Introduction

Measuring uranium is important in many studies such as the monitoring and warning of nuclear activity [1], the evaluation of the radiological naturally occurring radioactive material concentrations and the impact on workers and public members [2], the interpretation of the luminescence dating of sediment [3, 4], the assessment of radioactivity to prevent public health risks [5,6,7]. The activity of uranium isotopes and their decay daughters can be determined by inductively coupled plasma mass spectrometry [8], alpha spectrometry [9, 10], and liquid scintillation counting [11]. However, these methods require lengthy and complicated destructive techniques for the samples with an unknown chemical matrix which make the whole process inconvenient and costly.

Gamma spectrometry is a widely used non-destructive measurement technique for the determination of radioactive materials in environmental samples. Its advantages are not requiring laborious sample preparation whilst providing information of various radionuclides at the same time. 238U activity concentration is indirectly calculated based on the activities of 214Pb and 214Bi if the secular equilibrium exists in the analysis sample [12, 13]. In addition, 234Th is the nearest daughter of 238U and has a short half-life (24.10 ± 0.03 days [14]) compared to 238U (4.468 ± 0.005 billion years). This can lead to the secular equilibrium between 238U and 234Th in the soil, rock, and sediment samples if the effect of geochemical processes is ignored [15]. Therefore, the direct measurement of the 63.3 keV peak emissions can give simultaneous information on 234Th and its parent 238U in the sample [16, 17]. On the gamma-ray spectra, the energy region of 63 keV is overlapped by three gamma-rays including the 63.3 keV peak emitted from 234Th (3.75 ± 0.08% emission probability), 63.9 keV peak emitted from 231Th (0.0235 ± 0.0021%), and 63.8 keV peak emitted from 232Th (0.259 ± 0.015%). The nuclide 231Th is the nearest daughter of 235U. Because natural uranium comprises a small proportion of 235U (0.72% of natural uranium) and the emission probability of the 63.9 keV gamma-ray (231Th) is lower than the 63.3 keV (234Th) and 63.8 keVgamma-rays (232Th), the interference of 231Th at the 63 keV region can be neglected. However, the contribution of 232Th leads to the remarkably large systematic influence of 0.8–122% in the measured 238U activity via the gamma-ray 63.3 keV of 234Th [18]. Besides, the self-absorption correction (Cabs) is also a large uncertainty associated with 234Th measurements at the peak of 63.3 keV.

These Cabs factors of samples with 3.3 mm thickness are approximately 4% for moss soil (IAEA-447), 15% for phosphogypsum (IAEA-434) [19], on the contrary, it is 8% for a Marinelli beaker geometry with about 0.5 litter volume of soil [20], and 7–20% for phosphate rocks thickness varying from 10 to 50 mm [21]. Therefore, a reliable analysis of 238U activity according to the 63.3 keV peak requires taking into account the accurate corrections for the self-absorption effect as well as the contribution of 232Th at the 63 keV region.

Natural uranium consists of three main radioactive isotopes 238U (99.2745% abundance), 235U (0.72%), and 234U (0.0055%). The 235U analysis from the peak of 143.8 keV (0.94 ± 0.06% emission probability), 163.4 keV (5.08 ± 0.03%), and 205.3 keV (5.02 ± 0.03%) energy transitions is impossible because the counting rates due to these peaks are often below the detection limits of the HPGe p-type detector. For that reason, the activity concentration of 235U is generally determined from the peak of 185.7 keV (57.0 ± 0.3% emission probability) after the subtracting of 226Ra contribution at 186.2 keV (3.56 ± 0.02%) [22, 23]. The determination of 226Ra by gamma spectrometry has been based on the detection of emissions of its daughter nuclides 214Pb and 214Bi in the secular equilibrium [24,25,26]. The disadvantages of this method are that it requires a long waiting time to ensure the secular equilibrium of 226Ra—its progeny (at least a month) and it requires the calculation of the coincidence summing correction factor for gamma-rays emitted from 214Pb or 214Bi, which can lead to a relative deviation of 40% for the measured 238U activity concentration [27].

