Preamble

Development of a Nonsampling Atmospheric Radionuclide Online Measurement System

Chuan-Feng Tang¹, Liang-Quan Ge¹,², Sheng-Liang Guo³,⁴,†, Zhi-Peng Deng¹, Peng Yu¹,⁴, Yu-Chen Liu¹, Guo-Dong Xu¹, Liang Wang⁵, and Zhou Wei⁵

¹College of Nuclear Technology and Automation Engineering, Chengdu University of Technology, Chengdu 610059, China
²Applied Nuclear Technology in Geosciences Key Laboratory of Sichuan Province, Chengdu 610059, China
³Department of Engineering Physics, Tsinghua University, Beijing, 100084, China
⁴Chengdu New Ray Technology Co. Ltd, Chengdu 610052, China
⁵Sichuan Management and Monitoring Center Station of Radioactive Environment, Chengdu 611139, China

For the prompt monitoring of radionuclides released into the atmosphere by various nuclear facilities and sudden nuclear accidents, a nonsampling atmospheric radionuclide online measurement system (NSAROMS) based on NaI(Tl) scintillators was developed. Compared with traditional measurement methods, this online system eliminates the enrichment sampling process. The selection of the detector, the design of the ground gamma-ray shielding device, and the detection efficiency of the measurement system were simulated using Monte Carlo methods. A calibration experiment was subsequently carried out to measure the detection efficiency of the system, and the relative error between the detection efficiency obtained by calibration and that obtained by Monte Carlo simulation was within 5%. The minimum detectable activity concentrations (MDACs) for several common atmospheric radionuclides, including ²¹⁴Pb, ²¹⁴Bi, ⁷Be, ²²Na, ¹³⁴Cs, ¹³⁷Cs, ¹³¹I, and ⁴⁰K, were calculated based on the measured detection efficiencies for a system measurement duration of 30 minutes. Finally, preliminary applications were carried out in Mianyang, Leshan, Yibin, and Guangyuan, with measured average atmospheric radon concentrations of 7.87 ± 0.23 Bq/m³, 4.48 ± 0.15 Bq/m³, 4.30 ± 0.13 Bq/m³, and 9.90 ± 0.29 Bq/m³, respectively. The NSAROMS meets the requirements for monitoring atmospheric radionuclides in nuclear facilities. It can accurately measure the activity concentrations of radionuclides in the atmosphere and offers advantages such as convenience, a wide measurement range, low detection limits, and the ability to perform onsite online measurements at nuclear facilities.

Keywords: Atmospheric radionuclides, Online measurement, Gamma-ray measurements, Detection efficiency calibration

Introduction

Atmospheric radionuclides generally refer to radionuclides present in the atmosphere, typically as radioactive gases and aerosols. These radionuclides can be classified into primordial, cosmogenic, and artificial atmospheric radionuclides based on their sources [1]. Primordial atmospheric radionuclides, such as ²²²Rn, ²¹⁴Bi, and ²¹⁴Pb, are the decay progeny of natural uranium and thorium series and are present in the atmospheric environment with which humans commonly come into contact [2–4]. Cosmogenic atmospheric radionuclides, such as ⁷Be and ²²Na, are derived mainly from nuclear reactions of cosmic rays with the nuclei of C, H, O, and other elements in the atmosphere [5–7]. Artificial atmospheric radionuclides, such as ¹³¹I, ¹³⁷Cs, and ³H, are produced by nuclear tests, nuclear accidents, and routine emissions from nuclear power plants and other nuclear facilities within regulatory limits [8–10]. Atmospheric radionuclides can enter the human body through respiratory inhalation, skin deposition, and food intake, causing continuous ionizing radiation damage to the human body; thus, rapid monitoring of atmospheric radionuclides is particularly important [11–13].

Traditional atmospheric radionuclide activity concentration measurements are based mainly on enrichment sampling measurements. The commonly used enrichment sampling methods include the gas filtration method, inertial impact method, electrostatic collection method, etc. [14–16]. In traditional enrichment sampling methods, after enrichment sampling of atmospheric radionuclides, the samples are sent to a laboratory or transported to the detector part of the measurement instrument for radioactive measurement analysis [17–19]. The complete measurement process of the enrichment sampling method is complex and time-consuming. In the event of an emergency nuclear accident, various atmospheric radionuclides are transferred more rapidly and have greater impact ranges in the atmosphere than other environmental components do. Therefore, obtaining the activity concentrations of radionuclides in the atmosphere as early and accurately as possible is highly important for assessing and predicting environmental radioactive contamination, as well as for organizing effective measures to protect the public from external radiation and the continuous internal radiation damage caused by ingesting contaminated food or air.

