα and EB, the latter of which is equal to EA at the cross-over point (Fig. 2). Under the condition of this experiment, CA = 68873 cpm, CB = 66
872 cpm, Eα is mainly affected by EB and the ratio of CPKAα to CA. The difference between Eα and EB, EB − Eα, can be estimated as 1 − CPKAα/CA, which varies with the selection of PK area. The PK areas listed in Table 3 are selected with the following considerations: (1) including the peak of α emitter as more as possible; (2) excluding the interference from β emitter as more as possible. Due to these two contrary requirements, the selection of PK area will often lead to loss of counts for α emitter, especially when the LSC spectrum of α emitter has obvious tailing interference (refer to Fig. 1). Incidentally, as listed in Table 2, the Eα for the first group is less than that for the second group. This is because the LSC spectrum of α emitter in Ultima Gold AB has larger tailing interference than that in OptiPhase Hisafe 3.
To sum up, both Fig. 5 and 6 have manifested that the results from Present Method are in good agreement with those from Conventional Method.
We take the absolute measurement of uranium concentration in solution as an example. One sample was prepared by pipetting 0.7967 g (about 0.8 mL) uranium standard solution into a 20 mL polyethylene vial and adding 10 mL OptiPhase Hisafe 3. The sample was measured at PSA = 50, 60, 70, 80, 90, 100, 110 and 120. Fitting the count rate in channels 550–720 of α-MCA as described above can obtain that the count rate at the optimum (PSA = 82.2) is 505.5 cpm. Fig. 7 shows the LSC spectra of the sample near the optimum (PSA = 80). The LSC spectrum in α-MCA is assigned to the mixture of 234U, 235U and 238U, the radioactivity percentage of which can be obtained from α spectrometry (Fig. 8). Considering the half-life of 234U (2.445 × 105 years), 235U (7.038 × 108 years) and 238U (4.468 × 109 years),14 we can neglect the contribution of 234U to the uranium mass concentration.
![]() | ||
Fig. 7 The LSC spectra for 0.8 mL uranium standard solution in 10 mL OptiPhase Hisafe 3 at PSA = 80. |
By combining the data shown in Fig. 7 and 8 (peaks unlabelled in Fig. 8 are assigned to 239-240Pu and 241Am which are often measured in our laboratory and may contaminate the detector or chamber), the mass concentration of 235U and 238U can be calculated as 3.2 and 404.6 μg g−1 (the calculation method is similar to that described in ref. 9). As a result, the total uranium mass concentration is 407.8 μg g−1, which is very close to the nominal value 408.5 μg g−1.
One thing should be emphasized here that Present Method eliminates the need to prepare the quench curves for the measurement of samples with different quench levels, leading to that only one sample is needed for this kind of application. But for ref. 9, where Conventional Method was applied, a series of uranium samples with different quench levels had to be prepared and measured. Therefore, the present measurement method is much easier than that in ref. 9.
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