

ORIGINAL ARTICLE 

Year : 2019  Volume
: 42
 Issue : 1  Page : 59 


A comparative study for ^{235}U radioactivity concentration calculation methods in phosphate samples
A Salman^{1}, Z Ahmed^{2}, Kh A Allam^{3}, S ElSharkawy^{1}
^{1} Department of Physics, Faculty of Science, Sohag University, Sohag, Egypt ^{2} Department of Safeguards, Egyptian Nuclear and Radiological Regulatory Authority, Nasr City, Cairo, Egypt ^{3} Department of Nuclear Law, Egyptian Nuclear and Radiological Regulatory Authority, Nasr City, Cairo, Egypt
Date of Submission  17Dec2018 
Date of Decision  18Feb2019 
Date of Acceptance  19Feb2019 
Date of Web Publication  3Jun2019 
Correspondence Address: A Salman Department of Physics, Faculty of Science, Sohag University, Sohag, Egypt
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/rpe.RPE_77_18
In this study, a comparison is made between the selection of the most proper and accurate methods for ^{235}U activity determination according to the available conditions with the smallest error possible. The detection of ^{235}U activity is used to determine the mass of the ^{235}U in the samples and consecutively, the uranium enrichment which is important for the nuclear safeguards' needs and the monitoring of the radionuclides in the environment. Various methods have been studied to distinguish between counting rate contributions from both^{235}U and ^{226}Ra to the 186 keV energy region in samples of uranium in natural form.
Keywords: ^{235}U activity, activity ratios, gammaray spectrometry, phosphate samples
How to cite this article: Salman A, Ahmed Z, Allam KA, ElSharkawy S. A comparative study for ^{235}U radioactivity concentration calculation methods in phosphate samples. Radiat Prot Environ 2019;42:59 
How to cite this URL: Salman A, Ahmed Z, Allam KA, ElSharkawy S. A comparative study for ^{235}U radioactivity concentration calculation methods in phosphate samples. Radiat Prot Environ [serial online] 2019 [cited 2019 Oct 18];42:59. Available from: http://www.rpe.org.in/text.asp?2019/42/1/5/259674 
Introduction   
The validation of the gamma nondestructive assay technique to quantify the radioactivity of the uranium radioisotopes and to derive a reliable estimation of their isotopic activity ratios (ARs) in samples containing measurable uranium concentrations has become easier, especially after the advent of highresolution gammaray spectrometric techniques.^{[1]}
Furthermore, these measurements are convenient because they generally require less time and cost in comparison with the destructive radioanalytical methods such as αspectrometry or mass spectrometry.^{[2]} This technique is proper in cases where the measured items are sealed or products that cannot be opened or sampled.^{[3]}
The gamma spectroscopic determination of ^{238}U/^{235}U AR has been used as an indication of the presence of depleted uranium (DU) in the environment where it is well known that naturally occurring uranium has a constant^{238}U/^{235}U AR of 21.7.^{[4]}
Hyperpure germanium (HpGe) detectors are widely used for gamma spectrometry measurements. They have special features over other detectors due to their high characteristic resolution. In a few cases, some of the gamma rays emitted by one isotope are very close in energy to gamma rays emitted by other isotopes in the sample. An explicit example of that is the interference between the 185.7 keV photopeak of the ^{235}U and the 186.1 keV photopeak of the ^{226}Ra with branching ratios (fvalue) of 57.2% and 3.5% for ^{235}U and ^{226}Ra, respectively.^{[5]} This problem can be easily solved by many methods to calculate the activity of ^{235}U.