To simplify the measurement process for atmospheric radionuclide activity concentration and reduce measurement time, we developed an NSAROMS that uses a large-volume NaI(Tl) scintillation detector. Compared with traditional enrichment sampling atmospheric radionuclide measurement instruments, this system has a larger direct detection volume, which eliminates the enrichment sampling step and enables direct measurement of the activity of radionuclides in the atmosphere. However, the activity concentrations of various radionuclides in soil are much higher than those in air. For example, the activity concentration range of ⁴⁰K in soil in China is 269–7834.4 Bq/kg, whereas the activity concentration range of ⁴⁰K in air is only 5.04–483.72 µBq/kg (6.5–624 µBq/m³) [20–23]. This makes the NSAROMS seriously disturbed by ground gamma rays during measurement. Moreover, the traditional static calibration method (i.e., calibration of the enrichment sampling efficiency and the probe detection efficiency separately) and the dynamic calibration method (i.e., direct use of the corresponding aerosol or gas with stable activity concentration for instrument calibration) cannot be used to calibrate the online measurement system [24–28]. Owing to the large detection volume of the online measurement system, the use of the Monte Carlo method to simulate the detection efficiency of the system will result in slow convergence and be very time-consuming. In response to the challenges of ground gamma-ray interference and detection efficiency calibration for the NSAROMS, this paper designs a corresponding ground gamma-ray shielding device and proposes a mathematical model for detection efficiency calibration based on the point source simulation method. Both Monte Carlo simulation and experimental measurement validation are carried out for this model. Finally, based on the calculated detection efficiency and the measured background energy spectrum, estimates of the MDACs for several common natural and nuclear facility-emitted atmospheric radionuclides are provided.

Supported by the National Natural Science Foundation of China (Project No. 41774147) and the National Key Research and Development Program of China (Project No. 2017YFC0602100)

†Corresponding author, gsl33@qq.com

II. Principle

A. Measurement Principles

The detector is regarded as a point detector, and a spherical coordinate system is established with the detector as the origin (Fig. 1 [FIGURE:1]). The effective detection volume can be regarded as a spherical cone, and any volume differential element $dv$ within the effective detection volume can be expressed as follows:

$$dv = r^2 \sin\phi d\theta d\phi dr$$

where $r$ is the distance from the volume element to the origin, which corresponds to the measurement depth in the atmosphere, with the maximum value taken as the 95% attenuation distance for each measured energy; $\phi$ is the angle between the line that connects the volume element to the origin and the z-axis, with the maximum value being half of the angular aperture of the ground gamma-ray shielding device; $\theta$ is the angle between the projection of the line that connects the volume element to the origin in the x-y plane and the x-axis.

Assuming that the radionuclides are uniformly distributed in the air with an activity concentration of $AC$, the number of gamma-ray photons emitted by the radionuclides in an arbitrary differential volume element within the effective detection volume that reach the detector per unit time, $dI$, can be expressed as follows:

$$dI = \frac{AC e^{-\mu_E r}}{4\pi r^2} \sin\phi d\theta d\phi dr$$

where $\mu_E$ is the attenuation coefficient for gamma rays with energy $E$. This coefficient can be obtained by fitting the mass attenuation coefficients of radiation with energies that range from 0.001 to 20 MeV in dry air, as provided by the X-ray mass attenuation coefficient table (Standard Reference Database 126) from the National Institute of Standards and Technology (NIST), and then multiplying the fitted result by the air density [29]. By integrating Eq. (2), the total number of gamma-ray photons emitted by the radionuclides within the effective detection volume that reach the detector per unit time, denoted as $I$, can be obtained as follows:

$$I = \frac{AC}{4\pi\mu_E} (1 - e^{-\mu_E r})(1 - \cos\phi)$$

The number of specific gamma-ray photons that reach the detector is represented in the detection system by the net peak area of the corresponding characteristic peak in the energy spectrum [30]. Assuming that the gamma rays that come from the ground are completely shielded, and only the gamma rays produced by the decay of atmospheric radionuclides in the air are detected by the detection system, the activity concentration of the atmospheric radionuclides can be calculated via Eq. (4):

$$AC = \frac{n}{\varepsilon \eta V t}$$

where $n$ is the net peak area of the selected characteristic peak after the background is subtracted, $\varepsilon$ is the detection efficiency of the detector for the selected characteristic energy, $\eta$ is the branching ratio of characteristic gamma rays, $V$ is the effective detection volume of the detection system, and $t$ is the measurement time. The effective detection volume $V$ of the detection system can be calculated by Eq. (5):

