1. Introduction

Tritium (³H) is a radioactive isotope of hydrogen [1] primarily produced in nuclear reactors, where it combines with oxygen to form tritiated water (HTO) or, less commonly, tritiated heavy water (T₂O) [2]. Because of its similarity to ordinary water, tritium spreads easily throughout the environment and is readily absorbed by living organisms [3]. However, measuring low levels of tritium is challenging due to its low-energy beta emissions, which produce low signal counts easily masked by background events. Precise correction techniques and analytical methods are needed to ensure accurate measurement. LSC is commonly used for measuring tritium but is often affected by quenching, which reduces photon detection and attenuates the signal counts [4]. A quench curve is a calibration curve that shows the relationship between the counting efficiency and the degree of quenching. To create a quench curve, a series of standards with a constant amount of radioactivity but varying levels of quenching is necessary. The counting efficiency is calculated and plotted against the quenching degree [5,6].

In this study, it was observed that signal counts tend to decrease during repeated measurements when using plastic vials commonly employed for tritium measurements. This phenomenon is particularly evident when measuring tritium with relatively high radioactivity, such as quench standards, and impacts the determination of the sample’s radioactivity. To mitigate this effect, quench standards were measured between sample measurements and incorporated into the determination of the quench curve.

To assess the influence of the quench curve on determining the sample’s radioactivity, three ROIs were selected to explore the effect across various tritium radioactivity concentrations. The ROIs included: the energy spectrum region covering beta particles emitted by tritium, the commonly used region identified through FOM analysis to enhance the signal-to-background ratio in low-level tritium analysis, and the entire channel region. The radioactivity concentration of the samples was determined for each ROI to evaluate the impact. Six tritium samples were prepared and analyzed down to a low level of 5 Bq·L⁻¹, considering the minimum detectable radioactivity specified by the Nuclear Safety and Security Commission in South Korea [7].

2. Materials and Methods

2.1 Preparation of Quench Standards

The quench curve was plotted using ten quench standards, including a blank that did not contain any radioactivity. A certified reference material of tritium with an activity of (501.4 ± 8.9) Bq·g⁻¹ (k = 1) was diluted to an activity level of 100 Bq·g⁻¹. For each quench standard, 1 g of this diluted solution was used. Each of quench standards was prepared in 20 mL polyethylene (PE) vials containing liquid scintillator (Ultima Gold – Low Level Tritium (UG-LLT), PerkinElmer) [8,9]. To maintain consistency, the volumes of the cocktail and quencher (deionized water) were adjusted in 0.2 g increments, keeping the total volume at 20 mL for each sample set [5,6]. The 100 Bq activity level was selected as it provides sufficient counts for accurate statistical analysis while keeping the count rate low enough to avoid dead-time issues in the LSC. Additionally, all prepared quenched standards were stored in the LSC tray for 12 hours prior to counting to eliminate potential luminescence effects [10].

2.2 Quench Curve

The LSC used in this study is the Quantulus 1220 (PerkinElmer), designed for detecting low-level beta emitting radionuclides [11]. The set of quench standards was measured eight times and each standard was counted for 30 minutes. The resulting data were fitted to a second-degree polynomial equation as a function of quenching degree. In the Quantulus 1220 model, SQP(E) (Spectral Quench Parameter of the External standard) is used as a parameter to assess quenching and is derived from the external standard spectrum. This parameter indicates the channel below which 99% of the gamma radiation counts from the external source are located [11]. To ensure accuracy, the SQP(E) value is measured for 3 minutes before each quench standard measurement [12,13]. The counting efficiency (ε) was calculated using the equation:

where C_s is the sample count rate (min⁻¹), C_b is the background count rate (min⁻¹), A is the activity concentration of the diluted tritium source (Bq·g⁻¹), M_i is the mass of the added tritium source (g), where i ranges from 1 to 9, representing different samples.

Moreover, the counting efficiency curve, ε(q), which depends on the quench parameter q can be expressed as a quadratic equation:

In this equation, a, b, and c are coefficients that can be determined through curve fitting based on the measured data. This quadratic model represents how the counting efficiency (ε) varies as a function of the quench parameter (q), allowing for calibration of quench effects. The curve fitting process ensures that the relationship between the efficiency and quench fully covers the range of measurements [5,6].