In this work, a rapid and reliable analytical procedure is applied to determine the activity concentration of 238U and 235U using the gamma-rays of 63.3 keV emitted from 234Th and 185.7 keV emitted from 235U. This procedure is focused on the careful consideration of the detection efficiency, the self-absorption correction, the coincidence summing correction, and the contributions of 232Th and 226Ra for the energy region of 63 keV and 186 keV, respectively. Its advantage is it may be applied immediately after the sample preparation regardless of the existence of a secular equilibrium between 226Ra and its progenies (214Pb, 214Bi) and regardless of the existence of equilibrium between 238U and 226Ra or normal 235U-238U isotopic ratio. The certified reference material (CRM) samples with varying amounts of uranium and thorium are measured for the calculation of the activity concentration of 238U and 235U by using the advanced analytical procedure. The results of radioactivities are evaluated in the IAEA proficiency test.

Theory

Monte Carlo simulation

Monte Carlo simulation with MCNP-CP upgrade patch version 3.2 was a powerful and reliable tool for the simulation of modeling real source responses and efficiencies of the detector. It was developed to upgrade the standard MCNP version 6 software. The properties of a decay scheme of a particular radionuclide were considered from the evaluated nuclear structure data file [28]. CPS card (Correlated Particle Source) was used to perform the statistical simulation of processes accompanying the radioactive decay of a specified radionuclide, yielding correlated characteristics of emitted particles, and tracked within the same history. The model simulation of detector, lead shield, and the sample container was described in a similar way to the experimental system.

The element concentrations taken from Table 1 were used for the simulations. Two simulated responses were obtained for each radionuclide emitting cascade gamma-rays. The first output file was defined with an uncorrelated source, which can be obtained by tracking each gamma-ray in separate history (FEP efficiency “without—\(\varepsilon_{wo} ({\rm E})\)”). The second output file showed that the result corresponded to the case of total correlation between all the particles emitted, which were tracked within the same historical (FEP efficiency “with—\(\varepsilon_{w} ({\rm E})\)”). The relative uncertainty was adjusted to be less than 0.01% with the 109 number particles of 109 historical simulations. The coincidence summing correction factor (CSF) for gamma-rays emitted from radionuclides in the 235U, 238U, and 232Th series was calculated by the equation:

$$ CSF = \frac{{\varepsilon_{wo} ({\rm E})}}{{\varepsilon_{w} ({\rm E})}} $$
(1)
Table 1 The information of the samples
Full size table

The material samples were placed in a cylindrical container of the same geometric scale, but they were composed of entirely different materials. Therefore, the self-absorption correction factor (Cabs) was required to account for differences in attenuation coefficients for the samples as follows [29]:

$$ {\text{C}}_{{{\text{abs}}}} { = }\frac{{\mu_{2} {\text{(E)}}}}{{\mu_{1} {\text{(E)}}}} \times \frac{{1 - \exp ( - \mu_{1} {\text{(E)}} \times x)}}{{1 - \exp ( - \mu_{2} {\text{(E)}} \times {\text{x}})}}. $$
(2)

where \(x = 2\,cm\) is the thickness of the samples, \(\mu_{1} (E)\) and \(\mu_{2} (E)\) are the linear attenuation coefficients (cm−1) for energy E of the RGU standard and the analysis samples, respectively.

We considered three approaches for determining the self-absorption correction factor at the 63.3 keV peak, including:

  • First method the total attenuation of the sample, \(\mu_{\rho } {\text{(E)}}\) (cm2 g−1), was taken from the XCOM database [30] and calculated the linear attenuation coefficient by formula \(\mu = \mu_{\rho } {\text{(E)}} \times \rho\), where \(\rho \,(g\,cm^{ - 3} )\) was density. The self-absorption correction factor was determined by using Eq. (2).