$$V = \int_0^{2\pi} \int_0^{\phi_0} \int_0^d r^2 \sin\phi dr d\phi d\theta = \frac{2\pi d^3}{3} (1 - \cos\phi_0)$$

where $\phi_0$ is the half-opening angle of the shielding device of the detection system, and $d$ is the maximum detectable distance, which is defined as the distance at which the number of photons with the characteristic energy of the measured radionuclide attenuates to 5% in the air. $d$ can be calculated by Eq. (6) as follows:

$$d = \frac{\ln(20)}{\mu_E}$$

B. Source Peak Detection Efficiency (SPDE)

The source peak detection efficiency (SPDE) refers to the ratio of the full-energy peak count rate produced per unit activity in a source with an actual geometric structure (such as a volume source, surface source, or gaseous source) to the actual gamma-ray emission rate within the source. It can be understood as an equivalent estimate of the full-energy peak detection efficiency under complex source geometry. Owing to the extremely large detection volume of the NSAROMS for atmospheric radionuclides, traditional calibration methods cannot be applied for full-energy peak efficiency calibration. Therefore, the representative point method is used to calibrate the SPDE. This method calculates the SPDE of a volume source based on the full-energy peak detection efficiency measured at representative points within the detection region.

When a point source within the detection volume has an activity $A$, the full-energy peak detection efficiency at that point during experimental measurement, denoted as $\varepsilon(r, \phi, \theta)$, can be expressed as follows:

$$\varepsilon(r, \phi, \theta) = \frac{n}{A \eta t}$$

The SPDE $\varepsilon_p(r)$ of a spherical cap with a base radius of $r$ is as follows:

$$\varepsilon_p(r) = \frac{\int_0^{2\pi} \int_0^{\phi_0} \varepsilon(r, \phi, \theta) r^2 \sin\theta d\theta d\phi}{S}$$

where $S$ represents the surface area of the spherical cap. The SPDE $\varepsilon_v$ within the spherical conical detection volume from a distance $r_0$ to $r_1$ from the origin can be expressed as follows:

$$\varepsilon_v = \frac{\int_{r_0}^{r_1} S \varepsilon_p(r) dr}{\int_{r_0}^{r_1} S dr} = \frac{\int_{r_0}^{r_1} \varepsilon_p(r) dr}{r_1 - r_0}$$

Substituting the formulas for the spherical crown area and spherical cone volume into the equation yields:

$$\varepsilon_v = \frac{3 \int_{r_0}^{r_1} \varepsilon_p(r) r^2 dr}{r_1^3 - r_0^3}$$

The SPDE of a volumetric source can be calculated based on the full-energy peak detection efficiency at discrete points using Eq. (8) and (10).

C. Minimum Detectable Activity Concentration (MDAC)

The MDAC is the lowest activity concentration of a radionuclide that a detection system can reliably detect at a certain confidence level (e.g., 95%) [31]. By calculating the MDAC of the detection system, whether the system meets the monitoring requirements can be verified.

The MDAC of the detection system can be expressed as follows:

$$MDAC = \frac{L_D}{\varepsilon \eta V t}$$

where $L_D$ represents the detection limit, which can be calculated using Eq. (12) [32]:

$$L_D = k^2 + 2k\sigma_0$$

where $k$ represents the one-sided confidence interval factor that corresponds to the selected confidence level. When the confidence level is set at 95%, $k=1.645$; $\sigma_0$ is the standard deviation of the background counts. At the 95% confidence level, the MDAC of the detection system can be calculated using Eq. (13):

$$MDAC = \frac{2.71 + 4.65\sqrt{N_B}}{\varepsilon \eta V t}$$

where $N_B$ represents the total background count of the corresponding characteristic energy peak of the detection system within the measurement time. From Eq. (5), (10), and (13), it is indicated that the MDAC of the detection system is determined by the background count, detection efficiency, and maximum detectable distance.

III. Measurement System Design

A. Structural Design of the Measurement System

As shown in Fig. 2 [FIGURE:2], the NSAROMS consists of an atmospheric radionuclide detection unit, an analysis and control unit, and a meteorological detection unit. The atmospheric radionuclide detection unit consists of a ground gamma-ray shielding device, a NaI(Tl) scintillation detector, and a digital spectrometer, among other components. The ground gamma-ray shielding device is composed of a trumpet-shaped directional shielding section and a fixed base. Its primary function is to shield gamma rays from the ground and structures, thereby improving the detection limit of the measurement system and reducing the effect of surrounding environmental gamma rays on the measurement results. The primary functions of the NaI(Tl) scintillation detector and digital spectrometer are to detect the gamma rays produced by the decay of atmospheric radionuclides, collect and process them into gamma-ray spectra, and then transmit the spectra to the computer for calculation of the activity concentrations of the corresponding atmospheric radionuclides.

