Time optimization of ^{90}Sr determinations: sequential measurement of multiple samples during decay of ^{90}Y
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Abstract
This work presents an optimized method for the determination of multiple samples containing ^{90}Sr when its daughter ^{90}Y is measured after chemical separation and in sequence, i.e. during its decay. Consequently the measurement times will increase for each subsequent sample, since there has been a longer time for decay before measurement. Compared to a previously published approach, when ^{90}Y is measured during its ingrowth, the gain in total analysis time (time for ingrowth+ summation of measurement times) is not that large, particularly not for low background instruments. However, results for a large part of the samples can be delivered earlier.
Keywords
^{89}Sr ^{90}Sr ^{90}Y MDA Detection limit Interferences OptimizationIntroduction
Rapid measurement of one of the most hazardous fission products, radioactive strontium, within a couple of months of e.g. a reactor accident will need a thorough consideration of potential interferences. This is especially important as one relatively long lived radioisotope, ^{89}Sr (t _{½} = 54 days), will interfere when determining the other strontium isotope of interest ^{90}Sr (t _{½} = 28.8 years), via measurement of the daughter nuclide ^{90}Y (t _{½} = 64 hours).
When determining ^{90}Sr there are a multitude of different methods presented in the literature [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. A large part of the methods described in the literature consist of isolating strontium by chemical separation, in order to get samples free from interfering radionuclides, followed by spectrometric measurement of the emitted beta radiation [12, 13, 14, 15, 16]. Another approach is to make use of the fact that the daughter nuclide of ^{90}Sr, ^{90}Y, is a high energy beta emitter. It is therefore possible to measure ^{90}Y by Cherenkov counting, a measurement approach discriminating towards low energy beta radiation (energy threshold in water is 0.263 MeV). A third approach is to measure ^{89}Sr by Cherenkov counting and ^{89}Sr–^{90}Sr by liquid scintillation counting (LSC). By using the known ^{89}Sr activity and then performing spectrum deconvolution the ^{90}Sr activity can be calculated. This approach is however attached with great contributions to the total combined uncertainty for high ^{89}Sr/^{90}Sr activity ratios, a significant increase can be observed between ratios of 10–50, which makes it unsuitable for emergency preparedness situations [17].
Previous works in this area have studied how optimizing determination of ^{90}Sr via ^{90}Y with regards to one sample; n samples (optimizing with regards to the first sample) as well as for a sequential series samples (optimizing with regards to every sample) [18, 19, 20]. In the work by Tovedal et al. [19] and the recently published first part of this work [20] ^{90}Y was measured during ingrowth. Ramebäck et al. described a scenario in which ^{90}Y was isolated from ^{90}Sr, with regards to one sample, and measured during decay [18]. Herranz et al. published a work on optimizing the measurement time for ^{89}Sr/^{90}Sr determination in 2012 [21]. However, the work by Herranz presents a sub optimization seeing as it advocates awaiting full ingrowth of ^{90}Y (approximately 21 days) after chemical separation.
In this work a ^{90}Y measurement method is presented for a case where interference by other high energy beta radionuclides, e.g. ^{89}Sr, other short lived strontium and yttrium radioisotopes as well as ^{140}Ba/^{140}La etc., complicates the Cherenkov measurement approach. The presented work gives the relationship between time allowed for ingrowth of ^{90}Y, before chemical isolation of yttrium, and the allowed individual measurement time for a series of n samples. Important to note is that in this work the sum of all measurement times for all n−1 samples will also be time of decay for sample n (this work also takes into consideration the decay during measurement of sample n).

Total analysis time refers to the sum of the time allowed for ingrowth as well as the sum of all sample measurement times.

Time allowed for ingrowth is defined as the time passed between the first separation on the resin cartridge (i.e. from t = 0 for ^{90}Y) until the isolation of ^{90}Y, in order to determine ^{90}Y by Cherenkov counting.

Sample measurement time (t _{ m,n } ) the time of ^{90}Y measurement for any one individual sample in a sequence consisting of a total of n samples.

Time of decay (t _{ decay,n } ) is the time passed between isolation of ^{90}Y and the following measurement of the same radionuclide, using Cherenkov counting, for any one individual sample in a sequence consisting of a total of n samples.
Theory
Minimal detectable activity (MDA)
The results presented in this work were obtained by solving Eq. 1 with regards to t _{m,n} at an optimum time of ingrowth, and subsequently iterating the equation for the following samples, by means of the method presented by Dekker [22].
This gives a MDA of 0.11 Bq, i.e. a range of 0.57–57 Bq per sample, for ^{89}Sr depending on the sample volume and at the inhouse background count rate. This gives that the total measurement time for ^{89}Sr, and a time of ^{90}Yingrowth, of at least 2.5 h. The time needed for sample preparation as well as the separation procedure have not been taken into consideration in this work, seeing as the procedures differ greatly within the scientific community. However, for the separation method presented in Fig. 1 the time needed for separation and sample preparation can be estimated to 2.5–4 h depending on the sample volume. A rapid method for determination of strontium in milk, as described into Fig. 1, uses 5 ml of sample digested in a MARS5 microwave. Therefore this work will present most of the results for 5 mL, but it will also present some data for ranges of volumes.
Measurement uncertainties
The measurement parameters used in this work. The count rates as well as measurement efficiency are for Cherenkov counting
Parameter  Assumption  Unit 

