Uranium Series Disequilibrium and Precision Measurement of Radionuclides Activity in Sediment Sample Using Low Background Gamma Spectrometry

Abdul J. Khan^1*, Umme-Farzana Syed¹, Amy L. Roselan¹, Cynthia A. Costello²

¹Laboratory of Inorganic and Nuclear Chemistry, Division of Environmental Health Sciences, Wadsworth Center, New York State Department of Health, Empire State Plaza, Albany, NY, USA.
²Bureau of Environmental Radiation Protection, New York State Department of Health, Empire State Plaza, Albany, NY, USA.

DOI: 10.4236/gep.2023.1110010                

Abstract

Low background gamma spectrometry was used to measure the radionuclides activity of ²³⁸U, ²³²Th, and ²³⁵U series as well as ⁴⁰K and ¹³⁷Cs in a sediment sample. The goal of the study was to measure the ²³⁸U (63.3 keV peak of ²³⁴Th; 1001 keV peak of ^234mPa) and ²³⁵U (143.76 keV, 163.33 keV, and 205.31 keV peaks) activity by low background gamma spectrometry in sediment sample. ²³⁵U activity in environmental samples is difficult to accurately measure by gamma spectrometry due to its low abundance in nature and low gamma line intensities at 143.76 keV, 163.33 keV, and 205.31 keV. We have shown that by using low background gamma spectrometry, it is possible to accurately measure the ²³⁵U activity in sediment samples. The ²³⁵U activity was measured without using the major peak of 185.7 keV (I_γ = 57.2%) which requires interference correction from 186.21 keV of ²²⁶Ra. ²²⁶Ra activity was determined by measuring ²²²Rn daughters (²¹⁴Pb and ²¹⁴Bi). The precision and accuracy of the gamma activity measurement in the sediment sample were verified by using the HPGe detectors with Certified Reference Material (CRM) Irish Sea Sediment (IAEA-385). The results obtained for the 63.33 keV energy line of ²³⁴Th are compared with the 1001 keV energy line of ^234mPa. The values of ²³⁸U and ²³⁵U activities, as well as ⁴⁰K, ¹³⁷Cs, and ²²⁶Ra, agreed with the certificate values of CRM. The results show that the ²³⁸U is in equilibrium with its daughters (²³⁴Th, ^234mPa, and ²¹⁰Pb). ²³²Th is also in equilibrium with its daughters (²²⁸Ra, ²¹²Pb, ²¹²Bi and ²⁰⁸Tl). ²³⁵U/²³⁸U activity ratio of 0.046 ± 0.007 in the sediment is constant in nature but fluctuates due to geological processes. A value of 0.055 ± 0.008 was found in our sediment sample.

Keywords

Low Background Gamma Spectrometry, HPGe Detector, Sediment, ²³⁸U, ²³⁵U, Secular Equilibrium

1. Introduction

Natural uranium and thorium are present in all rocks, soils, and sediments. Natural uranium consists of ²³⁸U, ²³⁵U, and ²³⁴U. It has 99.284% of ²³⁸U, 0.711% ²³⁵U, and a trace amount of 0.0055% ²³⁴U. Thorium presents naturally in sediment as ²³²Th and ²³⁴Th (progeny of ²³⁸U). ²³²Th is less soluble and found mostly in secular equilibrium with its progeny i.e., ²²⁸Ra, ²¹²Pb, ²¹²Bi, and ²⁰⁸Tl. Gamma spectrometry is extensively used for ²³⁸U, ²³²Th, ²²⁶Ra, and ⁴⁰K determination in environmental samples because of its simplicity in terms of sample preparation. It can simultaneously perform multi-nuclide determinations based on the detection of photon emissions and, therefore, does not require sophisticated sample treatment, however, it requires precise calibration of gamma detectors with NIST traceable standards or Monte Carlo methods ( Semkow et al., 2015 ; Azbouche et al., 2015 ). Gamma spectrometry can be easily applied to determine ²³⁸U, ²²⁶Ra, and ²³⁵U in environmental as well as in food samples simultaneously without any radiochemical separation. In secular equilibrium, ²³⁸U can be determined by the gamma energy peak of ²³⁴Th at 63.3 keV (I_γ = 3.7%) or at ~92.6 keV (doublet: I_γ = ~4.8%). Other low-intensity gamma energy peaks of ^234mPa at 766.4 (I_γ = 0.1%) and 1001 keV (I_γ = 0.837%) were also often used ( Yücel et al., 1998 ) for ²³⁸U in materials rich in thorium. For environmental samples, the weak intensity of 766.4 keV and 1001 keV gamma lines together with the lower efficiency of HPGe detectors at higher energies often cause problems in detection. With the use of large-volume coaxial germanium detectors which provides better detection efficiency and counting statistics at 1001 keV of gamma energy for ^234mPa.