  • Second method the gamma spectra of MCNP-CP simulation was used to calculate the linear attenuation coefficient. The input file of MCNP-CP code was performed using the densities of samples from 0.2 to 2.2 (g cm−3) with an increment of 0.2 (g cm−3), the samples thicknesses from 0.2 to 3.0 cm with 0.2 cm increment. According to the method from Huy et al. [31], the effective attenuation coefficient \(\mu_{eff} \,(cm^{ - 1} )\) can be calculated from two fitting curves. The first curve was an exponential function for the relationship between the simulation FEP efficiencies and the sample densities. As the result, the effective attenuation coefficient was calculated with each thickness of the sample and a mass attenuation coefficient can be expressed by formula \(a\, = \mu_{eff} /\rho\), where \(a\,(cm^{2} \,g^{ - 1} )\). The second fitting curve was a quadratic polynomial function that illustrated the relationship between the mass attenuation coefficients and the samples thickness. Finally, the self-absorption correction factor was determined by using Eq. (2).

  • Third method the self-absorption correction factor can be obtained as the ratio of the FEP efficiencies between the standard sample (\(\varepsilon_{0} (E)\)) and the analytical sample (\(\varepsilon (E)\)) from the same sample-detector geometry (Eq. (3)), which were simulated by MCNP-CP code with an uncorrelated source:

    $$ {\text{C}}_{{{\text{abs}}}} { = }\frac{{\varepsilon_{0} (E)}}{\varepsilon (E)}. $$
    (3)

Experimental

Gamma spectrometric measurements are done using the coaxial p-type HPGe detector (supplied by ORTEC, GEM50P4-83 model) with a crystal diameter of 65.9 mm, crystal length of 77.0 mm, and relative efficiency of 50% [32]. The energy resolution (FWHM) at 122 keV (57Co) and 1332 keV (60Co) are 0.9 keV and 1.9 keV, respectively. The detector is shielded by a cylindrical low-background lead with different thicknesses of low-carbon steel, lead, tin, and copper layers of 13 mm, 101 mm, 0.5 mm, and 1.6 mm, from outside to inside, respectively. The gamma spectra are acquired 16,384 channels to record photon energy up to 3000 keV by Maestro software [33]. The analysis of spectrometric data is performed by Colegram software [34] aimed at obtaining the best results for the peaks of interest.

The RGU standard and the CRM samples, needed to validate the advanced analytical procedure, were supplied by the International Atomic Energy Agency (IAEA). Five rock samples (labeled from S1 to S5) were collected in Southern Vietnam. All samples were prepared by grinding to powder, then drying the powder at 105 ± 10 °C to a constant weight. They were sieved using a 200 µm sieve, then the powder obtained was homogenized. Each sample was split. One part was used to analyze radionuclides. The powder was packed in a cylindrical polyethylene container with an external diameter of 75 mm, an external height of 47 mm, a wall thickness of 1 mm, and was pressed to a thickness of 20 mm. This process had been applied to handle geological samples and has proven reliable to get radon (222Rn, had an approximate half-life of 3.82 days) not escape from the container [25]. The sample containers were positioned on the detector endcap, aligned with the detector axis. Acquisition time ranged from 86 400 to 172 800 s for the gamma spectra of the background and samples.

The analytical procedure to determine direct radioactivity in solid samples is presented in Fig. 1. The heavy metals in samples were analyzed by the X-ray fluorescence system (model S2-Puma, [35]). Oxygen concentration was calculated by excluding the total of other elements. The element concentration results to be used for the correction of self-absorption for each sample are presented in Table 1.

Fig. 1
figure 1

Overview of the advance analytical procedure applied to determine directly the activity concentration of 238U and 235U by gamma spectrometry

Full size image

Calculations

The activity concentration of radionuclide for each peak with energy E is calculated by the following formula:

$$ {\text{A}}_{i} { = }\frac{{{\text{N}}_{P} \left( {E_{i} } \right)}}{{{\text{I}}_{\gamma } \left( {E_{i} } \right) \times \varepsilon_{P} \left( {E_{i} } \right) \times {\text{m}} \times {\text{t}}}}\Pi C_{i} , $$
(4)

where \(A_{i}\), m, t, \({\text{N}}_{P} \left( {E_{i} } \right)\), \({\text{I}}_{\gamma } \left( {E_{i} } \right)\), \(\varepsilon_{P} \left( {E_{i} } \right)\) are the activity concentration (Bq kg−1), the dry mass (kg), the acquisition live time (s), the net peak areas, the emission probability of separate gamma-rays, the FEP efficiency, respectively. \(\Pi C_{i}\) is the product of different correction factors such as the coincidence summing effect, self-absorption effect, etc.