2.3 Measurement of Tritium Samples

2.3.1 Preparation of tritium samples

The tritium samples were prepared by mixing UG-LLT scintillation cocktail and tritium solution in an 8:12 ratio. Each sample was prepared in 20 mL PE vials, with approximately 8 g of tritium solution and 12 g of UG-LLT cocktail. The concentrations of six samples were 1,028.74, 100.11, 49.84, 24.98, 15.16, and 5.61 Bq·kg⁻¹, respectively. The corresponding disintegrations per minute (dpm) were calculated as 494.11, 48.16, 23.82, 12.04, 7.30, and 2.71 dpm. These values were based on a certified reference material, and the tritium activities were obtained by applying dilution factors to the certified reference value.

2.3.2 Measurement of tritium samples

For the analysis, regions of interest (ROI) were applied to optimize signal detection. Each sample was counted for 60 minutes to ensure a precise measurement of tritium activity. To improve measurement consistency and reduce the impact of instrumental or environmental factors, all samples were measured nine times. Five background samples were also measured nine times each, and their counting results were averaged to enhance the precision of the background correction.

The detection efficiency was determined using the quench curve. The specific activity concentration was calculated using the following equation:

where M_s is sample mass (kg) and ε(q) is detection efficiency derived from the quench curve.

2.4 Uncertainty

To ensure the reliability of the measurements, the uncertainty associated with each measurement parameter was also evaluated [14]. The combined uncertainty was calculated from the error propagation of uncertainty components, which have resulted from the sample count rate (u(C_s)), the background count rate (u(C_b)), the sample mass (u(M_s)), and the detection efficiency (u(ε)).

Additionally, the uncertainty in the detection efficiency is influenced by both the detection efficiency (u_εq) of the quenched sample, and the quench curve fitting (u_fit), which were combined to calculate the final uncertainty. The u_fit was quantified by applying 68% confidence bands [15].

2.5 Figure of Merit

Figure of Merit (FOM) is calculated according to following equation:

where ε is the detection efficiency (%), and B is the background count rate (min⁻¹). FOM is commonly used to assess the performance of a detection system by maximizing the signal-to-background ratio. A higher FOM indicates better detection sensitivity, as it reflects both high detection efficiency and low background counts [16]. This equation allows for an effective comparison between different measurement setups or channels by considering both the accuracy of the detection and the influence of background.

3. Results and Discussion

3.1 Optimizing ROI Ranges

Using the FOM (Fig. 1), the tritium spectrum (Fig. 2(a)), and the background spectrum (Fig. 2(b)), we defined three distinct ROIs. The first range, channels 20-148, was determined based on FOM for its highest sensitivity and minimal background interference. The second range, 20-250, was selected from the tritium spectrum to include all tritium signals, although it includes a slight increase in background signal. Finally, the third range, 1-1024, includes the full spectrum range. Among these ROIs, the 20-148 range showed the best signal-to-background ratio, followed by the 20-250 range, with the 1-1024 range having the lowest. The setting of ROIs and their corresponding FOM values used in this study are shown in Table 1.

Fig. 1

FOM vs. channel, with fixed at 1 and reduced upper bound (blue), and fixed at 1024 and increased lower bound (orange).

Fig. 2

Tritium beta spectrum (a), and its background (b).

3.2 Determination of the Quench Curve

All data points were included to create an accurate quench curve. As time progresses, both the SQP(E) values and count rates tend to decrease, which shifts the curve to the left, as illustrated in Figs. 3 and 4. The decrease in the efficiency and SQP(E) is attributed to the imperfect sealing of the PE vial, which allows minute amounts of deionizing water and tritium to leak through the vial walls or cap over time. By using all the data points, we assessed the uncertainty based on residuals and applied prediction bands to account for variations. Additionally, quench curves were plotted for each ROI, with the corresponding equations and parameters presented in Table 2. Fig. 5 shows the quench curves and relative residuals by three ROI ranges. From Fig. 5, it was observed that the residuals remained consistently around 1.5% across all SQP(E) values. This consistency supported the use of a uniform uncertainty of 1.5% for all values, corresponding to a 68% confidence level. For the efficiency point, a 2% uncertainty was applied, as 2% represents the largest uncertainty in the counting efficiency. This approach ensures that both the overall trend of the quench curve and the small variations in the efficiency at specific points are accurately reflected in the final uncertainty calculation. Based on the calculation following Equation 5, the uncertainty in the detection efficiency is determined to be 2.5% at k = 1. This value will then be incorporated into the combined uncertainty in the subsequent calculations.