For the measurement of uranium series radionuclide concentrations, radiochemical analysis followed by alpha spectrometry is mostly used ( Minteer et al., 2007 ; Carvallo & Oliveira, 2009 ). However, this method is time-consuming and complicated. On the other hand, gamma-ray spectrometry is a simple, non-destructive, and fast method, and is suitable for accumulating data for many radionuclides simultaneously. So, high-resolution gamma-spectrometry has been extensively used for the quantitative analysis of uranium and thorium ( Papadopoulos et al., 2013 ) and for the absolute determination of uranium content in rocks ( Kaste et al., 2006 ). If one wishes to measure the ²³⁸U content of a sample independent of the ²³⁵U content, one is faced with the problem that the ²³⁸U isotope emits directly only very weak gamma radiation which is at 49.55 keV (0.064%).

It is possible, however, to measure the emission of gamma rays from a daughter nuclide that is in equilibrium with the ²³⁸U parent. In many cases, this equilibrium state in a natural system may not have been reached, especially for a daughter that is quite far down the decay chain. Under secular equilibrium, radionuclides (Figure 1) in the ²³⁸U series should have the same activity. ²³²Th is less soluble than ²³⁸U and found mostly in secular equilibrium with its progeny i.e., ²²⁸Ra, ²¹²Pb, ²¹²Bi, and ²⁰⁸Tl. Disequilibrium results from geochemical sorting, whereby a process acts to move a parent or daughter into or out of a system at a rate that is significant relative to the half-life of the daughter ( Osmond & Cowart, 1982 ). The decay chains in deeply buried, unweathered materials are generally in equilibrium. However, weathering processes that occur at or near the earth’s surface operate on a sufficiently short time scale that disequilibrium results. Other mechanisms by which disequilibria are established in the surficial environment are 1) solution and precipitation reactions (because of different chemical properties of the elements in the decay chains), 2) gaseous diffusion of the radon isotopes, and 3) alpha particle recoil.

The development of low-background gamma-ray spectrometer (LBGS) was originally for basic physics research such as neutrino oscillation, 0νββ decay, and dark matter search ( Heusser, 1995 ; Povinec et al., 2004 ; Laubenstein et al., 2004 ; Aalseth et al., 2012 ; Armengaud et al., 2013 ; Khan et al., 2014 ) during the last two decades, however, LGBS has found several important applications such as monitoring natural radionuclides such as ²²⁶Ra, ²²⁸Ra ( Semkow et al., 2019 ; Khan et al., 2020 ) as well as anthropogenic radionuclides such as fission products in the environment for contamination control and nonproliferation applications.

Figure 1. ²³⁸U series decay chain.

The Nuclear Chemistry Laboratory (NCL) at the New York State Department of Health has been operating LBGS for over two decades ( Semkow et al., 2002 ; Haines et al., 2011 ; Khan et al., 2014 ). NCL has one ultra-low background HPGe p-type coaxial spectrometer and three low background HPGe spectrometers. Details of the available HPGe spectrometers at NCL are given in Table 1. By lowering the gamma background, the sensitivity (hence the signal-to-noise ratio) of the gamma spectrometers is improved, which greatly enhances studies involving environmental radioactivity. Background reduction is another way to lower the decision limits of samples containing only traces of the radionuclides under investigation.

In gamma-ray spectrometry procedures, secular equilibrium in the natural radioactive decay series is assumed. However, the equilibrium between progeny particularly with ²²⁶Ra and uranium can be strongly affected by several geological processes (weathering, exhalation of gases, passage to groundwater). Due to the constant ratio between ²³⁵U and ²³⁸U in nature, the 185.71 keV (57.2%) peak from ²³⁵U may be a good choice for the ²³⁵U measurement. To measure ²³⁵U accurately it must be de-convoluted together with the 186.21 keV (3.64%) peak of ²²⁶Ra which is not trivial. In this paper, we aim to show that ²³⁸U (using 63.3 keV peak of ²³⁴Th) and ²³⁵U activity can be accurately measured by using 143.76 keV (10.96%), 163.33 keV (5.08%), and 205.31 keV (5.01%) peaks by using our low background gamma spectrometry method. We also examine the equilibrium condition of both the ²³⁸U and ²³²Th radioactive decay chains in a recently deposited fluvial sediment sample collected from the vicinity of the Nine Mile Point nuclear power plant in the town of Scriba, approximately five miles northeast of Oswego, New York, on the shore of Lake Ontario. Further, to obtain the precise and accurate results of the radioactivity of the environmental samples and the capability of the gamma spectrometry method at the NCL, we analyzed the sediment sample using our ultra-low background HPGe spectrometer (called GE12) and three low background HPGe spectrometers (GE03, GE08, and GE09) and one GC8021 (GE11) detector which has comparatively high gamma background. The gamma measurement results were validated using Certified Reference

Table 1. Characteristics of p-type co-axial HPGe detectors at NCL.

*Outside the steel room.

Material (CRM) Irish Sea sediment (IAEA-385).