Because the total counts of the 63 keV region includes the contribution counts of 232Th (63.8 keV, 0.26 ± 0.02% emission probability) and 234Th (63.3 keV, 3.75 ± 0.08%), the counts at the peak 63.3 keV (234Th) can be calculated by using the formula:

$$ N_{{{}^{234}Th}}^{63.3} = N_{total}^{63} - N_{{{}^{232}Th}}^{63.8} = N_{total}^{63} - \frac{{A_{{{}^{232}Th}} \times \varepsilon_{63.8} \times I_{{{}^{232}Th}}^{63.8} \times m \times t}}{{\Pi C_{i}^{63.8} }}. $$
(5)

The activity concentration of 232Th \((A_{{^{232} Th}} )\) is calculated based on the mean activity of respective progenies such as 228Ac (338.3, 911.2 and 969.0 keV), 212Pb (238.6 keV), and 208Tl (583.2 keV), using the following formula:

$$ {\overline{\text{A}}}\,\;{ = }\frac{{\sum\limits_{{\text{i = 1}}}^{{\text{n}}} {\frac{{{\text{A}}_{{\text{i}}} }}{{{\text{u}}_{{\text{i}}}^{{2}} }}} }}{{\sum\limits_{{\text{i = 1}}}^{{\text{n}}} {\frac{{1}}{{{\text{u}}_{{\text{i}}}^{{2}} }}} }}, $$
(6)
$$ \overline{u} \, = \, \frac{1}{{\sqrt {\sum\limits_{i = 1}^{n} {\frac{1}{{u_{i}^{2} }}} } }}. $$
(7)

where n is the number of isotopes, Ai and ui are the activity concentration and absolute uncertainty of ith isotopes, respectively.

Similarly, the counts of the 186 keV region includes the contribution counts of 235U (185.7 keV, 57.0 ± 0.3% emission probability) and 226Ra (186.2 keV, 3.56 ± 0.02%). The contribution of 235U at the 186 keV energy region can be calculated by the formula:

$$ {\text{N}}_{{^{235} U}}^{185.7} = N_{total}^{186} - \frac{{{\text{A}}_{{^{226} Ra}} \times {\text{I}}_{{^{226} Ra}}^{186.2} \times \varepsilon_{186.2} \times {\text{m}} \times {\text{t}}}}{{\Pi C_{i}^{186.2} }}. $$
(8)

The half-life of 226Ra is very small compared with 238U (1600 years compared with 4.468 billion years, respectively). When the sampling area has not undergone recent geochemical changes and there are no natural disturbances of the decay series, the secular equilibrium can exist between 238U and its progenies (234Th, 226Ra, 214Pb, 214Bi). The present work considers three options for the evaluation of 226Ra content including the calculated activity of 226Ra based on the direct measurement of 234Th 63.3 keV line (First option), using the correction factor of 57.2% 226Ra at the 186 keV region (Second option), and the calculating mean activity of 226Ra based on its daughters (214Pb and 214Bi) (Third option). The 235U specific activity will be determined by using Eq. (4) and Eq. (8).

