• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.20 no.2
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• pp.171-183
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• 2022

The parent and daughter nuclides in a radioactive decay chain arrive at secular equilibrium once they have a large half-life difference. The characteristics of this equilibrium state can be used to estimate the production time of nuclear materials. In this study, a mathematical model and algorithm that can be applied to radio-chronometry using the radioactive equilibrium relationship were investigated, reviewed, and implemented. A Bateman equation that can analyze the decay of radioactive materials over time was used for the mathematical model. To obtain a differential-based solution of the Bateman equation, an algebraic numerical solution approach and two different matrix exponential functions (Moral and Levy) were implemented. The obtained result was compared with those of commonly used algorithms, such as the Chebyshev rational approximation method and WISE Uranium. The experimental analysis confirmed the similarity of the results. However, the Moral method led to an increasing calculation uncertainty once there was a branching decay, so this aspect must be improved. The time period corresponding to the production of nuclear materials or nuclear activity can be estimated using the proposed algorithm when uranium or its daughter nuclides are included in the target materials for nuclear forensics.

• Journal of Radiation Protection and Research
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• v.42 no.1
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• pp.33-41
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• 2017

Background: Phosphate rock and its by-product are widely used in various industries to produce phosphoric acid, gypsum, gypsum board, and fertilizer. Owing to its high level of natural radioactive nuclides (e.g., $^{238}U$ and $^{226}Ra$), the radiological safety of workers who work with phosphate rock should be systematically managed. In this study, $^{238}U$, $^{232}Th$, $^{226}Ra$, and $^{40}K$ levels were measured to analyze the transport characteristics of these radionuclides in the production cycle of phosphate rock. Materials and Methods: Energy dispersive X-ray fluorescence and gamma spectrometry were used to determine the activity of $^{238}U$, $^{232}Th$, $^{226}Ra$, and $^{40}K$. To evaluate the extent of secular disequilibrium, the analytical results were compared using statistical methods. Finally, the distribution of radioactivity across different stages of the phosphate rock production cycle was evaluated. Results and Discussion: The concentration ratios of $^{226}Ra$ and $^{238}U$ in phosphate rock were close to 1.0, while those found in gypsum and fertilizer were extremely different, reflecting disequilibrium after the chemical reaction process. The nuclide with the highest activity level in the production cycle of phosphate rock was $^{40}K$, and the median $^{40}K$ activity was $8.972Bq{\cdot}g^{-1}$ and $1.496Bq{\cdot}g^{-1}$, respectively. For the $^{238}U$ series, the activity of $^{238}U$ and $^{226}Ra$ was greatest in phosphate rock, and the distribution of activity values clearly showed the transport characteristics of the radionuclides, both for the byproducts of the decay sequences and for their final products. Conclusion: Although the activity of $^{40}K$ in k-related fertilizer was relatively high, it made a relatively low contribution to the total radiological effect. However, the activity levels of $^{226}Ra$ and $^{238}U$ in phosphate rock were found to be relatively high, near the upper end of the acceptable limits. Therefore, it is necessary to systematically manage the radiological safety of workers engaged in phosphate rock processing.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.15 no.1
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• pp.35-44
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• 2017

A gamma-ray peak of $^{226}Ra$ (186.2 keV) overlaps with one of $^{235}U$ (185.7 keV) in a gamma-ray spectrometry system. Though reference peaks of $^{235}U$ can be used to correct the peak interference of $^{235}U$ in the analysis of $^{226}Ra$, this requires a complicated calculation process and a high limit of quantitation. On the other hand, evaluating $^{226}Ra$ using the correction constant in the overlapped peak can make a rapid measurement of $^{226}Ra$ without the complicated calculation process as well as overcome the disadvantage in the indirect measurement of $^{214}Bi$, which means the confinement of $^{222}Rn$ gas in a sample container and a time period to recover the secular equilibrium. About 93 samples with 6 species for raw-materials and by-products were prepared to evaluate the activity of $^{226}Ra$ using the correction constant. The results were compared with the activity of $^{214}Bi$, which means the indirect measurement of $^{226}Ra$, to validate the method of the direct measurement of $^{226}Ra$ using the correction constant. The difference between the direct and indirect measurement of $^{226}Ra$ was generally below about ${\pm}20%$. However, in the case of the phospho gypsum, a large error of about 50% was found in the comparison results, which indicates the disequilibrium between $^{238}U$ and $^{226}Ra$ in the materials. Application results of the contribution ratio of $^{226}Ra$ were below about ${\pm}10%$. The direct measurement of $^{226}Ra$ using the correction constant can be an effective method for its rapid measurement of raw materials and by-products because the activity of $^{226}Ra$ can be produced with a simple calculation without the consideration of the integrity of a sample container and the time period to recover the secular equilibrium.

• The Journal of the Petrological Society of Korea
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• v.10 no.3
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• pp.148-156
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• 2001

We report $^{230}Th/^{234}U$ disequilibrium ages of fracture-filling carbonate veins from the Ipsil and Janghangri fault zones, Gyeongju, Korea by multiple collector inductively coupled plasma mass spectrometry. The U and Th fraction was extracted from totally dissolved samples by rapid and convenient coprecipitation and ion exchange chemistry. The recovery was around 80% for Th and 70% for U. The $^{234}U/^{238}U,\;^{230}Th/^{232}Th$ ratios were analysed for this preconcentrated fraction and the U/Th ratio was directly analysed for untreated sample solution. The $^{234}U-^{230}Th$ system is in secular equilibrium for the Ipsil carbonate samples, supporting previously reported ESR ages. The detrital-corrected $^{230}Th/^{234}U$ age of the Janghangri carbonate samples is $48\pm$41 ka, which constrains the minimum age of the fracture zone.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.12 no.2
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• pp.97-105
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• 2014

In the case of the direct measurement of $^{226}Ra$ using a HPGe gamma-ray spectrometer, the interference between gammarays with 186.21 keV of $^{226}Ra$ and 185.7 keV of $^{235}U$ should be corrected to calculate the net peak area in the energy spectrum. In general, it is very difficult to conduct peaks stripping with difference of about 0.5 keV, although a HPGe with the superior resolution is applied and the maximum channels is applied to the spectrometer. In this study, several interference correction techniques in the direct measurement were surveyed to evaluate the feasibility for the measurement of $^{226}Ra$ using the gamma-ray spectrometery. Applying the interference corrections to the analysis of raw materials and by-products, the method validation for the direct measurement of $^{226}Ra$ was conducted by evaluating the measurement uncertainty, linearity, and range. As a result, the optimum method of the interference correction was selected by comparing with the indirect measurement of which progenies of $^{226}Ra$, such as $^{214}Pb$ and $^{214}Bi$, were analyzed in the secular equilibrium state.