2. Radioactivity and Secular Equilibrium in Sediment Samples

Secular equilibrium due to the radioactive disintegration in the rocks and sediment is discussed in detail ( Ivanovich & Harmon, 1992 ). If the daughter’s half-life is much shorter than that of the parent nuclide: i.e., ${\lambda }_0\ll {\lambda }_{\text{1}}$ , where ${\lambda }_i={\left(\ln 2/{\zeta }_{1/2}\right)}_i$ , is the decay constant for the “i”th radionuclide and ζ_1/2 is the half-life of the radionuclide. Consequently, the activity of the parent does not decrease markedly over many daughters half-lives than for a parent-daughter pair, which simplifies to

$N_1{\lambda }_1=N_0{\lambda }_0\left(1-{\text{e}}^{-}{}^{{\lambda }_{1}t}\right)$ (1)

where N₀ and N₁ are the numbers of radioactive atoms of the parent and daughter nuclides, respectively, λ₀ and λ₁ are the respective decay constants, and t is the elapsed time. Then for values of t much greater than the daughter’s half-life:

$N_1{\lambda }_1=N_0{\lambda }_0$ (2)

This is the condition known as secular equilibrium. For a decay chain, where the parent half-life is much longer than that of the longest-lived daughter, secular equilibrium implies

$N_0{\lambda }_0=N_1{\lambda }_1=N_2{\lambda }_2=\cdots =N_i{\lambda }_i$ (3)

In secular equilibrium, the activity concentration of longer-lived radionuclides for ²³⁸U decay chain (Figure 1) should be the same, in other words, parent and daughter activity become equal as given below:

$A_{({}^{\text{238}}\text{U})}=A_{({}^{\text{234}}\text{U})}=A_{({}^{\text{23}0}\text{T}\text{h})}=A_{({}^{\text{226}}\text{R}\text{a})}=A_{{}^{(\text{222}}\text{R}\text{n})}=A_{({}^{\text{21}0}\text{P}\text{b})}$ . (4)

Disequilibrium is the condition where the activity concentrations of the parent and daughter nuclides are not equal.

3. Materials and Methods

3.1. Sample Collection and Preparation

The sediment sample was collected from the vicinity of the Nine Mile Point Reactor located in the town of Scriba, approximately five miles northeast of Oswego, New York (Figure 2). This is a sediment sample collected from the shoreline of Lake Ontario boat launch collected right where the water meets land. Distance from the reactor is ~1.44 miles E of Unit 2 with a heading of 82 deg. Depth is skimmed off the top at approximately 2 cm and sifted in the field to remove large rocks. The sample was kept in a cooler and brought to the lab where the sample was kept at 105˚C overnight to dry and gain constant weight. The sample was then weighed and transferred into 800 ML Marinelli beaker up to the top and sealed with Phenoseal Vinyl Adhesive Caulk (PHENOSEAL, Baltimore, MD 21224) and black electric tape (S-17841; Uline, Pleasant Prairie, WI

Figure 2. Location of the sediment samples collection.

53158) to avoid the escape of ²²²Rn gas from the container. The sediment sample was kept for four weeks to reach ²²⁶Ra in equilibrium with ²²²Rn Progeny (²¹⁴Pb and ²¹⁴Bi) before counting. The sample was counted for 60,000 s on all HPGe detectors. The background was counted for 240,000 s. The characteristics of HPGe detectors are given in Table 1.

3.2. Gamma Spectrometry

In this study, we have utilized five p-type high purity Germanium co-axial detectors (HPGe) having relative efficiencies varying from 80% to 140% by Mirion Technologies (Canberra) Inc. (Meriden, CT, USA). The detectors (except GE11) are situated inside a 15-cm thick wall steel room made of pre-World War II steel (Dixie Manufacturing Co., Baltimore, MD, USA), which is located under a 47-story building providing 33 meters of water equivalent (mwe) shielding from cosmic rays in the vertical direction. GE03, GE08, and GE09 detectors have general low-background lead shields and are equipped with custom active muon shields made of plastic scintillators positioned on the top, which reduce cosmic muon background by a factor of 2. The 140% detector (GE12) has a custom 3-layer ultra-low background lead shield of a 17 cm total thickness, which is surrounded by plastic scintillators from five sides for muon rejection ( Khan et al., 2014 ). This spectrometer has an integrated background rate of 2.4 counts per minute (cpm) in the gamma energy range between 50 - 2700 keV, corresponding to a background rate of 15 counts∙ks⁻¹∙kg⁻¹ Ge.

To quantify radionuclides by their gamma rays, calibration of Ge gamma spectrometers is performed which involves determination of detector peak efficiency as a function of gamma energy and geometry. In addition, the density and coincidence-summing (cascade-summing) corrections to the peak efficiency are applied, the latter requiring either measured or calculated total efficiency. One can categorize the variety of the HPGe spectrometer calibration techniques into four major categories: empirical, semi-empirical, computational Monte Carlo (MC), and efficiency transfer. We used a semi-empirical method that is based on a direct measurement of the efficiency at a given geometry as a function of gamma energy for a set of radionuclides in a mild acidic solution (often called calibration in water). The measured water peak efficiencies, ε_p, are corrected for the coincidence-summing (as in Equation (5) below). Then, a smooth efficiency curve is often fitted to the water calibration using algorithms ln(ε_p) against polynomials of (lnE)ⁿ or (ln(c/E))ⁿ, where E is gamma energy, n is the polynomial order, and c is a constant. There are also other algorithms that were not used here ( Gilmore, 2011 ). When analyzing activity in real samples, the corrections are applied to the efficiency curve, to convert the peak efficiency for water at a particular gamma energy to the peak efficiency of the matrix and a particular radionuclide at the same energy as follows:

${\epsilon }_p\left(\text{matrix};\text{radionuclide}\right)={\epsilon }_p\left(\text{water};\text{energy}\right)C_d{C}_s$ (5)

where C_d is the density correction factor and C_s is the coincidence-summing correction factor.