Fig. 3

Shift in the count rate (a), and SQP(E) (b) across the quench set for different standards (STD1 to STD9). Each marker represents a specific standard, and dashed lines indicate trends over varying measurement points.

Fig. 4

Shift in the quench curve between the first (Day+0, blue) and last (Day+23, orange) measurement day.

Fig. 5

Quench curves and relative residuals for ROIs 1, 2, and 3.

Each marker represents a specific standard, and dashed lines indicate trends over varying measurement points.

3.3 Difference From Massic Activity

Table 3 presents the results for six tritium samples, showing both their measured activity and the associated uncertainties across three ROIs. The massic activity values range from 1,028.74 Bq·kg⁻¹ to 5.61 Bq·kg⁻¹, and the average measured activity and its corresponding uncertainty are provided. At higher concentrations, the measured activity values are close to the actual massic activity, but as the concentration decreases, the differences become more significant. For instance, in the lowest concentration sample (5.61 Bq·kg⁻¹), the measured activity in ROI 1 is (6.51 ± 1.30) Bq·kg⁻¹, with an uncertainty of 19.92%, illustrating how precision decreases at lower concentrations.

Among the three ROIs, the measured activity shows little variation, but there are slight differences in uncertainty depending on the ROI. These variations become more noticeable at lower concentrations, where the uncertainties increase, highlighting the importance of selecting the appropriate ROI for accurate low-level tritium analysis.

As shown in Fig. 6, the measured activity closely matches the massic activity at higher concentrations (e.g., 1,028.74 Bq·kg⁻¹ and 100.11 Bq·kg⁻¹), with smaller uncertainties. However, at lower concentrations (e.g., 5.61 Bq·kg⁻¹ and 15.16 Bq·kg⁻¹), the differences between the massic and measured activities become more noticeable, and the uncertainties grow across all ROIs. This confirms that ROI selection is more important in lower concentration measurements.

Fig. 6

Massic and measured specific activities of six tritium samples across ROIs, with error bars indicating measurement uncertainties.

As the activity decreases, using ROI 2 (channels 20- 250) results in values that align better with the massic values. However, for the last sample (5.61 Bq·kg⁻¹), the uncertainty is relatively large, though not enough to make the result completely unreliable. This increased uncertainty highlights the challenge of measuring low concentrations accurately. Therefore, choosing the right ROI and improving the method’s sensitivity for lower concentrations is key to getting more accurate and reliable results.

4. Conclusion

This study emphasizes the critical role of ROI selection in measuring tritium activity. The first ROI (channels 20-148) achieved the highest FOM, making it the optimal choice for effectively including tritium signals. Its strong signal-to-background ratio is crucial for reliable detection, especially in low-concentration samples. Conversely, the broader ROI (1-1024) introduces more background, which negatively impacts the FOM and complicates the distinction between signal and background, particularly in lower concentrations. This highlights the importance of selecting an appropriate ROI to ensure accurate measurements.

Detecting low concentrations of tritium is challenging due to the increased influence of background radiation, which makes isolating the true signal more difficult. Quench curve analysis showed that uncertainties increase as background influence grows. Therefore, it is crucial to use all available data points to enhance the accuracy of quench corrections and reduce measurement uncertainties.

While higher tritium concentrations produced results that closely matched massic values, differences became more apparent in lower concentrations. This reinforces the importance of careful ROI selection and highlights the need for ongoing improvements in measurement techniques. Specifically, for single isotope analyses, tritium signals may be better detected using channels 20-250, which cover the full tritium beta spectrum.