By using the other gamma transitions (143.76 keV [10.96%] and 163.33 keV [5.08%]) with their reasonable branching ratios, one can calculate the activity of ^{235}U. Another approach in deducing^{235}U and ^{226}Ra radioactivity is the determination of ^{226}Ra activity from its daughters (^{214}Pb and ^{214} Bi) in secular equilibrium and subtracts its contribution from the multiple at 186 keV providing an indirect determination of ^{235}U activity. This method is improper in the case of no radioactive equilibrium between^{238}U and ^{226}Ra.^{[6]} If a radioactive equilibrium exists between^{238}U and ^{226}Ra, the contributions of the photons emitted from^{235}U and ^{226}Ra recorded to this multiple photopeak may be calculated, thus allowing for an estimation of the activities of the two isotopes. A mathematical treatment can be performed to extract the net counts contributed by the 185.7 keV photopeak of the ^{235}U and the 186.1 keV photopeak of the ^{226}Ra.^{[7]235}U activity can also be determined through the determination of ^{238}U assuming^{235}U/^{238}U isotopic ratio to be constant for the samples in natural ratio at 7.2 × 10^{−3}.^{[8]}
This work aims to study various methods to distinguish between counting rate contributions from both^{235}U and ^{226}Ra to the 186 keV energy region and also the effects on the results, discuss the advantages and disadvantages of each method to easily calculate both uranium isotopes, and distinguish between samples containing normal, enriched, and DU.
Techniques and Methods   
Nineteen representative samples of phosphate ore were collected from ElSebaiya area, Aswan, Egypt. These samples were prepared for the gamma measurement.
The samples were transferred to cylindrical containers. The container material was polypropylene with a density of 0.946 g/cm^{3}, inner diameter of 6.5 cm, wall thickness of 1.0 mm, height of 6.0 cm, and tare weight of 22.0 g.
The samples were analyzed for their gamma emitters using a spectrometer based on HpGe detector for 43,200 s. The HpGe detector (EG and G Ortec Model GEM100P4) has 100% relative efficiency and a 2.1keV full width at halfmaximum at the 1.33MeV gamma transition of ^{60}Co. The Ortec^{®} GammaVision software (Model A66B32, version 6.00) was used for data analysis.
In the first method, the Ortec GammaVision analytical technique is used to obtain peak areas of the components of a multiplet. It uses peak areas from other parts of the spectrum to determine the areas of some of the components and calculates the remaining areas. It is called peakinterference correction. The activity of ^{235}U is calculated from the area of the peak at the next most probable energy, i.e., 143.76 keV (10.96%). Then, the area of the 185.72 keV (57.2%)^{235}U peak is calculated using the branching ratio of that gamma ray, the efficiency, and the activity. The^{235}U area is subtracted from the area of the peak at 186 keV to obtain the area due to^{226}Ra. From this, the activity of ^{226}Ra in the sample is calculated.
This technique is useful for calculating the activity of ^{235}U and ^{226}Ra, especially in samples that are rich with uranium in natural ratios. That condition is verified in these samples as shown in [Table 1].  Table 1: The specific activities of 238^{U} and the calculated specific activities of 235U by using the interested methods for the measured samples
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In the second method,^{235}U activity can be determined through the determination of ^{238}U assuming^{235}U/^{238}U isotopic ratio to be constant for the samples of phosphate at 7.2 × 10^{−3}. Then,^{235}U activity is calculated using the following equation:^{[8]}
^{235}U (Bq/kg) = (T_{1/2}[^{238}U] × M [^{238}U]/T_{1/2}[^{235}U] × M [^{235}U]) ×^{238}U (Bq/kg) × F (1)
Where T_{1/2}(AX) is the halflife and M (AX) is the atomic mass of the radionuclide AX. Factor F is the ^{235}U/^{238}U isotopic ratio, which is assumed to be constant for soil and rocks at 7.2 × 10^{−3}.^{[9]}
This technique is useful for calculating the activity of ^{235}U and ^{226}Ra, especially in samples that are rich in uranium in a natural ratio and also in^{226}Ra which is not in equilibrium with^{238}U.
The specific activity of ^{238}U activity was determined indirectly from the energy transitions of its daughter^{234}^{m} Pa based on 1001.03 keV (0.837%).^{[10]}
In the third method, ^{226}Ra activity in the sample is estimated using the average activity of ^{214} Bi and ^{214}Pb, where^{226}Ra is in equilibrium with^{214} Bi and ^{214}Pb. Using the reference branching values of ^{226}Ra and ^{235}U,^{235}U activity is determined by the following equation:^{[6]}
A_{U}= 1.75 (CR_{T}/ε_{186}) – 0.063 (A_{Ra}) (2)
Where A_{U} and A_{Ra} are the activities of ^{235}U and ^{226}Ra, respectively. ε_{186} is the detection efficiency (ε) at 185.7 keV and 186.2 keV, which was considered the same for simplicity since the difference would be minimal.
