Preamble

Vol. XX, No. X, XXX 20XX
NUCLEAR TECHNIQUES

Efficiency Calibration and Coincidence Correction Factor Measurements for Well-Type HPGe

Yu Guobing¹, Gu Xianbao¹*, Xiang Yunxiang², Liu Yi¹, He Xu¹, Zhang Wenliang¹, Wang Jinlong¹
¹ Anhui Radiation Environment Supervision Station, Hefei 230071, China
² Anhui Fusion New Energy Ltd., Hefei 230000, China

Abstract

[Background] Well-type HPGe detectors offer high detection efficiency and are commonly used for measuring small-volume samples. While summation corrections are necessary in such measurements, relevant data for this detector type remain scarce in the literature. [Purpose] This study aims to calculate detection efficiency curves and coincidence correction factors for well-type HPGe detectors. [Methods] We calibrated the detection efficiency of an HPGe detector using conventional monoenergetic γ-ray standard sources and measured cascade coincidence correction factors for common radionuclides including ⁶⁰Co, ⁸⁸Y, ¹³¹I, ¹³⁴Cs, ¹⁵²Eu, and ¹³³Ba. [Results] Measurements revealed that efficiency values obtained using ¹³⁹Ce from conventional monoenergetic γ standard sources can deviate from fitted values by up to 49%. The coincidence effect in well-type HPGe significantly impacts activity measurements, with smaller sample heights yielding larger correction factors. At a sample height of 0.5 cm, the coincidence correction factor for the 563.23 keV γ-ray full-energy peak of ¹³⁴Cs reached 8.00, while that for the 604.70 keV γ-ray peak was 3.01. When sample activity exceeds approximately 1000 Bq, accidental coincidence contributions to the total correction factor become increasingly significant. For ¹³¹I, increasing the activity from 1300 Bq to 6300 Bq raised the correction factor for the 80.19 keV γ-ray full-energy peak by 10%. [Conclusions] These measurement data provide valuable references for selecting appropriate efficiency calibration sources for well-type HPGe detectors and for correcting radionuclide activity measurements.

Keywords: Well-type HPGe, Coincidence Factor, ¹³⁹Ce, ¹³⁴Cs, ¹³¹I

Introduction

High-purity germanium (HPGe) detectors are routinely used in laboratories to measure the activity of γ-emitting radionuclides in samples. Well-type HPGe detectors, characterized by their well-shaped crystal geometry, offer large solid angles and high detection efficiencies, making them particularly suitable for small-sample measurements. For instance, environmental samples such as fallout ash or biological ash typically weigh only a few grams and are best measured by placing them inside the detector well to maximize detection efficiency. However, this high efficiency also increases the probability of cascade coincidence effects, which can compromise measurement accuracy. Due to the limited time resolution of γ-spectrometry systems, cascading photons emitted by a nuclide cannot be distinguished and are often recorded as a single event, causing the count rate in the full-energy peak of interest to decrease or increase [1,2]. Cascade coincidence effects can occur between γ-rays and X-rays [3,4].

The standard method for obtaining cascade coincidence correction factors involves calibrating HPGe detection efficiency using a series of monoenergetic γ standard sources [5-7]. However, the applicability of common monoenergetic γ standard sources to well-type HPGe detectors and detectors with large sensitive areas requires investigation. Accurate activity measurements of radionuclides susceptible to cascade coincidence effects necessitate proper corrections. While numerous studies have investigated cascade coincidence corrections for top-mounted HPGe detectors (where samples are placed on the detector crystal surface) [8-11], few have reported measurement data for well-type HPGe detectors. O. Sima et al. [12] used Monte Carlo methods to calculate coincidence correction factors for ¹³⁴Cs and ⁶⁰Co in well-type HPGe measurements and validated their results using ²¹⁰Pb, ⁵⁷Co, ⁵¹Cr, ⁷Be, ¹³⁷Cs, ⁵⁴Mn, ⁶⁵Zn, and ⁴⁰K standard sources. Wang Shilian et al. [13] calculated coincidence correction factors for these nuclides in well-type HPGe based on their decay schemes. Neither study considered the potential effects of X-rays emitted by standard sources, sample geometry characteristics, or accidental coincidence caused by high activity on the correction factors.

This paper investigates the applicability of common monoenergetic γ standard sources for efficiency calibration of well-type and large-area HPGe detectors, measures cascade coincidence correction factors for radionuclides commonly encountered in environmental radiation monitoring, examines their relationship with sample height, and studies the relationship between activity and accidental coincidence for certain nuclides. These findings provide valuable guidance for accurately measuring radionuclide activities using well-type HPGe detectors with large solid angles.