Number of samples in a series  10  Samples 
Sample volume (V_{sample})  2–200  mL 
^{90}Sr action limit^{a}  100  Bq/L 
MDA per sample  0.1–10  Bq 
Total chemical yield of the strontium analysis  0.5  
Measurement efficiency ^{90}Y  0.65  cps/Bq 
Background countrate  0.007–0.7  cps 
Inhouse background count rate^{b}  0.0136  cps 
Decay constant of ^{90}Y^{c}  3.006 · 10^{−6}  s^{−1} 
Results and discussion
Calculated optimized times for ingrowth and measurement, for a series of ten samples and a MDA of 0.1 Bq
Background count rate (cps)  t _{ingrowth} (h)  Σ(t _{m,n}) (h)  Total analysis time (h)  Measurement time, t _{m,n} (h) 

0.7  Full  N/A  N/A  N/A 
0.35  139  65  204  3.5–13 
0.07  54  28  82  2.1–3.7 
0.007  22  12  34  1.1–1.3 
Moreover, Fig. 3 also illustrates that for higher background count rates (graphs in the lower right and left hand corner) the contribution of the measurement time from the 10th sample to the total measurement time will be larger than for lower count rates. This information is helpful when choosing what volume/mass of sample to analyze (MDA is lowered with increasing volume/mass of sample), as well as what type of instrument to buy.
In order to compare the results, and also the effectiveness, of this work the calculated optimized times are put in contrast to a standard approach. This standard approach assumes that the individual measurement time, t _{m,n}, is the same for each sample. And therefore the solution to Eq. 1 is solved for the 10th sample. The measurement time obtained will result in that all samples in the series will meet the MDA criterion, however, it requires longer t _{ingrowth}.
The difference in measurement, ingrowth and total analysis time (for n = 10), at different MDA and backgrounds, for a standard approach and the results obtained when using the optimized approach presented in this work. All measurement times are given in hours
Method  MDA (Bq)  0.007 cps  0.07 cps  0.7 cps  

t _{ingrowth}  Σ(t _{m,n})  Total  t _{ingrowth}  Σ(t _{m,n})  Total  t _{ingrowth}  Σ(t _{m,n})  Total  
Standard  0.1  26.1  11.4  37.5  85.6  23.0  108.6  Full  N/A  N/A 
1  4.7  2.6  7.3  10.1  4.8  14.9  24.7  10.0  34.7  
5  1.6  1.0  2.6  3.2  1.7  4.9  7.1  3.4  10.5  
10  1.0  0.7  1.7  2.0  1.1  3.1  4.3  2.1  6.5  
Optimized  0.1  22.0  12.5  34.5  56.0  27.6  83.6  Full  N/A  N/A 
1  4.5  2.7  7.2  9.3  5.1  14.4  21.3  10.9  32.2  
5  1.6  1.0  2.6  3.2  1.7  4.9  6.8  3.5  10.2  
10  1.0  0.7  1.7  2.0  1.1  3.1  4.2  2.2  6.4 
Furthermore, this work presents a method that allows for earlier measurement of samples compared to a standard measurement approach, i.e. the first results will be available for decision makers at an earlier point in time. Table 3 shows that the time saved, with regards to total analysis time, is in the range of tenths of hours for low MDA on high background instruments e.g. 0.1 Bq at a background of 0.07 cps.
However the greatest gain is that this method allows whole sets of samples, which will meet the MDA criteria, to be measured at higher background contributions than an unoptimized method.
Conclusions
When performing measurements of ^{90}Y with a purpose of delivering reliable ^{90}Sr results above the action limit [23] it is important to consider the impact of sample volume and instrumental background in order to choose the most time efficient method. This work shows that at low background count rates in combination with a high MDA, e.g. when measuring large amounts of sample, the difference in total analysis time between a standard measurement method and the optimized method is negligible. Nonetheless, there is a great deal of time to save, with regards to sample throughput, for measurements at higher background count rates at low MDA, e.g. small amounts of samples. This implies that for small sample volumes, which generally require less time for sample preparation and strontium separation, the analysis time will be reduced significantly with this method. For a medium background count rate of 0.07 cps there is a total gain of 25 h when measuring to a MDA of 0.1 Bq. Finally, this work shows that by using an optimized measurement approach one can measure eight samples, in the same time frame as it would take to measure three by a standard measurement method, at high background count rates aiming to meet the MDA criterion of 0.1 Bq.
To conclude, the benefits of adjusting the measurement time for each individual sample in a series is most prominent when dealing with anything but low background count rates.
Notes
Acknowledgments
The Swedish Radiation Safety Authority, SSM, Project No. B40082, and the Swedish Ministry of Defence, Project No. A404316, are gratefully acknowledged for funding this work.
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