This technique is useful for calculating the activity of ^{235}U and ^{226}Ra, especially in samples that are rich with uranium in a natural ratio and also in^{226}Ra which is not in equilibrium with^{238}U.
In the fourth method, Ebaid et al., 2005,^{[7]} have suggested a reliable empirical equation to separate between counting rate contributions from both^{235}U and ^{226}Ra to the 186 keV energy region. The equation is based on an assumption that^{226}Ra is in equilibrium with^{238}U in the natural samples. It showed that the total count rate of the 186 keV peak consists of 58.3% of ^{226}Ra and 41.7% of ^{235}U at radioactivity equilibrium. Then,
CR_{T}(186) = CR_{Ra}(186.21) + CR_{U}(185.72) (3)
CR_{U}(185.72) = 0.417 × CR_{T}(186) (4)
CR_{Ra}(186.21) = 0.583 × CR_{T}(186) (5)
Where CR_{T} is the total count rate (counts/s) in the 186 keV energy peak, CR_{U} is the count rate due to 185.72 keV of ^{235}U, and CR_{Ra} is the count rate due to 186.21 keV of ^{226}Ra. In addition, these calculations are useful in estimating the ^{226}Ra in samples with no need for the secular equilibrium to happen between^{226}Ra and its respective progenies.^{[6]}
[TAG:2]Results and Discussion[/TAG:2]
The specific activities of ^{238}U and ^{235}U in the samples were calculated in Bq/kg by using the previous four methods, and the values are illustrated in [Table 1].
The specific activity of ^{238}U is ranged from 731.9 ± 106.9 to 905.7 ± 195.0 Bq/kg with an average of 796.1 ± 112.4 Bq/kg. The high errors associated with^{238}U activities are due to the low probability of gamma line intensity of ^{234}^{m} Pa (1001.03 keV [0.837%]).
For^{235}U, it is ranged from 26.4 ± 2.0 to 47.6 ± 3.7 Bq/kg with an average of 37.3 ± 2.7 Bq/kg, from 33.9 ± 5.0 to 41.9 ± 9.0 Bq/kg with an average of 36.9 ± 5.2 Bq/kg, from 26.8 ± 0.8 to 48.6 ± 2.0 Bq/kg with an average of 37.0 ± 1.1 Bq/kg, and from 32.7 ± 1.5 to 43.2 ± 3.1 Bq/kg with an average of 35.7 ± 1.9 Bq/kg by using the methods 1, 2, 3, and 4, respectively.
The agreement in the maximum values of ^{238}U and ^{235}U activity concentrations with the sample number 13 and approximate agreement of the average values of ^{235}U activity concentrations in Bq/kg (37.3 ± 2.7, 36.9 ± 5.2, 37.0 ± 1.1, and 35.7 ± 1.9, by using the methods 1, 2, 3, and 4, respectively) verify the validation of all these methods for calculating the ^{235}U activity, and ^{235}U can be measured directly if corrected to subtract the contribution from^{226}Ra.
By using the activity concentrations of ^{238}U and ^{235}U in [Table 1], the average values of the ^{238}U/^{235}U ARs were 22.0, 21.6, 21.9, and 22.3 by using the methods M1, M2, M3, and M4, respectively. [Figure 1] shows how^{238}U/^{235}U ratios vary from the natural ratio (21.7).  Figure 1:^{238}U/^{235}U ratios versus the sample ID by using the different methods
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By using the first method (M1), the little deviation in the ^{238}U/^{235}U AR (22.0) from the natural ratio (21.7) maybe due to the selfabsorption effects and the low yield value in 143.76 keV (10.96%) gamma line. The low precision of the ^{238}U/^{235}U ARs around the natural ratio (21.7) as shown in [Figure 1] and the absence of correlation (R^{2}= −0.021) within the results as shown in [Figure 2] would have also been arisen from these effects. Despite these effects, this method provides an uncertainty of 1.5% based on the natural ratio 21.7.