The NIST traceable mixed-gamma radionuclide standards containing ²⁴¹Am, ¹⁰⁹Cd, ⁵⁷Co, ¹³⁹Ce, ²⁰³Hg, ¹¹³Sn, ⁸⁵Sr, ¹³⁷Cs, ⁵⁴Mn, ⁸⁸Y, ⁶⁵Zn, ⁶⁰Co were provided by EZ Analytics, Atlanta, GA, USA. The radionuclides and their standardized gamma energies are listed elsewhere ( Semkow et al., 2015 ). Gamma-ray spectra were acquired using Apex Gamma software of Mirion Technologies (Canberra) Inc. (Meriden, CT, USA) however, the spectra were analyzed using Genie 2000 software for the sediment sample as well as for efficiency calibration.

Calculations of radionuclide activities need to account for emission probabilities (Table 2), full energy peak efficiency, geometry-dependent true coincidence summing, density correction factor, and background characteristics of the detector. The gamma activity using the HPGe detector can be measured by the

Table 2. Key Gamma-emitting radionuclides from natural radioactive series (Values taken from NNDC , Brookhaven National Laboratory).

following equation ( Joel et al., 2017 ):

$A\left(\text{Bq}\cdot {\text{kg}}^{-\text{1}}\right)=\frac{\frac{N_s}{t_s}-\frac{N_B}{t_B}}{M_s\ast \mathcal{E}\ast I_{\gamma }\ast C_d\ast C_s}$ (6)

where A denotes the activity concentration of a radionuclide, N_s/t_s, and N_B/t_B are the count rates of the radionuclide and background, M_s is the mass of the sample, $\mathcal{E}$ is full energy peak efficiency, and I_γ denotes an emission probability of the specific γ-ray, C_d is the density correction factor and C_s is the coincidence-summing correction factor. Density and coincidence summing corrections were calculated with the Gespecor program ( Sima et al., 2001 ). Table 2 also lists gamma energies used for the activity of the radionuclides and emission probabilities for key members of the ²³⁸U, ²³²Th, and ²³⁵U series. For radionuclides with multiple energy lines, a weighted mean of each gamma line’s measured activities was taken. The other main natural source, ⁴⁰K, emits 1461 keV photons with a probability of 10.66% ± 0.16%.

The error σ_A for a radionuclide activity is calculated using:

${\left(\frac{{\sigma }_A}{A}\right)}^2={\left(\frac{{\sigma }_s}{S}\right)}^2\pm {\left(\frac{{\sigma }_{\mathcal{E}}}{\mathcal{E}}\right)}^2\pm {\left(\frac{{\sigma }_{I_{\gamma }}}{I_{\gamma }}\right)}^2\pm {\left(\frac{{\sigma }_{C_d}}{C_d}\right)}^2\pm {\left(\frac{{\sigma }_{C_s}}{C_s}\right)}^2$ (7)

The uncertainty (σ_A) of activity calculation is a built-in function of the Genie2000 software. Our reported total uncertainty is expressed at the 95% confidence level, i.e., 1.96σ.

Minimum detectable activity (MDA) is defined by ( Gilmore, 2011 ) as being the smallest quantity of activity that can be detected in a sample with a predefined probability of 95% (approximately k = 2), considering of 5% probability of making type I errors (false positive) and making type II errors (false negative). MDA of a particular radionuclide is calculated by Genie 2000 software (Mirion Tech) which used the Currie (1968) formulation as given below:

$\text{MDA}=\frac{k^2\pm 2k\sqrt{B+B\frac{N}{2m}}}{M_s\ast \mathcal{E}\ast I_{\gamma }\ast t\ast C_d\ast C_s}$ (8)

where B is the background, $\mathcal{E}$ is the detection efficiency, I_γ is the emission probability of the specific γ-ray, t is the measurement time in sec, N is the number of channels of the region of interest (ROI) and m is the number of channels to the left and to the right of the ROI. k is a confidence level equal to 1.645. The sediment sample was counted for 60,000 s at each detector and the background was counted for 240,000 s. Table 3 gives the MDA of radionuclides for specific energy in the sediment sample as well as in the distilled water sample (method blank) measured at each detector for 60,000 s. The verification of the radionuclides’ activity and the capability in terms of precision and accuracy of our gamma spectrometry measurements were established by using a Certified Reference Material called Irish sea sediment (IAEA-385) under the same conditions.

