1 INTRODUCTION

In general, accurate determination of thorium in ores is an objective of states planning to use thorium either for R&D or fuel of research and nuclear power plants. It can be identified and amounted by destructive and non-destructive assay techniques. NORMs mean naturally occurring radioactive materials and it is found in nature since the earth creation. NORMs were formed in supernovae and the primary particles from our universe continually bombard the forming earth’s crust. The NORMs can be found almost everywhere, in soil, air, water supplies and oil. Therefore, NORMs always has been a part of our world and hence the sources of radioactive isotopes in the environment that can be divided into two main categories, natural sources that contribute by 96% of total radiation dose to the world population and on the other hand artificial sources contribute by 4% of total radiation dose to the world population [1, 2].

The terrestrial (primordial) radionuclides are main source of (NORMs) in the environment. In addition, there are also three naturally decay series; 238U, 232Th and 235U [3].

2 EXPERIMENTAL WORK

Most of gamma-ray spectroscopic studies for analysis of 232Th decay series use its gamma decays daughters such as 208Tl (583.19 keV), 228Ac (911.2 and 968.97 keV) and 212Pb (238.63 keV). This is due to the fact that these gamma lines have the highest branching ratio and have approximately no energy interferences with the other daughter’s transitions [4–6].

2.1 Measurements Arrangement and Detection System Set-Up

In this study, the collected samples analyzed using a high-purity germanium (HpGe) [7] with relative efficiency ∼50%. The main specifications of the detection system are given in Table 1. The HpGe detector with its built-in preamplifier is operated at high voltage power ∼3 kV. For cooling the Ge crystal, it was in contact with cold finger which is fully immersed in liquid nitrogen (LN2) at (–77°C) thermally isolated under vacuum in cryostat to reduce the noise of leakage current. The output signal was connected to spectroscopy shaping amplifier followed by a multi-channel analyzer (MCA) with (16 384) channels. To avoid contribution of the background radiation and various natural radiation sources in nearby surrounding to the measured activity of samples, a lead shield with approximately 10 cm thick with an inner layer of 1 mm tin and 1.6 mm copper to minimize the participation from Pb X-ray florescence and to inhibit the effect of x-rays peaks were used [3, 8, 9].

Table 1. The main specifications of the HpGe detector [7]
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2.1.1. Calculation of detector resolution. HPGe resolution is the main specific characteristic than other solid-state detectors and it can be determined by different parameters like conversion factor and full width at half maximum (FWHM) and full width at tenth maximum (FWTM). It has been achieved using 60Co radioisotope, which was counted for 30 min to obtain high enough number of counts for its two energy peaks; 1173.2 and 1332.5 keV. The conversion factor was calculated using Eq. (1).

$${\text{Conversion factor = }}\frac{{\Delta E}}{{\Delta N}},$$
((1))

where ∆E is the difference between two energy peaks in keV (1332.5–1173.2 = 159.3 keV).

∆N is the number of channels between the two peaks. The conversion factor should be in the range of (0.16 keV/channel). If it isn't then something is set up improperly [7]. The calculated conversion factor was found to be 0.157 which is in the proper range.

2.1.2. Peak/Compton (P/C) ratio calculation. The peak to Compton ratio (P/C) of coaxial detectors depends on many characteristics like resolution, efficiency, as well as peak shape, charge collection. The peak to Compton measurement has been done under the same condition as the resolution measurement was done but it uses peak height not peak area in calculating the (P/C) value, the Compton region that has been used for (P/C) calculations as defined in IEEE standard 325, is from 1040 to 1096 keV for 60Co [7, 10] Finally, the (P/C) ratio was calculated using Eq. (2).

$${\text{(P/C) }} = \frac{{{\text{number of counts in the highest channel of 1332}}{\text{.5 keV peak }}}}{{{\text{average counts per channel (1040 keV and 1096 keV)}}}}.$$
((2))

The (P/C) ratio result was found to be (74.7 : 1) which is matched and better than the certified value as shown in Table 1.

2.1.3. Relative efficiency calculation. Relative efficiency calculation was performed using point standard source 60Co which placed 25 cm away from the end-cap and counted for 1000 s [7]. It was calculated using Eq. (3).

$$\begin{gathered} {\text{Relative efficiency (\% )}} \\ {\text{ = (N/T)} \times (1/}{{R}_{{\text{s}}}}{\text{) } \times (1/1}{\text{.2}} \times {\text{1}}{{{\text{0}}}^{{ - {\text{3}}}}}{\text{) } \times 100}{\text{,}} \\ \end{gathered} $$
((3))

where N, is the number of counts in 1332.5 keV peak. T is the preset time. Rs, is the source strength in gamma rays per second. The 1.2 × 10–3 is the efficiency of 3'' × 3'' NaI detector at 25 cm. The relative efficiency result was found to be 51.6 which is almost as the certified value given in Table 1.