Minimum detectable activity (MDA) is an important parameter in low-level activity measurements using the gamma spectrometry. It depends on the detector efficiency for photon energy, emission probability, acquisition time, etc. In the case of peaked backgrounds, the MDA for each energy of radionuclide is calculated by the formula [36]:

$$ {\text{MDA}} = {\text{w}} \times \frac{{k^{2} + 2k\sqrt {B + B\frac{N}{2n}} }}{{1 - (k \times \sigma_{{\text{w}}} )^{2} }}. $$
(9)

where N is the number of channels in the peak region, B is the background number of counts in N channels, n is the number of channels at the left and right of the ROIs, \({\text{w}} = \frac{1}{{\varepsilon_{P} (E_{i} ) \times I_{\gamma } (E_{i} ) \times m \times t}}\), \(\sigma_{{\text{w}}}\) is the fractional uncertainty of w. The coverage factor used is \(k = 1.645\). The count number of the background is calculated by interpolating the continuous background under the peak from the adjacent regions in a gamma-ray spectrum. The ROIs used for calculating B is four times the FWHM and adds two channels to the left and two channels to the right of an expected centroid. According to the law of uncertainty propagation, MDA's relative uncertainty is evaluated.

Results and discussion

Validation of MCNP-CP calculating the coincidence summing and self-absorption corrections

The reliability of MCNP-CP code for calculating coincidence summing correction factor (CSF) in gamma spectrometry considering volume source has been performed by the testing equivalence of computer codes [32, 37]. In this study, the CSF for 235U, 234Th, 226Ra, 214Pb, 214Bi, 228Ac, 212Pb, and 208Tl were determined by MCNP-CP simulation (Supplementary data). The CSF results were ranging from 0.97 to 1.21 and presented a good agreement with the results from Ordóñez et al. [38].

Figure 2 illustrates the self-absorption correction factors for 63.3 keV gamma-ray which were calculated by all three methods with the range of 0.93 to 1.08. These results were compared to the correction factors from Thanh et al. [19] and showed a good agreement with the maximum relative deviation of 5.8% and 3.2% for IAEA-434 and IAEA-447 samples, respectively. Table 2 presented the statistical pairwise comparison of the self-absorption correction factors at the peak of 63.3 keV (234Th) for the samples including IAEA-434, IAEA-447, RGTh, and S1-S5 samples. The contrast means the differences in the comparison of the different methods. The result of the contrast was -0.0038 showing that the self-absorption correction factor at the peak of 63.3 keV with the second method was lower than the first method by 0.0038 with a 95% confidence interval -0.0623 to 0.0548. In contrast, the self-absorption correction factor of the third method was higher than that of the first and second methods by 0.0038 and 0.0075, respectively. This confirms that the self-absorption correction factor calculated by the third method was reliable to apply to the measurement of gamma-emitting radionuclides in solid samples. There were several explanations including:

  • The first method was simple and quick to estimate the self-absorption factor for the analytical sample. However, it was based on the assumption of a parallel photon beam in Eq. (2), which was not fulfilled in the applied close measurement geometry. In fact, the radiations originating from the side of the sample near the detector would be less likely to be attenuated than the radiations from deep within the sample, which must pass through the material of the sample to reach the detector.

  • The second method confirmed the reliability of the Monte Carlo calculation for the self-absorption factor of the 63.3 keV gamma-ray. However, this method required a large amount of data from the simulation, which was used to fit with the mathematical functions.

  • Regarding the third method, the self-absorption correction factor was determined by the ratio of FEP efficiency between the standard sample and the analytical sample that was calculated by the MCNP-CP simulations in the same close measurement geometry. Therefore, it depended only on the sample thickness, density and chemical composition and not on geometry effects [31, 39].

Fig. 2
figure 2

The self-absorption correction factor at the peak of 63.3 keV (234Th) for the samples

Full size image
Table 2 The pairwise comparisons of the results of the self-absorption correction factor at the peak of 63.3 keV (234Th) for the samples
Full size table

Impact of the 186.2 keV peak on the experimental full energy peak efficiency calibration curve