4. Results and Discussions

The results of the radionuclides activity of ²³⁸U and ²³²Th series in sediment samples measured by available HPGe detectors at NCL are presented in Table 4. The spectra of the major gamma energy lines of the background and the sediment sample are presented in Figure 3 and Figure 4. The details of the results

Table 3. MDA of radionuclides due to major gamma lines measured by HPGe detectors using Genie 2000 software.

Table 4. Radionuclides activity (Bq∙kg⁻¹) in sediment sample measured by various HPGe detectors.

*Not detected.

Figure 3. Background spectra for 240,000 s in GE03, GE08, GE09 and GE11 HPGe detectors.

Figure 4. Major gamma lines from natural and man-made sources in the sediment sample.

are discussed below. The results are density and coincidence summing corrected.

4.1. ²³⁸U Series Measurement

4.1.1. ²³⁸U Activity Measurement

Usually, the activity of ²³⁸U in a sediment sample cannot be directly determined by gamma spectrometry since the ²³⁸U emits a weak gamma-ray at 49.55 keV (0.064%). However, its activity can be measured by means of its progeny ²³⁴Th (63.3 and 92.5 keV) and ^234mPa (1001 keV) as both are reached in secular equilibrium with ²³⁸U in ~120 days in a closed system due to their short half-life. ²³⁴Th at 63.3 keV (4.5%) peak is a cleaner peak and suitable for ²³⁸U analysis. However, the 92.5 keV peak is a doublet consisting of 92.37 (2.61%) and 92.79 keV peaks (2.58%) and is affected by several other peaks i.e., ²³¹Th X-ray (0.42%), ²¹⁴Bi X-ray (0.083%), ²²⁸Ac X-ray (3.19%) and ²³⁵U X-ray (5.56%). Due to these interferences, the use of the 92.5 keV peak for directly quantifying ²³⁴Th is not possible and we use the 63.3 keV peak for ²³⁴Th determination. Another possibility is the use of ^234mPa at the 1001 keV gamma line. The weak intensity of the ^234mPa gamma line (1001 keV; 0.837%) in conjunction with the low efficiency of HPGe detectors at higher energies, often leads to a non-detectable peak in sediments. However, the 1001 keV peak does not have any interference with any other peaks and is not affected by self-absorption ( Yücel et al., 1998 ), hence this peak is useful to determine the ²³⁸U concentrations in the sediment samples. However, analysis of ²³⁸U by 1001 keV gamma peak requires a long-integrated counting time. By using our low background gamma spectrometers (GE03, GE08, and GE09) and ultralow background spectrometer (GE12), we can easily determine the ²³⁸U by using ^234mPa, 1001 keV peak accurately. The ²³⁸U activity in the sediment sample by using ²³⁴Th (63.3 keV) and ^234mPa (1001 keV) peak is presented in Table 4 and plotted in Figure 5. The ²³⁴Th and ^234mPa activities in the sediment sample give very similar results within the measurement uncertainty among all five HPGe detectors. The ²³⁴Th activity varies from 19.4 ± 7.5 Bq∙kg⁻¹ to 23.2 ± 3.7 Bq∙kg⁻¹ and ^234mPa activity varies from 19.7 ± 4.4 Bq∙kg⁻¹ to 26.2 ± 5.1 Bq∙kg⁻¹ among the detectors. The large uncertainties and the variation in radionuclide activities are due to the low emission probability of 3.70% ± 0.04%

Figure 5. ²³⁴Th and ^234mPa activities in sediment sample.

for the 63.3 keV gamma line and 0.0837% for the 1001 keV gamma line. The low efficiency of the HPGe detectors at low energies is another factor for the variation in ²³⁴Th activity as well as in ^234mPa activity (Figure 6). GE12 (XtRa HPGe) detector has higher efficiencies as compared to GE03 shown in Figure 7 for both the radionuclides due to its unique thin-window contact on the front surface which extends the useful energy range down to 3 keV. Conventional p-type coaxial detectors e.g., GE03, GE08, GE09, and GE11 have a lithium-diffused contact typically between 0.5 and 1.5 mm thick. This dead layer stops most photons below

Figure 6. Measured efficiency of the HPGe detectors for ²³⁴Th and ^234mPa.

Figure 7. Comparison of the efficiency with conventional p type HPGe detector (GE03) vs HPGe p-type (XtRa) low energy detector (GE12).

40 keV which is not a good choice for low-energy gamma detection. The precision of the ²³⁴Th activity measurement is good in all five detectors, however, the GE12 HPGe ultralow background detector is the better choice for ²³⁸U measurements due to its low uncertainty. The mean gamma activities of ²³⁴Th and ^234mPa are 20.9 ± 2.5 Bq∙kg⁻¹ and 23.9 ± 2.5 Bq∙kg⁻¹ respectively and the ratio of ²³⁴Th/^234mPa is 0.87 ± 0.16 which shows that ²³⁴Th and ^234mPa are in secular equilibrium with ²³⁸U.