2.2 Energy Calibration

Energy calibration of the HpGe detector system were performed using IAEA certified reference material RGU-1 [11] which has been counted for 24 h to obtain high enough statistics. A plot between the channel number and the energy was obtained as shown in Fig. 1 with its correlation Eq. 4 [12].

$$\begin{gathered} {\text{Energy (keV) = 0}}{\text{.167 }} \\ {\text{ + 0}}{\text{.1747}} \times \,{\text{channel}}\,{\text{number}}{\text{.}} \\ \end{gathered} $$
((4))
Fig. 1.
figure 1

Energy calibration curve of HpGe spectrometer.

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2.3 Efficiency Calibration

The absolute photo-peak efficiency which depends on many parameters like; source and detector geometry–gamma energy–density–distance between the source and detector–specifications of the used HPGe detector, was measured. The efficiency calibration of the detector carried out using certified reference material IAEA (RGU-1) [11], which counted three times for 86 400 s and then Microsoft excel program used to calculate the efficiency curve at every gamma energy using Eq. (5). Then, the Genie 2000 program was used to obtain the correlation as shown in Fig. 2 [3, 13].

$${{\xi }_{{abs}}} = \frac{c}{{{{I}_{{\gamma (E)}}}t{{A}_{c}}m}},$$
((5))

where ξabs, is the detector photo-peak efficiency at specific energy and conditions. C, is the number of counts at certain region of interest in the spectrum minus the number of counts in background spectrum at the same region of interest. Iγ(E), the emission probability of gamma having certain energy per disintegration. t, the counting time 24 h (86 400 s). Ac is the activity concentration of the reference source (Bq/kg). m, mass of the reference source in (kg).

Fig. 2.
figure 2

Efficiency calibration curve for (RGU-1) using Genie2000.

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The results of efficiency calculations for different gamma energies for 232Th activity using Eq. (5) are given in Table 2.

Table 2.   The system efficiency calculation results
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2.4 Samples Collection and Preparation

Evaluation of the terrestrial radioactivity levels (mainly 232Th through its decay daughters) and its radiological hazard indices in black sand samples of Rashid area and other natural environmental area are topic of this work. Many natural soil samples were collected then prepared through the following steps [3]. Sieving step: the collected samples sieved using a 2 mm mesh to obtain a uniform particle size and also because no radioactive materials exist on large size sand surface [14]. Drying step: The sieved samples were dried in a drying oven at 110°C until removal of the moisture because the existence of moisture may affect the samples analysis results as it may act as attenuation material [15].

The prepared samples were then weighted and transferred to the Marinelli containers and sealed to kept undisturbed for 28 days to attain material equilibrium between 232Th and its decay chain daughters [13].

3 RESULTS AND DISCUSSION

3.1 Minimum Detectable Activity (MDA) and Figure of Merit (FOM) Calculations

When detecting environmental radioactivity, it is necessary to determine the MDA of the counting system, environmental background radiation in the detection system can differ from place to another one and come from different sources like (10% of the background created through the detector itself—40% from its environment—10% from radon in the air—40% due to interactions of cosmic rays with the detector and its shield) [13].

The MDA calculations were carried out using Eq. (6) [3, 13] and the obtained results are given in Table 3.

$$MDA = \frac{{4.66\sqrt {B.G.C} }}{{{{I}_{{\gamma (E)}}}t{{\xi }_{{abs}}}m}},$$
((6))

where MDA is the minimum detectable activity of certain energy (Bq/kg). ξabs, is the detector photo peak efficiency at certain energy and known measurement condition. B.G.C is the number of counts at certain region of interest in the back ground spectrum. m is the mass and assuming an average mass of all samples and equal to 0.3 kg.

Table 3. The calculated MDA and Figure of merit (FOM) of the detection system
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Figure of merit (FOM) calculations were assessed using Eq. (7) [16] and the obtained results are given in Table 3. Figure of merit (FOM) parameter can be used to characterize the performance of two or more detection systems and also can be used to determine the gamma lines that can be used to measure the activity of 232Th with the highest precision [16]. Figure of merit calculations results obtained are given in Table 3.

$$FOM = \frac{{{{{\left( {{{\xi }_{{abs}}}} \right)}}^{2}}}}{{B.G.C}},$$
((7))

where B.G.C is the count rate at certain region of interest in the background spectrum. ξabs, is the detector photo peak efficiency at certain energy and known measurement condition.

3.2 Specific Activity of 232Th of Rashid Black Sand Samples

Ten representative black sand samples (Ac-1–Ac-10) were investigated for assay of 232Th. These samples were collected from ten different locations along the Rashid city coast, the activity, in Bq kg–1, of gamma lines emitted from daughter nuclides of 232Th decay series in the measured samples were calculated. The activity concentration of 232Th in the ten samples was estimated using all the measured γ ray transitions related to their decay products, such as 212Pb, 228Ac and 208Tl. The daughter nuclides are assumed to be in material equilibrium with their parents. Table 4 shows the activity (AC) values for the ten black-sand samples based on the daughter nuclides of the 232Th decay series including the 583 keV line of 208Tl [13].