The RGU sample (activity concentration 4940 ± 30 Bq kg−1) was used to establish the calibration FEP efficiency curve for the HPGe detector in the energy range from 46.5 to 2447.9 keV. The experimental efficiencies were determined at the sixteen energies of gamma-rays which were emitted from radionuclides such as 210Pb (46.5 keV), 234Th (63.3 and 92.5 keV), 226Ra (186.2 keV), 214Pb (242.0, 295.2, and 351.9 keV) and 214Bi (609.3, 768.4, 934.1, 1120.3, 1238.1, 1281.0, 1764.5, 2204.2, and 2447.9 keV). The CSF of these radionuclides was calculated by MCNP-CP code. The relative uncertainty of experimental efficiency for the 234Th doublet gamma emission at 92.5 keV (total emission probability 4.33 ± 0.38%) was 8.8%, which corresponded to the combined standard uncertainties (k = 1) [40]. This doublet was the mean energy of 92.4 keV (2.18 ± 0.19%) and 92.8 keV (2.15 ± 0.19%) energy transitions from 234Th decay. Moreover, several researchers have noted that thorium has Kα1 X-ray at 93.3 keV, which will overlap at 92.5 keV, so it is very difficult to correct for analyzing 234Th at this energy on the gamma spectrum [41]. The relative uncertainties of the experimental efficiencies for the other gamma-ray energies were less than 2.5%. Two cases were applied to investigate the results of the calibration FEP efficiency curves (Fig. 3), given by:

  • Case I using fifteen values of the experimental efficiencies for radionuclides 210Pb, 234Th, 214Pb, 214Bi, and without experimental efficiency at the peak of 186.2 keV (226Ra).

  • Case II using sixteen values of the experimental efficiency for radionuclides. The correction factor of 0.572 was used to correct the count of 226Ra at the peak of 186.2 keV [25].

Fig. 3
figure 3

Calibration of full energy peak efficiency curves using the RGU standard

Full size image

Each case of FEP efficiency was fitted with a log–log polynomial by using the ACORES software [42]. Single way ANOVA [43] with the in-significant value for Bartlett's statistic (0.994) proved a statistically insignificant difference among the three group means. The result showed that the significance level (p-value) was 0.9917, which was over 0.05. In other words, there were no discriminants among FEP efficiencies (Table 3).

Table 3 Analysis of ANOVA presents the homogeneity of variances
Full size table

Figure 3 illustrates the sixteen values of the experimental efficiencies and case I of the FEP efficiency curve and case II of the FEP efficiency curve. At energies 46.5 keV, 63.3 keV, 186.2 keV, the relative deviations between the experimental value and the interpolated value from the case I curve are − 23.2%, 16.7%, − 6.3%, respectively, and the relative deviations between the experimental value and the interpolated value from the case II curve are − 4.7%, 5.3%, 5.3%, respectively. These lead to the efficiency values at the 46.5 keV, 63.3 keV, and 186.2 keV peak interpolated from the case I and case II of FEP efficiencies curves having the relative deviation of 10.5%, 35.6%, and 3.3%, respectively. It showed that the FEP efficiency value at 186.2 keV energy strongly affected the calibration FEP efficiency curve for the HPGe detector.

Figure 4 shows the ratio of MDA results and reference activity for CRM samples. The MDA-II value of 234Th (63.3 keV) in the RGTh sample is compared with the MDA-I value, with an improvement of 35.6%, and is lower than the certified reference activity. In addition, the MDA-II for 226Ra (186.2 keV) for S1-S5 samples had a range from 3.42 ± 0.4 (Bq kg−1) to 6.23 ± 0.5 (Bq kg−1) and they were lower than the calculated MDA results by liquid scintillation counting [44], and by alpha spectrometry [45].

Fig. 4
figure 4

Comparison of the minimum detectable activity with the reference activity for the IAEA-434, IAEA-447, and RGTh samples

Full size image

Confirmation of the analytical procedure using certified reference materials

In this work, the samples of the certified reference materials IAEA-434, IAEA-447, and RGTh were used to confirm the analytical procedure. According to Eq. (4), the activity concentration of radionuclides for the 232Th, 238U, and 235U series were derived from the net peak areas, the photon emission probability, the calibration FEP efficiency curves of both cases (Case I and Case II), the self-absorption factor and coincidence summing correction factor. Relative bias (RB) between the measured and certified activity was determined by the formula:

$$ RB(\% ){ = }\frac{{\left| {{\text{A}}_{{{\text{measured}}}} - {\text{A}}_{certified} } \right|}}{{{\text{A}}_{certified} }} \times { 100}{\text{.}} $$
(10)