4.1.2. ²¹⁰Pb Activity Measurement

²¹⁰Pb (E = 46.54 keV; I_γ = 4.25%) occurs naturally as one of the decay products of the ²³⁸U series. Disequilibrium between ²¹⁰Pb and its parent nuclide ²²⁶Ra (T_1/2 = 1600 y), arises through the diffusion of the intermediate gaseous isotope, ²²²Rn (T_1/2 = 3.8 d). Direct gamma counting of the 46.54 keV gammas produced in 4.25% of the ²¹⁰Pb decays. There are two challenges related to this measurement: the low intensity of this gamma decay; and the very low energy of the photon, for which the detection efficiency of HPGe detectors is low (Figure 7). The results presented in Table 4 show that ²¹⁰Pb is not detected by GE03, GE08, and GE09) detectors. The reason is that they are very old p-type HPGe coaxial detectors (more than 25 years old). The thickness of the dead layer in p-type HPGe coaxial detectors increases with time which attenuates the low-energy photons and these photons do not reach the detectors’ active volume ( Huy, 2011 ; Kaya et al., 2022 ). This also affects the efficiency of the detector in low-energy regions. The ²¹⁰Pb activity in the sediment sample measured by GE11 and GE12 was 24.2 ± 7.5 and 24.2 ± 3.8 Bq∙kg⁻¹, respectively, however, the uncertainty in GE12 is much lower as compared to GE11 because of its low background and higher efficiency at 46.5 keV (Figure 7). The result presented in Figure 8 shows that

Figure 8. ²³⁴Th and ²¹⁰Pb activity in sediment sample showing secular equilibrium.

²³⁴Th (²³⁸U) and ²¹⁰Pb are in good agreement which clearly shows that both the radionuclides are in secular equilibrium with ²³⁸U. This also shows that if secular equilibrium breaks due to the emanation of ²²²Rn it is recovered afterward.

4.1.3. ²²⁶Ra Activity Measurement

²²⁶Ra is determined either directly by measuring the 186.21 keV γ-peak or indirectly by measuring the γ-peaks of ²²²Rn progeny i.e., ²¹⁴Pb and ²¹⁴Bi after secular equilibrium established with ²²⁶Ra (~4 weeks). Direct measurement of ²²⁶Ra with 186.21 keV by gamma spectrometry is difficult due to the interference of 185.7 keV γ-peak from ²³⁵U and requires interference correction from ²³⁵U (185.71 keV) peak ( Suárez-Navarro et al., 2018 ). We measured ²²⁶Ra activity in the sediment sample by sealing the Marinelli beaker against ²²²Rn escape via the emissions from its short-lived daughters ²¹⁴Pb and ²¹⁴Bi. ²²⁶Ra activity was calculated based on the assumption that it is a weighted mean of the activities of the gamma rays of ²¹⁴Pb (295.22 keV, 351.93 keV) and ²¹⁴Bi (609.32 keV, 1120.29 keV, 1377.67 keV, 1764.49 keV). The ²²⁶Ra results of the ²¹⁴Pb and ²¹⁴Bi activities measured by each detector are presented in Table 4. The results from each detector for both the radionuclides are in good agreement and show the high precision of our gamma spectrometry method. The results also suggest that the ²²⁶Ra is in secular equilibrium with ²³⁴Th.

To conclude, we would like to add that the measured activity of ²³⁸U series radionuclides (i.e., ²³⁴Th, ^234mPa, ²²⁶Ra, and ²¹⁰Pb) is found to be in good agreement as given by equation 4 suggesting that the ²³⁸U progeny are in secular equilibrium with ²³⁴Th. The ratio of ²³⁴Th activity to the weighted mean activities of ^234mPa, ²²⁶Ra, and ²¹⁰Pb presented in Table 4 varies from 0.94 ± 13 to 1.10 ± 0.18 with a mean value of 1.01 ± 0.07 among HPGe detectors in the sediment sample which shows good agreement and precision of the measurements.