Table 4.   The activity (Bq/kg) for 232Th daughters in black sand samples
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The activity of 232Th decay series of these samples were varied from 94.24 to 579.84 with average value 140.38 ± 21.7 Bq/kg. The activity of 232Th in samples are compared with the worldwide mean range as reported by the UNSCEAR 2000 [17]. The high activity of 232Th, may be attributed to either the mobility or fixation of 232Th in the crystal structure of black sand and its geochemical nature [13, 18–21].

It can be observed from Table 4 that the results of 208Tl gamma line (583.1 keV) are slightly different and relatively less than these calculated by the other gamma lines. This will be discussed in the next paragraph under 208Tl activity correction factor.

3.3 Activity Calculations of Natural Environmental Samples Using 232Th Daughters

Specific radionuclides in this decay chain are noteworthy because of their decay characteristics (224Ra decays by alpha to 220Rn; 212Bi and 208Tl are gamma emitters). The 232Th activity was estimated using the γ‑rays of its main decay daughters 208Tl (583.19 keV), 228Ac (911.2 and 968.97 keV) and 212Pb (238.63 keV). A Microsoft excel program was used to calculate the average activity of 232Th radionuclide assuming that material equilibrium is attained. The results of calculations for ten natural soil samples (coded from D1–D10) are given in Fig. 3, and for another ten soil samples (coded from D11–D20) as in Fig. 4.

Fig. 3.
figure 3

The activity (Bq/kg) of 232Th daughters in ten soil samples (D1–D10).

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Fig. 4.
figure 4

The activity (Bq/kg) of 232Th daughters in ten soil samples (D11–D20).

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Where the avg Ac, is the average 232Th activity results using only three gamma lines of its daughters; 911.2 and 968.97 keV of 228Ac and 238.63 keV of 212Pb. While, Tl208 Ac is the 232Th activity results based on 583.19 keV γ-line of 208Tl. The Tl208Ac/avgAc is the ratio between 232Th activity results when using only 208Tl (583.19 keV) γ-line. When using three gamma lines of its daughters; 228Ac of 911.2 keV and 968.97 keV and 212Pb of 238.63 keV. EFF. is the efficiency calculations results of the detection system. B.R. is the branching ratio values of specific gamma lines.

As shown in Figs. 3 and 4, there is a difference between the calculation results of 232Th activity using 208Tl (583.19 keV) and the other daughters 228Ac (911.2 and 968.97 keV) and 212Pb (238.63 keV). In spite of, almost identical results due to the material equilibrium between 232Th and its daughters must be obtained. The difference in the results can be explained based on the fact that decay chain of 232Th at 212Bi daughter (Fig. 5) has two probabilities of decay to reach the stable 208Pb. The first one is the decay route of 212Bi to 208Tl through an alpha emission with probability of 35.93%. The second decay is to 212Po through beta process with 64.07% probability. In other words, only 35.93% of 212Bi decays to 208Tl daughter, while, 100% of 228Ac and 212Pb decay in real material equilibrium with the parent 232Th.

Fig. 5.
figure 5

The 212Bi–208Tl decay probability.

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So, the 208Tl activity value should be divided by the branching ratio (0.3594) to represent 232Th equivalent [16, 22–25]. This correction for 208Tl in calculation of 232Th activity was also observed and given in other work [13].

As shown from the results given in Figs. 3 and 4, the Microsoft excel program was used to validate that only 35.93% of 212Bi decay leads to 208Tl daughter. This is clear by comparison of the results of the average activity of 232Th (avgAc) using only the three γ-lines 911.2, 968.97 keV and 212Pb of 238.63 keV with 232Th activity (Tl208Ac). When using 208Tl (583.19 keV) which is presented by (Tl208Ac/avgAc), its value was found to be different from the 35.93%. Finally, the ratio (Tl208Ac/avgAc) was calculated for 20 soil samples as shown in Figs. 3 and 4. The total average of results was found to be (0.3394 ± 0.0167). In other words, a difference of about 0.3593 was found at assessment of 232Th through its 208Tl of 583 keV.

The difference between activity of 232Th as calculated by 208Tl daughter and its other daughters was also found in other published work [26].

4 CONCLUSIONS

Based on the results obtained in this study using HpGe spectrometer, the specific activity calculation of 232Th based on its daughter 208Tl of 583.19 keV shows different values rather than the other 228Ac (911.2 and 968.97 keV) and 212Pb 238.63 keV daughters. A correction factor was deduced and should be applied when using 208Tl (583.19 keV) with its branching ratio 0.85 for calculation of 232Th activity. This correction factor is quantified to be 0.3394 ± 0.0167. The difference is mainly due to the 33.9% of 212Bi decay probability that leads to 208Tl daughter. The same correction is to be applied for other gamma lines of 208Tl. It was applied on samples collected from Rashid black sand and natural environmental soil.

In general, accurate determination of thorium activity, by destructive or non-destructive technique, is very crucial measure to evaluate its feasibility to be used in nuclear fuel cycle.