The IAEA assesses the proficiency test procedure in terms of both accuracy and precision. The accuracy-test compared the relative bias to the maximum acceptable relative bias (MARB) which had a range from 15 to 30% for gamma-ray emitting radionuclides [46]. For all radionuclides in this study, the MARB value was set at 15%. If RB > MARB, the accuracy-test marked the value as “Not accepted”. Precision-test was applied if the measured value satisfied the accuracy-test (RB ≤ MARB): RB ≤ k × P and P ≤ MARB. The coverage factor k = 2.58 with a probability of confidence level of 99%. The precision-test (P) was calculated by the equation:

$$ P(\% ) = \sqrt {\left( {\frac{{u_{{A_{measured} }} }}{{A_{measured} }}} \right)^{2} + \left( {\frac{{u_{{A_{certified} }} }}{{A_{{certifie{\text{d}}}} }}} \right)^{2} } \times 100. $$
(11)

where, \(A_{{c{\text{er}}tified}}\) and \(A_{measured}\) were the certified value from IAEA and the measured value of activity concentration, respectively; \(u_{{A_{{certifie{\text{d}}}} }}\) and \(u_{{A_{measured} }}\) were the corresponding standard uncertainties (k = 1), respectively. When both accuracy-test and precision-test achieved “Accepted”, the final score for all analytical determinations of the proficiency tests was “Accepted”. Conversely, if the accuracy was “Accepted” but the precision was “Not Accepted”, the final score was “Warning”.

Figure 5 illustrates the activity ratio between the measured results and the certified values of 232Th and 238U for the various types of reference material such as rich thorium (RGTh), secular equilibrium (IAEA-447), and disequilibrium of uranium (IAEA-434). The activity concentration of 226Ra, 214Pb, 214Bi in the 238U chain and 228Ac, 212Pb, 208Tl in the 232Th chain are higher than the MDA values and receive “Accepted” for the final scores. For the 234Th activity concentration in the IAEA-447, RGTh, IAEA-434 samples, the results of measured radioactivity compared with the certified values have a relative bias of 34.3%, 127.0%, 35.7%, and 4.0%, 3.2%, 0.1% with the case I and case II of FEP efficiency curves, respectively (Table 4). It shows the accuracy of the measured 234Th activity using the 63.3 keV gamma ray depends on the FEP efficiency, the self-absorption and the interference correction factors. The final score for the activity concentration of 234Th with case II of the FEP efficiency curve is “Accepted”. This verifies that the FEP efficiency curve for case II is reliable and can be applied for measuring the radioactivities in the enviromental sample.

Fig. 5
figure 5

Activity ratio between the measured results and the certified values of 238U and 232Th for the IAEA-434, IAEA-447, and RGTh samples

Full size image
Table 4 Measured activities of 232Th and 238U series for the CRM samples
Full size table

The p-type HPGe detector with the low energy resolution can not deconvolute the 186 keV area, the counts of both 185.7 keV (235U) and 186.2 keV (226Ra) are shown as a total count of 186 keV region in the gamma-ray spectrum. Therefore, to rapidly and accurately determine the 235U activity concentration in environmental samples, the correction factor for the contribution of 226Ra was needed (Eq. (8)). In this work, we developed an analytical process that was used to calculate the 226Ra activity concentration based on the direct measurement of 234Th 63.3 keV line (Eq. (5)) (called the first option). This option required a precise efficiency calibration curve, the self-absorption correction factor and the assumption has radioactivity equilibrium between 238U and 226Ra. Its advantage is it may be applied immediately after sample preparation as it does not rely on the equilibrium of the 226Ra daughters. The second option assumed the proportions of the count rates at the 186 keV region for 226Ra and 235U were 57.2% and 42.8%, respectively [25], which relies on two equilibrium assumptions of the 238U–226Ra daughters and the natural ratio of 235U–238U. So this procedure will give misleading results if the measurements on samples from places where the chemical or isotopic composition has been altered. The third option relied on the secular equilibrium of 226Ra and its daughters (214Pb and 214Bi). This technique is widely used in many environmental laboratories to determine the 226Ra content, but it requires complicated sample preparation and a waiting period (about thirty days). Table 5 shows the 235U activity concentration in the RGTh sample which was calculated by the direct method (first and second options) and the equilibrium method (third option). Although the results for 235U with the second and third options have the status “Accepted”, their assumptions need special consideration for each type of environmental sample. Regarding the calculation of 235U using the reference to the 234Th activity (the direct method), the result with the case II of FEP efficiency curve is compared with the reference value, with a relative bias of less than 3%, and the final score shows “Accepted”. It confirmed that an advanced analytical procedure which was detailed in Fig. 1 can be applied to determine the 235U activity in the solid sample by using the gamma spectrometry.