4.2. ²³²Th Series Measurement

²³²Th decays to stable ²⁰⁸Pb by a series of alpha and beta decay modes. The decay of the daughters is always accompanied by the emission of gamma radiation and this mode of decay provides an opportunity to apply low-level gamma spectrometry for the determination of ²²⁸Ra and its progeny. ²³²Th is less soluble than ²³⁸U and found mostly in secular equilibrium with its progeny i.e., ²²⁸Ra, ²¹²Pb, ²¹²Bi, and ²⁰⁸Tl in rocks, soil, and sediments. However, it should be noted that in the case of ²⁰⁸Tl, only 35.94% of ²¹²Bi decay leads to this nuclide while 100% of ²²⁸Ac or ²¹²Pb activity is in secular equilibrium with ²³²Th. The results of the ²²⁸Ra, ²¹²Pb, ²¹²Bi, and ²⁰⁸Tl are presented in Table 4. ²²⁸Ra activity in the sediment sample is measured by the weighted mean of the activities of the ²²⁸Ac peaks of 270.24 keV, 338.32 keV, 911.20 keV, 964.77 keV, 968.97 keV, and 1588.2 keV. ²²⁸Ac (T_1/2 = 6.15 h) is the immediate daughter of ²²⁸Ra (T_1/2 = 5.75 ± 0.03 y) and expected in secular equilibrium with ²²⁸Ra in the sediment sample. ²¹²Pb activity was measured by the gamma peaks of 238.63 keV and 300.09 keV; ²¹²Bi activity was determined by using gamma energy of 727.33 keV and ²⁰⁸Tl activity was calculated using the weighted mean activities of gamma peaks 583.19 keV, 860.56 keV and 2614.51 keV. The gamma activity of the radionuclides in the sediment sample measured by available HPGe detectors is agreed very well within uncertainty. The average activities of the radionuclides ²²⁸Ra, ²¹²Pb, ²¹²Bi and ²⁰⁸Tl in the sediment sample are found to be 22.7 ± 0.27 Bq∙kg⁻¹, 22.5 ± 0.23 Bq∙kg⁻¹, 21.8 ± 0.32 Bq∙kg⁻¹and 21.7 ± 0.33 Bq∙kg⁻¹, respectively. The ²³²Th series radionuclides activity agrees with each other which shows that the ²³²Th is in secular equilibrium with its radioactive progeny.

4.3. ²³⁵U Measurement

²³⁵U emits several gamma lines between 70 and 300 keV however the main gamma line at 185.71 keV (emission probability 57.2%) is interfered with the ²²⁶Ra gamma line at 186.21 keV. The best gamma line is at 205.31 keV which is sufficiently well separated from other likely peaks (e.g., 204 keV peak from ²²⁸Ac) to use for determination although its low intensity (4.7%) precludes its use in many samples. Two other lines of interest are those at 143.76 keV and 163.33 keV with intensities of 10.5% and 4.7%, respectively, however, the former is interfered with ²³⁰Th peak at (143.87 keV; 0.048%), and by the 144.2 keV emission of the daughter ²²³Ra. The interference at 163.1 keV (0.154%) of the short-lived ²³¹Th is assumed to be in equilibrium with ²³⁵U. We used the weighted mean of the activities of gamma lines at 143.76 keV, 163.33 keV, and 205.31 keV and the results are presented in Table 4.

The measured ²³⁵U activity in the sediment sample shows (Figure 9) good precision in all HPGe detectors. The ²³⁵U activity varied from 1.12 ± 0.4 Bq∙kg⁻¹ to 1.39 ± 0.4 Bq∙kg⁻¹ with a mean value of 1.22 ± 0.18. ²³⁵U activity measured by GE11 and GE12 detectors show 1.26 ± 0.4 Bq∙kg⁻¹ and 1.39 ± 0.4 Bq∙kg⁻¹, respectively. Our results suggest that ²³⁵U activity in the environmental sample can be

Figure 9. ²³⁵U activity in sediment sample by low background gamma spectrometry.

measured precisely and accurately by low background gamma spectrometry. The activity ratio of the radionuclides ²³⁵U to ²³⁸U is constant in all environmental samples, except where contaminated by processed uranium or taken from certain specific, well-known locations. The ²³⁵U/²³⁸U activity ratio is 0.046 ± 0.007 ( Dowdall et al., 2004 ). The mean activity ratio of the ²³⁵U to ²³⁸U in the sediment sample is found to be 0.055 ± 0.007. The high ²³⁵U/²³⁸U ratio either may be uncertainty in ²³⁵U measurements or washed-out of ²³⁸U from the surficial sediment.

4.4. ⁴⁰K and ¹³⁷Cs Measurement

⁴⁰K is a primordial natural radionuclide and is present in all rocks, sediment, and soil however ¹³⁷Cs is a manmade radioactive isotope released in the atmosphere by nuclear testing during the 1950s and 1960s and nuclear accidents like Chernobyl in 1986 and Fukushima in 2011. The activity of ¹³⁷Cs was calculated from the 661.6 keV peak and ⁴⁰K from the 1461.0 keV peak by HPGe detectors. The ⁴⁰K activity in the sediment sample is presented in Table 4. The ⁴⁰K activity varies from 549 ± 11 Bq∙kg⁻¹ to 557 ± 11 Bq∙kg⁻¹ with a mean of 554 ± 5 Bq∙kg⁻¹. ⁴⁰K activity in the sediment sample was measured very precisely with our gamma spectrometers. ¹³⁷Cs activity in the sediment sample varies from 0.84 ± 0.06 to 0.95 ± 0.05 Bq∙kg⁻¹ among the five HPGe detectors. ¹³⁷Cs value in the sediment sample is very low and measured very precisely by all detectors presented in Table 4. The ¹³⁷Cs values are in good agreement with uncertainty.

