²³²Th is a naturally occurring, long-lived radioactive element essential in environmental radioactivity, geochemistry, and nuclear fuel research. Measuring it directly via gamma spectrometry is difficult because of its low gamma emission. Instead, gamma rays emitted by decay products like ²²⁸Ac, ²¹²Pb, ²¹²Bi, and ²⁰⁸Tl are used for indirect detection under the assumption of secular equilibrium. The activity of ²³²Th is determined by analyzing characteristic gamma-ray peaks from these decay products, such as the prominent 238.6 keV peak from ²¹²Pb, the 338.3 keV, 911.2 keV, and 968.97 keV peaks from ²²⁸Ac, the 727.3 keV peak from ²¹²Bi, and the 583.2 keV and 860.6 keV peaks from ²⁰⁸Tl ([6]). These peaks can be influenced by other radioactive elements like ²²⁶Ra, ²³⁵U, and ²³⁸U, which are often present in samples containing ²³²Th. While these decay series peaks are generally reliable in gamma spectrometry, spectral interference and true coincidence summing (TCS) corrections are often necessary ([16]). In environmental samples with low activity, positioning the source close to the detector improves counting statistics but increases TCS, which impacts accuracy. Corrections for TCS are significant in near-geometry detection due to cascading decay transitions ([3]). Studies show that the 338.3 keV peak of ²²⁸Ac is least affected by interference, making it a preferred marker for ²³²Th.

²⁰⁸Tl is particularly useful because of its intense 2614.5 keV gamma emission (~99.8%), which is easily detectable and less affected by matrix effects. However, relying solely on this marker can be problematic if secular equilibrium is not established or if interference corrections are insufficient. Its presence also contributes to natural background radiation. Monitoring its levels helps assess radiation risks to humans and ecosystems, particularly in areas with high natural radioactivity, such as monazite-rich soils and uranium mines ([1]; [4]).

Thorium is relatively immobile in the environment, making it a useful tracer for geochemical processes such as sediment sourcing, weathering, erosion, and particle transport in waterways. ²³²Th and its decay products, such as ²²⁸Ra and ²²⁸Ac, are used for sediment dating, particularly short-lived radionuclides in the ²³²Th decay series, to estimate recent sedimentation over decades to centuries. Thorium also plays a key role in monitoring nuclear materials and non-proliferation efforts. Although not fissile itself, thorium can be converted into fissile ²³³U in reactors. Tracking it in environmental samples helps detect illegal nuclear activities or contamination. Elevated thorium levels in soils may indicate industrial pollution or phosphate fertilizer use. The activity concentration of ²³²Th ranged from 15.3 ± 2.24 to 58.3 ± 4.92 Bq∙kg⁻¹ in topsoil and river sediments from the Jinding Pb-Zn mine catchment in Southwest China ([15]). In sediment samples from Novaya Zemlya in the Russian Arctic, ²³²Th activity ranged from 21.11 ± 1.27 to 46.15 ± 3.61 Bq∙kg⁻¹ ([17]). ²³²Th measurement supports environmental cleanup near mines, waste sites, or nuclear facilities ([13]). Agencies such as the EPA and IAEA monitor radionuclides like ²³²Th in drinking water, soil, and building materials to ensure safety standards. This paper discusses correction methods for accurately measuring ²⁰⁸Tl activity to reflect ²³²Th levels in low-background gamma spectrometry, comparing these results with other decay products such as ²²⁸Ac, ²¹²Pb, and ²¹²Bi.

The novelty of this study lies in the systematic metrological evaluation of multiple gamma emissions within the ²³²Th decay series under ultra-low background conditions, with particular emphasis on the analytical performance of the 2614.5 keV emission of ²⁰⁸Tl. While this high-energy line is often avoided in close-geometry measurements due to true coincidence summing (TCS), the present work demonstrates that, when rigorous summing corrections are applied using GESPECOR ([12]) simulations, the ²⁰⁸Tl line provides superior statistical precision and analytical reliability for environmental thorium determination. This study therefore establishes a practical methodology for reliable ²³²Th quantification in environmental matrices using ultra-low background HPGe gamma spectrometry.

The primary objective of this study is to establish a metrologically robust methodology for the determination of ²³²Th in environmental matrices using ultra-low background HPGe gamma spectrometry. The analytical performance of selected gamma emissions from ²²⁸Ac, ²¹²Pb, ²¹²Bi, and ²⁰⁸Tl is systematically evaluated based on 1) agreement with certified reference values, 2) inter-line consistency within the decay series under secular equilibrium, and 3) statistical precision following correction for true coincidence summing (TCS). These criteria provide a quantitative framework for identifying the most reliable gamma-ray indicators for routine environmental analysis.