1. Methods for Coincidence Correction

Two primary methods are commonly employed for coincidence correction: the standard source method and the distance method [14].

1.1 Standard Source Method

This method uses a set of monoenergetic γ-ray standard sources to calibrate the HPGe detection efficiency, yielding an efficiency curve ε(E) as a function of energy E that is free from coincidence effects. Under the premise that the sample matrix, geometry, mass, and other parameters are identical to those of the monoenergetic standard sources, the detection efficiency ε₀(E₀) at the energy of interest is obtained using a standard source of the target nuclide. The coincidence correction factor F for the full-energy peak of γ-rays with energy E₀ emitted by the target nuclide is then calculated as:

F = ε₀(E₀) / ε(E₀)

The standard source method requires a standard source of the target nuclide with known activity and demands high accuracy in the source activity.

1.2 Distance Method

In this approach, monoenergetic γ standard sources and the sample to be measured, having identical matrix, geometry, and mass, are measured at two positions: a far position F (where coincidence summing effects are negligible) and a near position N (close to the detector). This yields two efficiency curves, εF(E) and εN(E), and count rates nF and nN for the full-energy peak of interest at energy E₀. The coincidence correction factor F is then given by:

F = (εN(E₀) × nF) / (εF(E₀) × nN)

While the distance method does not require knowledge of the target nuclide's activity, it is not applicable for samples placed inside the well of a well-type HPGe detector.

2. Experimental Equipment

2.1 γ-Spectrometry Detectors

The well-type γ-spectrometer used in this study was a Canberra GCW5021 HPGe detector with a crystal measuring ø70 mm × 60 mm, an energy resolution of 2.0 keV at 1332 keV (⁶⁰Co), a well inner diameter of 10 mm, and a well depth of 40 mm. Additionally, a BE5030 broad-energy HPGe detector with a large sensitive area was employed, featuring a crystal size of ø81 mm × 31 mm and an energy resolution of 1.9 keV at 1332 keV.

2.2 Standard Sources

The monoenergetic γ standard sources used were standard solutions produced by LEA (France), containing ²⁴¹Am, ¹⁰⁹Cd, ¹³⁹Ce, ⁵⁷Co, ⁵¹Cr, ¹¹³Sn, ⁸⁵Sr, ¹³⁷Cs, ⁵⁴Mn, and ⁶⁵Zn. The specific activity uncertainty for ¹⁰⁹Cd was 5% (k=2), while other nuclides had uncertainties ≤3.5% (k=2). The ⁴⁰K solution was prepared using KCl with an uncertainty of approximately 4.0% (k=2). The ¹³³Ba, ¹³⁴Cs, ¹⁵²Eu, and ²²⁶Ra standard sources were produced by China Isotope & Radiation Corporation, with specific activity uncertainties of ≤2.9%, 3.5%, 3.2%, and 3.6% (k=2), respectively.

3. Results and Discussion

3.1 Efficiency Calibration

Monoenergetic γ standard sources are commonly used to obtain HPGe efficiency curves. The radionuclides in these sources typically emit only one γ-ray energy and do not produce cascade coincidence effects. However, some nuclides emit X-rays in addition to a single γ-ray, potentially creating γ-X-ray coincidences. ¹³⁹Ce is a frequently used nuclide in standard sources [1-7,11], emitting a 166 keV γ-ray along with possible X-rays at 33 keV and 38 keV [15]. Conventional P-type HPGe detectors have negligible response to photons below 40 keV [16-17], thus avoiding cascade coincidence effects and making them suitable for efficiency calibration. To investigate the applicability of ¹³⁹Ce for well-type and broad-energy HPGe detectors that exhibit good low-energy response and high detection efficiency, we prepared aqueous standard source samples of various geometries to calibrate the detection efficiencies of the GCW5021 (well-type) and BE5030 (broad-energy) HPGe detectors. The calibration results are shown in [FIGURE:1] and [FIGURE:2].

Standard source samples were prepared in commonly used environmental monitoring containers: ø50 mm × 2 mm, ø50 mm × 20 mm, ø70 mm × 65 mm, ø75 mm × 10 mm, and ø10 mm × 47 mm. These containers were placed on the detector surfaces during measurement, with the ø10 mm × 47 mm container used exclusively for in-well measurements with the well-type HPGe detector.

For the well-type HPGe detector, the efficiency deviation at 166 keV obtained using ¹³⁹Ce relative to the fitted efficiency curve was ≤2% for the ø50 mm × 2 mm, ø50 mm × 20 mm, ø70 mm × 65 mm, and ø75 mm × 10 mm containers. However, for the ø10 mm × 47 mm in-well container, this deviation reached 38%. For the broad-energy HPGe detector, deviations were ≤2% for the ø70 mm × 65 mm and ø75 mm × 10 mm containers, but increased to 12% for the ø50 mm × 2 mm container and 6% for the ø50 mm × 20 mm container.