By using the second method (M2), the tiny deviation in the ^{238}U/^{235}U AR (21.6) from the natural ratio (21.7) maybe due to the low probability of gamma line intensity (low yield value) of ^{234}^{m} Pa (1001.03 keV [0.837%]) and the low value of the detector efficiency at high energies that used of calculating of ^{238}U by^{234 m} Pa in 1001.03 keV. An extreme precision in the ^{238}U/^{235}U ARs around the natural ratio (21.7) is clear as shown in [Figure 1], and a perfect correlation (R^{2} = 1.0) within the results as shown in [Figure 3] that can be attributed to the ^{238}U activity is the only variable factor in the calculations. Hence, this method provides an insignificant uncertainty of 0.5% based on the natural ratio 21.7.
By using the third method (M3), the little deviation in the ^{238}U/^{235}U AR (21.9) from the natural ratio (21.7) can be interpreted due to the emanation of radon from the sealed sample, the samples' homogeneity error effects, the collection of the gaseous radon on the surface of the samples, the selfabsorption effects, especially in 295.1 keV and 351.93 keV gamma lines, and the low values of the detector efficiency at the high energies that are used in calculating^{214} Bi by using 1120.28 keV (15.12%) and 1764.5 keV (15.4%) gamma line emission. The low precision of the ^{238}U/^{235}U ARs around the natural ratio (21.7) as shown in [Figure 1] and the small correlation (R^{2} = 0.04) within the results as shown in [Figure 4] may be because the calculations depend on the assumption^{226}Ra is in equilibrium with^{214} Bi and ^{214}Pb, the ^{226}Ra /Avg.^{214} Bi &^{214}Pb activity ratio has always a little deviation from unity resulting from the previous effects, and in addition to these effects, the calculations are depending on variable factors CR_{T} and A_{Ra} also the detection efficiencies (ε) at 185.7 keV and 186.2 were considered the same for simplicity as described in details in an earlier work.^{[11]} However, this method provides an uncertainty of 1.0% based on the natural ratio 21.7.
By using the fourth method (M4), the little deviation in the ^{238}U/^{235}U AR (22.3) from the natural ratio (21.7) is maybe due to the selfabsorption effects, especially in 185.72 keV gamma line, the low probability of gamma line intensity (low yield value) of ^{234}^{m} Pa (1001.03 keV [0.837%]), and the low value of the detector efficiency at high energies that used of calculating of ^{238}U by^{234 m} Pa in 1001.03 keV. This method appears to have a high precision of the ^{238}U/^{235}U ARs around the natural ratio (21.7) as shown in [Figure 1] and a strong correlation (R^{2} = 0.54) within the results as shown in [Figure 5]. In addition, this method gave the largest average^{238}U/^{235}U AR above the natural ratio (21.7) because the total count rate of the 186 keV peak consists of 58.3% of ^{226}Ra and 41.7% of ^{235}U at radioactivity equilibrium as shown in an earlier work.^{[11]} This method provides an uncertainty of 2.9% based on the natural ratio 21.7.
Conclusions   
Various methods have been used to distinguish between counting rate contributions from both^{235}U and ^{226}Ra to the 186 keV energy region provided consistent and similar results in the calculation of the radioactivity of ^{235}U either^{226}Ra in equilibrium or not with^{238}U.
The comparison between the activity concentration results of ^{235}U calculated by using different methods has been studied with associated uncertainties. The studied methods provide a mean^{238}U/^{235}U AR with little deviations from the natural ratio.
By comparing the ^{238}U/^{235}U ARs by using different methods, it is clear that the second method gives the most accurate and precise results in the present studied samples. Hence, it is recommended to use this method in the similar samples.
The proposed work might be very useful to calculate the concentration of ^{235}U in other types of samples, especially lowactivity samples by using different HPGe crystals.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5]
[Table 1]