Table 5 The activity concentration of 235U for the RGTh sample
Full size table

Determination of the radioactivities for the rock samples

The activity concentrations of radionuclides in the rock samples were determined by using the developed analytical procedure. The activity concentration of 232Th had a range from 11.4 ± 0.2 (Bq kg−1) to 77.7 ± 0.8 (Bq kg−1), while the activity concentration of 238U had a range from 9.5 ± 0.2 (Bq kg−1) to 41.1 ± 0.4 (Bq kg−1). These results were in agreement with the reported data for samples of various rocks collected in many countries such as China [47], Saudi Arabia [48], Egypt [49], India [50], Poland [51], and Iran [52] (Table 6).

Table 6 Comparison of activity concentration of 238U and 232Th series for rock samples in the present study to the other researches
Full size table

Figure 6 shows the activity concentrations of 234Th (Fig. 6a) and 235U (Fig. 6b) for the rock samples, which are higher than the MDA values. A t-distribution with the two-tailed probability value (p-value) for the null hypothesis [53] is used to compare the measured activity for 234Th with the 226Ra mean value (214Bi, 214Pb). This statistical analysis is a reliable assessment method and has been validated by several studies such as Daoushy and F. Hernández [16], Ordóñez et al. [38], Vesterbacka et al. [54], and Giubrone et al. [55]. The relative deviations less than 2% and the p-value over 0.05 for the t-test statistical analysis prove no statistical difference in the activity concentration of 234Th and the mean of 226Ra value. For the activity concentration of 235U, the results clearly indicate that a good agreement between the analytical procedure using the reference to 234Th activity and the 235U mean of activity with a relative deviation of less than 3%. Moreover, the specific activity ratio of uranium isotopic (235U/238U) is also calculated and ranges from 0.046 to 0.051. It turned out that there are no uranium ratio anomalies in the samples [56].

Fig. 6
figure 6

The activity concentrations of 234Th (a) and 235U (b) for the rock samples

Full size image

Conclusions

This study has described a rapid and reliable analytical procedure to determine the radioactivities in cylindrical solid samples using gamma spectrometry in detail. The self-absorption and the coincidence summing factors which were calculated by using the MCNP-CP code were also considered in the measurements. The 238U activity concentration was determined according to the measurement of 234Th (63.3 keV) taking into account the self-absorption correction factor and the contribution count of 232Th (63.8 keV). The measurement of 235U activity will be obtained from the new analytical procedure regardless of the secular equilibrium of 226Ra—its daughters (214Pb and 214Bi) as well as the natural ratio of 235U–238U. The radioactivities obtained for the CRM samples showed good agreement with the certified reference values with relative deviations of less than 3%. Moreover, the IAEA proficiency test received “Accepted” for all radionuclides analysis. This verifies that the advanced analytical procedure was simple, useful, and reliable for analytical laboratories using gamma spectrometry. This procedure can be applied immediately after the sample preparation regardless of the existence of a secular equilibrium between 226Ra and its progenies (214Pb, 214Bi) and regardless of the existence of equilibrium between 238U and 226Ra or normal 235U–238U isotopic ratio. However, it was important for this procedure that the FEP efficiency and the self-absorption correction and the interference correction must be taken into consideration for good quality analysis.