To verify the consistency of HPGe detection efficiency near 166 keV with the fitted curve, we prepared a ø10 mm × 47 mm ²²⁶Ra standard source sample, taking advantage of its 186 keV γ-ray being close in energy to 166 keV. Measurements showed the deviation for the 186 keV γ-ray was ≤1%. [FIGURE:2] presents γ-ray spectra of ¹³⁹Ce standard source samples measured by the two HPGe detectors: ø10 mm × 47 mm and ø50 mm × 20 mm samples with the GCW5021, and ø50 mm × 2 mm and ø50 mm × 20 mm samples with the BE5030. When the efficiency deviation from the fitted curve was large, coincidence peaks of the 166 keV γ-ray with 33 keV and 38 keV X-rays were clearly visible; when the deviation was small, these coincidence peaks were barely detectable.

Detection efficiency is the primary factor influencing coincidence effects. The GCW5021 and BE5030 HPGe detectors used in this study have larger solid angles and crystal volumes than conventional P-type HPGe detectors, increasing the detection efficiency for both γ-rays and X-rays. Additionally, the detector housing materials and electrode configurations of these models facilitate low-energy photon detection, further increasing the probability of γ-X-ray coincidences. Therefore, when using monoenergetic standard sources containing ¹³⁹Ce for HPGe efficiency calibration, it is essential to verify whether the specific detector and sample geometry induce coincidence effects. The higher the detection efficiency for X-rays below 40 keV, the more pronounced the coincidence effect and the greater its impact on efficiency calibration results. Many studies [4,6] have overlooked the coincidence effects caused by ¹³⁹Ce, potentially leading to inaccurate efficiency calibrations.

3.2 Effect of Sample Height on Efficiency

To investigate the relationship between detection efficiency and sample height in well-type HPGe detectors, we calibrated the efficiency using aqueous standard source samples with a diameter of 10 mm and heights H of 0.5 mm, 1 mm, 2 mm, 3 mm, 4 mm, and 5 mm. We also measured the efficiency for simulated soil standard source samples (SiO₂ and Al₂O₃ mass ratio 5:2, density 1.4 g/cm³). The results are shown in [FIGURE:3].

For the GCW5021 well-type HPGe detector, the maximum detection efficiency for aqueous solutions occurred at H = 2 cm. For heights below 2 cm, efficiency decreased with decreasing height; above 2 cm, efficiency decreased with increasing height. For simulated soil samples, the maximum efficiency occurred at H = 1 cm. At the same height, aqueous samples showed higher efficiency than simulated soil samples, primarily due to the higher density of simulated soil increasing self-absorption. For aqueous standard sources with H = 0.5 cm, 1 cm, 2 cm, 3 cm, 4 cm, and 5 cm, the deviations at 166 keV relative to the fitted efficiency curve were 49%, 48%, 46%, 41%, 40%, and 38%, respectively. For simulated soil standard sources with H = 0.5 cm, 1 cm, 2 cm, 3 cm, and 4 cm, the deviations were 44%, 41%, 38%, 35%, and 30%, respectively. The deviation increased with decreasing height, and for the same height, aqueous samples showed larger deviations than simulated soil samples. Thus, larger detector solid angles relative to the sample and higher detection efficiencies for ¹³⁹Ce γ-rays and X-rays increase the probability of coincidence effects and their impact on results.

The detection efficiency for γ-rays and X-rays is primarily determined by the detector solid angle and sample self-absorption. For well-type HPGe detectors, when more sample material is positioned within the central region of the well, the probability of γ-ray and X-ray interactions with the crystal increases, and Compton-scattered photons are less likely to escape, thereby enhancing detection efficiency. However, increased sample density and mass raise the probability of self-absorption for γ-rays and X-rays, reducing efficiency. Therefore, the observed efficiency variations result from the combined effects of detector solid angle and sample characteristics.

3.3 Coincidence Correction Factors

Using the standard source method, we measured the full-energy peak coincidence correction factors for ⁶⁰Co, ⁸⁸Y, ¹³⁴Cs, ¹⁵²Eu, and ¹³³Ba placed inside the well-type HPGe detector. For ¹³¹I, we employed a combination of distance and standard source methods. We also measured correction factors for these nuclides placed on the detector surface. The in-well standard source samples were ø10 mm × 47 mm, while surface-placed samples were ø50 mm × 20 mm. The results are presented in [TABLE:1].