4.5. Certified Reference Material

Certified reference materials (CRMs) and Standard Reference Materials (SRMs) are important for method development and validation. They can indicate the need to improve or change existing methods and/or the need for further training. It is well known that the use of Proficiency Tests (PTs) and CRMs is among the most important quality control tools to produce reliable and valid measurement results and to fulfill international standards requirements regarding method validation, quality control, and metrological traceability. IAEA-385 Irish Sea sediment ( Pham et al., 2008 ) was used for verification of our gamma spectrometry results for radionuclides in the sediment sample. 55 g of IAEA-385 sample was measured on GE08, GE09 and GE12 detector. The sample was counted for 60,000 s on each detector. The results of the radionuclide activities are presented in Table 5. The same gamma energy lines were chosen to calculate the activities of individual radionuclides as discussed in section 3.4. Good agreement was found with the certificate values and the measured values by our low background gamma spectrometry measurement of radionuclides with some exceptions. Th-234 (63.3 keV) activity by GE08 shows 16.8 ± 13.4 Bq∙kg⁻¹ which is lower than the certificate value with large uncertainty may be due to the low intensity (I_γ = 3.7% ± 0.4%) of gamma-ray (Figure 10), however, the activity of ²³⁸U measured by GE09 and GE12 show good agreement with the certificate value. The precision of the measured activity of ²³⁵U in GE08, GE09, and GE12 show

Table 5. Radionuclides activity in Certified Reference material (IAEA-385 Irish Sea Sediment).

*Not detected.

Figure 10. ²³⁴Th and ²³⁸U (^234mPa) activity in CRM IAEA-385 sediment.

2.0 ± 1.8 Bq∙kg⁻¹, 1.85 ± 1.3 Bq∙kg^−1, and 2.03 ± 0.6 Bq∙kg⁻¹ which agrees with the certificate value of 1.36 ± 0.11 Bq∙kg⁻¹ (95%) confidence interval is (1.24 – 1.51 Bq∙kg⁻¹) as shown in Figure 11. The certificate value of ²³⁵U activity is based on the 16 measurements either by Alpha Spectrometry or ICPMS. Our measured activity values of 15.3 ± 0.5 Bq∙kg⁻¹, 15.1 ± 0.5 Bq∙kg⁻¹_, and 15.8 Bq∙kg⁻¹ on GE08, GE09, and GE12 HPGe detectors for ¹³⁷Cs do not agree with the certificate value of 19.8 ± 0.6 Bq∙kg⁻¹ presented in Table 5, however, our ¹³⁷Cs activity results show good agreement and precision among three detectors. To validate our ¹³⁷Cs results further, we used a PT soil sample from IAEA-CU-2006-03 World-Wide Open Proficiency Test on the Determination of Gamma Emitting Radionuclides ( Shakhashiro et al., 2007 ). Our laboratory participated in this PT exercise in 2006. Soil sample from the 2006 PT batch was analyzed for this study on GE08 and GE12 for 60000 s and the results agree with the PT value (Figure 12). The results of the Certified Reference Material IAEA-385 sediment and 2006 IAEA PT soil sample show the accuracy and precision of NCL’s low background gamma measurement capability for measuring radionuclides in environmental samples, particularly for ²³⁸U and ²³⁵U.

Figure 11. ²³⁵U activity in CRM IAEA-385 sediment.

Figure 12. ¹³⁷Cs activity in PT sample of IAEA 2006 radionuclide testing exercise.

5. Conclusion

Artificial radionuclides produced in nuclear fission and activation processes have been released into the environment during nuclear explosions and nuclear accidents. In addition, naturally occurring radionuclides also contribute to the environmental radiological hazard. Low background gamma spectrometry was applied to determine activity concentration due to naturally occurring radionuclides of ²³⁸U, ²³²Th, ²³⁵U decay series, and ⁴⁰K, ¹³⁷Cs in a sediment sample. This study shows that low background gamma spectrometry can be successfully applied to accurately measure ²³⁸U and ²³⁵U activity in sediment or similar matrix without any interference correction from nearby peaks. The sediment results show that the ²³⁸U is in equilibrium with its daughters i.e., with ²³⁴Th, ^234mPa as well as with ²¹⁰Pb. ²³²Th is also in equilibrium with its daughters (²²⁸Ra, ²¹²Pb, ²¹²Bi and ²⁰⁸Tl. ²²⁶Ra activity in sediment is best determined by using the activities of ²²²Rn short-lived daughter radionuclides ²¹⁴Pb and ²¹⁴Bi rather than the direct peak of 186.21 keV which is influenced by 185.71 keV peak of ²³⁵U. Care must be taken to avoid any escape of radon gas from the container. Certified Reference Material (IAEA-385 Sediment) was used to verify the radionuclide activities in the sediment by gamma spectrometry. The results are in good agreement with the certificate values. Multi-detector analysis of radionuclides in sediment samples as well as in CRM shows that the NCL gamma spectrometry program is robust, precise, and accurate. ²¹⁰Pb (E = 46.5 keV; I_γ = 4.25%) is not detected by GE03, GE08 and GE09) detectors. The reason is that they are old p-type HPGe coaxial detectors (more than 25 years old). The thickness of the dead layer in p-type HPGe coaxial detectors increases with time which attenuates the low-energy photons and these photons do not reach the detectors’ active volume. This also affects the efficiency of the detector in low-energy regions.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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