²³²Th decays into stable ²⁰⁸Pb through a series of alpha and beta emissions involving various short-lived isotopes, as shown in Figure 1. ²⁰⁸Tl is produced via beta decay of ²¹²Bi (~36% branch) and has a short half-life. Its presence and activity strongly depend on upstream equilibrium, especially involving ²²⁸Th and ²¹²Bi. ²⁰⁸Tl decays through a cascade of photon emissions over picoseconds or nanoseconds as given in Figure 2 ([8]). Some excited states of ²⁰⁸Pb, populated during ²⁰⁸Tl decay, can de-excite by internal conversion (IC) rather than gamma emission. During IC, inner-shell electrons (usually K or L shell) are ejected, resulting in characteristic X-ray emissions as outer-shell electrons fill the vacancies, such as Pb Kα (~74 keV) and Kβ (~85 keV) X-rays. These events are often accompanied by a β⁻ particle and/or gamma photon, notably the 2614.5 keV gamma line. When a γ-ray or β particle triggers a coincidence in a surrounding or coupled detector (like a scintillator or plastic veto), and a low-energy X-ray is detected within the coincidence window, the system can veto the low-energy event.

Secular equilibrium occurs in a decay chain when the parent isotope’s half-life is much longer than its daughters’, and the system remains undisturbed for several half-lives, allowing activities to synchronize. Under these conditions, each daughter decays at the same rate at which it is produced, leading to equal activities across the chain. Achieving secular equilibrium in natural samples requires that the sample remain sealed for at least 5 - 6 half-lives of the intermediate daughters. To ensure secular equilibrium within the ²³²Th decay chain, samples were sealed for at least three weeks before counting. At this timescale, short-lived progeny such as ²¹²Pb (T_1/2 = 10.64 h) and ²¹²Bi (T_1/2 = 60.6 min) are fully equilibrated within 2 - 3 days, while longer-lived ²²⁴Ra (T_1/2 = 3.66 d) and its progeny, including ²⁰⁸Tl, approach equilibrium within 15 - 20 days.

At the Wadsworth Center of the New York State Department of Health (NYSDOH), we have been conducting low-background gamma spectrometry for over thirty years ([10]). This technique is used for diverse applications, including environmental, food, air, and water monitoring, facility surveillance, as well as health physics and homeland security. Low-background gamma spectrometry is suitable for measuring samples with very low activity, such as water or chemically separated materials. Typical projects involve the mandated analysis of radium in drinking water ([7]) and the monitoring of cesium at nuclear sites. Additionally, we serve as a reference laboratory and participate in radiological exercises. In this study, we used high-purity Germanium coaxial detectors (HPGe) GX13023 XtRa, with 140% relative efficiency from Mirion Technologies (Canberra) Inc. The detector features a copper cryostat and end cap. Its top entry window is made of 0.62-mm-thick carbon composite, enabling sensitivity to photons down to about 10 keV. The detector is housed inside a three-layer lead shield: an outer 7.6 cm (3″) layer of Boliden lead with 20 Bq∙kg⁻¹²¹⁰Pb content; an inner 7.6 cm (3″) layer from Plombum Firma-Laboratorium (Kraków, Poland), <3 Bq∙kg⁻¹²¹⁰Pb, and <1 mBq∙kg⁻¹⁴⁰K; and a 2 cm-thick Alpha-grade lead inserts

Figure 1. Thorium series (→alpha emission; ↓beta emission).

by Pure Technologies (Tequesta, FL, USA), with an alpha emission rate of 0.0007 counts/hr/cm² and 0.01 ppm ⁴⁰K. The Ge detector chamber is purged with boil-off nitrogen from its Dewar to limit radon ingrowth and its progeny. Details about the spectrometer’s low background features are documented elsewhere ([5]). The lead shield is topped and flanked by a 6-panel plastic scintillator muon shield, each panel 5.1 cm (2'') thick, one side divided into two for cryostat access. Made of BC-408 plastic scintillator (Saint-Gobain Crystals, Newbury, OH, USA), each panel contains two hemispherical photomultiplier tubes (Model 9900, ET Enterprises, Rockaway, NJ, USA). The entire setup is enclosed in a steel room with 15.2 cm (6'') thick walls of pre-World War II steel (Dixie Manufacturing Co., Baltimore, MD, USA), situated beneath a 47-story building that provides approximately 33 meters of water-equivalent (mwe) shielding from cosmic muons. The signals from the scintillator panels are synchronized via high-voltage bias, then combined, preamplifier, amplified, and discriminated to produce a 40 μs TTL gate. This gate vetoes the Ge detector signals processed by the Lynx Digital Signal Analyzer (LYNX).

Figure 2.²⁰⁸Tl decay scheme ([8]).