The measurements reveal substantial differences between in-well and surface placement correction factors for the same nuclide, with maximum differences reaching 5.5 times. The coincidence probability is clearly higher for in-well samples due to greater detection efficiency. The 245 keV γ-ray peak of ¹⁵²Eu showed the largest correction factor at 6.69. Significant variations in correction factors among different γ-ray energies from the same nuclide reflect the specific decay processes of each radionuclide.

When measuring atmospheric fallout ¹³¹I with a well-type HPGe detector, analyzing the 364 keV γ-ray peak yields a correction factor of 0.99, requiring no coincidence correction. However, analyzing the 80 keV or 284 keV peaks necessitates correction. For ¹³⁴Cs in fallout samples measured in-well, the 605 keV peak area must be multiplied by 1.94, whereas surface placement requires only a factor of 1.09.

To investigate the relationship between correction factors and sample height in the well, we prepared ¹³⁴Cs aqueous standard source samples with a diameter of 10 cm and heights H of 0.5 cm, 1 cm, 2 cm, 3 cm, 4 cm, and 5 cm. The correction factor measurements are shown in [FIGURE:4].

The results demonstrate that smaller sample heights yield larger correction factors. At H = 0.5 cm, the correction factor for the 563.23 keV γ-ray peak reached 8.00, while that for the 604.70 keV peak was 3.01. At H = 5 cm, these factors decreased to 3.38 and 1.94, respectively. According to the ¹³⁴Cs decay scheme, the 563.23 keV γ-ray has the highest probability of cascade emission, resulting in a larger correction factor than other energies. Smaller sample heights increase the detector solid angle and the probability that two or more cascade-emitted photons will simultaneously interact with the crystal, thereby increasing the correction factor.

3.4 Accidental Coincidence Effects

When two or more photons from different atomic nuclei enter the sensitive volume within the HPGe's time resolution and are recorded as a single event, the count in the peak of interest may be reduced or increased. This phenomenon is termed accidental coincidence. Experimentally measured coincidence correction factors include contributions from both cascade coincidence (independent of activity) and accidental coincidence (activity-dependent). While accidental coincidence is generally neglected in environmental sample measurements [17], it must be considered when measuring high-activity samples with large-solid-angle, high-efficiency well-type HPGe detectors.

To study the relationship between accidental coincidence and sample activity, we measured correction factors for ø10 mm × 47 mm standard source samples of ¹³¹I, ¹³⁴Cs, and ¹³³Ba at various activities. The results are shown in [FIGURE:5], while [FIGURE:6] displays several accidental coincidence peaks in the ¹³³Ba γ-ray spectrum.

The data in [FIGURE:5] indicate that for ¹³¹I and ¹³³Ba, correction factors increase with activity above approximately 1000 Bq, remaining essentially constant below this threshold. For ¹³⁴Cs, correction factors remain constant even below 1000 Bq. Increasing ¹³¹I activity from 1300 Bq to 6300 Bq raised the correction factor for the 80.19 keV γ-ray peak by 10%, while increasing ¹³³Ba activity from 1600 Bq to 27000 Bq increased the 276.40 keV peak correction factor by 20%. Below 1000 Bq, cascade coincidence dominates the correction factor and accidental coincidence can be neglected. Above 1000 Bq, accidental coincidence contributions become increasingly significant, a consequence of the γ-spectrometry system's time resolution capabilities. Under current spectrometry technology, accidental coincidence must be considered when measuring high-activity samples with well-type HPGe detectors.

Conclusions

1. When calibrating HPGe detection efficiency using monoenergetic γ-ray standard sources, coincidence effects between ¹³⁹Ce γ-rays and X-rays can be ignored for detectors that do not respond to photons below 40 keV. However, for well-type and broad-energy HPGe detectors with good low-energy response and high efficiency, the impact of ¹³⁹Ce standard sources on calibration results must be verified. Larger detector solid angles relative to the sample and higher detection efficiencies for ¹³⁹Ce γ-rays and X-rays increase the probability of coincidence effects and their influence on calibration accuracy.

2. Few radionuclides emit monoenergetic γ-rays in the 150–300 keV energy range, and most have short half-lives. With its relatively long half-life of 137 days, ¹³⁹Ce is commonly used for HPGe efficiency calibration. In this energy region, detection efficiency varies significantly with energy and calibration points are sparse, making it difficult to identify deviations caused by ¹³⁹Ce coincidence effects during curve fitting.

3. For well-type HPGe measurements, smaller sample heights do not necessarily yield higher detection efficiencies. The optimal sample height for maximum efficiency must be determined experimentally and varies with sample matrix.

4. When measuring radionuclide activities with large-solid-angle HPGe detectors, coincidence effects significantly impact results and must be corrected based on the decay scheme of the target nuclide and sample geometry. For high-activity samples, accidental coincidence effects may also need to be considered.

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