Sediment samples (S1 - S4) were collected between 2018 and 2023 from the shoreline of the Lake Ontario boat launch, specifically at the water-land interface. At each location, approximately the upper 2 cm of surface material was collected and sieved in the field to remove coarse debris and stones. A topsoil sample (~500 g) was collected from a backyard site at a depth of approximately 15 cm (6 inches) and similarly sieved to remove gravel and larger particles. In addition, a soil sample from the IAEA-2006 proficiency testing (PT) exercise was included. This PT material was previously milled, sieved to <0.1 mm, and homogenized to ensure uniformity.

All environmental samples were air-dried, homogenized, and transferred into counting containers corresponding to two geometries: a 49 mL jar and an 800 mL Marinelli beaker. For the 49 mL geometry, approximately 50 - 60 g of sample was used, whereas for the 800 mL geometry, sample masses ranged from 1000 to 1200 g. Samples were hermetically sealed and stored for at least four weeks prior to counting to ensure the establishment of secular equilibrium within the ²³²Th decay series.

Gamma spectrometric measurements were performed using an ultra-low background HPGe detector. Counting times ranged from 60,000 s to 240,000 s, depending on sample mass, geometry, and activity level. Each sample was measured in duplicate, and the reported activity values represent the mean of the two measurements to improve counting statistics and reproducibility. The relative difference between duplicate measurements was typically less than 5%, confirming good measurement reproducibility.

Secular equilibrium was verified experimentally by comparing activities derived from multiple daughter radionuclides (²²⁸Ac, ²¹²Pb, ²¹²Bi, and ²⁰⁸Tl). Equilibrium was considered established when the activities agreed within ±10% or within combined 1σ uncertainties. This criterion was satisfied for all samples analyzed. It should be noted that ²⁰⁸Tl is produced via a branching decay of ²¹²Bi, with a branching ratio of approximately 36%. However, under conditions of secular equilibrium, the activity of ²⁰⁸Tl is equal to that of its parent ²³²Th, as the branching fraction is inherently accounted for in the decay constant governing its production and decay. Background spectra were acquired for 240,000 s under identical conditions.

Method validation and quality control were performed using certified reference materials (CRMs), including IAEA-447 (Moss Soil), IAEA-412 (Pacific Ocean Sediment), and IAEA-385 (Irish Sea Sediment), as well as the PT sample. These materials ensured traceability and accuracy of the analytical procedure. Detection limits were calculated following the formulation of [2] for the critical level and detection limit, incorporating counting statistics of both sample and background spectra and accounting for unequal counting times, with modifications as described in ([9]; [14]).

Efficiency calibration was performed for both counting geometries using a mixed gamma-ray standard traceable to the National Institute of Standards and Technology (NIST, Gaithersburg, MD, USA) over the energy range of 50 - 1840 keV. Efficiencies outside this range were obtained by extrapolation. The total uncertainty of the efficiency calibration included contributions from the certified source activity and counting statistics. Sample-specific corrections for density and true coincidence summing were calculated using the Monte Carlo-based GESPECOR software ([12]; [11]), and the resulting correction factors were applied to the measured peak areas prior to activity determination.

This study highlights the effectiveness of ultra-low background high-purity germanium (HPGe) gamma spectrometry in accurately measuring ²³²Th in environmental samples. By analyzing various gamma-emitting daughter radionuclides such as ²²⁸Ac, ²¹²Pb, ²¹²Bi, and especially ²⁰⁸Tl under secular equilibrium, ²³²Th activity can be reliably determined even at low levels typical of natural soils and sediments. Of all the gamma lines studied, the 2614.5 keV emission from ²⁰⁸Tl yielded the most accurate and consistent results, with minimal variation across certified reference materials and environmental samples. Although this line is affected by true coincidence summing (TCS), applying proper correction factors restored measurement accuracy without reducing sensitivity. Other lines, particularly from ²²⁸Ac and ²¹²Pb, showed trivial summing effects and supported the activity estimates, further confirming the equilibrium assumption. The consistent activity measurements of ²³²Th across multiple gamma lines, combined with statistical analysis and summing corrections, demonstrate the validity of this method for routine environmental radioactivity evaluations. The results endorse using ²⁰⁸Tl, alongside other thorium progeny, as a dependable tracer for ²³²Th in soil and sediment samples, with applications in geochemical tracing, environmental monitoring, and radiological safety assessments. This method therefore provides a reliable analytical approach for routine environmental monitoring and regulatory compliance applications.

Abdul J. Khan: Project Design, Conceptualization, Methodology, Data Analysis, Data curation, Writing-Original Draft, Literature Survey, Supervision; Umme-Farzana Syed: Sample Preparation, Review and Editing; Cynthia A. Costello: Sample Collection and Distribution, Review and Editing.