The analysis and control unit is composed of an industrial computer, a power controller, and an uninterruptible power supply (UPS), among other components. Its primary function is to analyze and calculate the collected gamma-ray spectra, meteorological information, and GPS information. It controls both the atmospheric radionuclide detection unit and the meteorological detection unit, while also ensuring a stable power supply. The UPS ensures that the measurement system can continue to operate normally for approximately 10 hours in the event of a loss of the main power supply.

The meteorological detection unit comprises a small integrated weather station, a video monitor, and a GPS module. Its primary functions include recording meteorological parameters such as temperature, humidity, PM2.5, PM10, and rainfall during measurements, as well as providing video surveillance of the entire system. The meteorological data collected by the detection unit are utilized in subsequent studies to trace the sources of atmospheric radionuclides, analyze their atmospheric dispersion and transport, and assess climatic impacts.

B. Design of the Detector and Ground Gamma-Ray Shielding Device

In the selection of the detector for the online measurement system, detection efficiency, energy resolution, intrinsic radioactivity, and cost-effectiveness should be considered. To ensure that the detection efficiency of the online measurement system for airborne radionuclides meets the required standards, the Geant4 toolkit was used to simulate the gamma-ray detection efficiencies of scintillation detectors of various types and sizes (such as NaI(Tl), CeBr₃, LaBr₃(Ce), BGO, CsI(Tl)) in the energy range of 0.1–3 MeV. Geant4 is a Monte Carlo simulation toolkit written in C++ [32]. Using this toolkit, a hemispherical source with a 10-meter radius filled with atmospheric radionuclides above the ground was used as the simulated radiation source to model detection efficiency and reduce simulation computation time. The detector was placed vertically to improve detection efficiency for atmospheric radionuclides. Fig. 3 [FIGURE:3] shows the simulated detection efficiency curves for NaI(Tl) detectors with sensitive volumes of 1 in. (ϕ1 in. × 1 in.), 2 in. (ϕ2 in. × 2 in.), 3 in. (ϕ3 in. × 3 in.), 5 in. (ϕ5 in. × 5 in.), 2 L (2 in. × 4 in. × 16 in.), and 4 L (4 in. × 4 in. × 16 in.). Fig. 3 shows that the detection efficiency for gamma rays at different energies increases with increasing sensitive volume of the detector, with a more pronounced effect in the low-energy region. Fig. 4 [FIGURE:4] shows the detection efficiencies of different types of detectors with the same sensitive volume (ϕ3 in. × 3 in.). When the gamma-ray energy exceeds 0.2 MeV, the BGO detector has the highest detection efficiency, followed by CeBr₃, LaBr₃(Ce), and CsI(Tl), whereas NaI has the lowest detection efficiency. However, when the gamma-ray energy is in the range of 0.1 MeV to 0.2 MeV, the detection efficiency tends to vary among detectors, which is caused by the encapsulation materials (MgO and Al) used [34, 35].

Combining Fig. 3 and Fig. 4, we observe that increasing the sensitive volume of the detector has a more significant effect on improving detection efficiency than changing the detector type does. Therefore, a NaI(Tl) scintillation detector is selected for the online measurement system, as it offers a typical large sensitive volume (i.e., 2 L or 4 L) available from manufacturers, acceptable energy resolution, no intrinsic radioactivity, and a relatively low cost [36–39].

To ensure that the detection volume of the detection system is easy to calculate and can effectively shield ground gamma rays, the ground gamma-ray shielding device adopts a trumpet-shaped design. Moreover, to determine the optimal detection efficiency for atmospheric radionuclide measurement and the best shielding effect against ground gamma radiation, we used the Geant4 toolkit to simulate the detection efficiency and shielding performance of ground gamma shielding devices with different opening angles. A moderately priced NaI(Tl) scintillation detector with a sensitive volume of 2 L was initially selected. To simulate and evaluate the ground gamma shielding performance of the detection system, an interfering radiation source located 10 meters away from the system and 6 meters high—which matches the typical building height around nuclear facilities—was used in the simulation.

The ratio of the detection efficiency for atmospheric radionuclides to that for the interfering source is used as a parameter to evaluate the optimal opening angle of the ground gamma-ray shielding device, which is referred to as the optimal opening angle parameter (OAP), as expressed in Eq. (14):

$$OAP = \frac{\varepsilon_E}{\varepsilon_{SE}}$$

where $\varepsilon_E$ is the detection efficiency for gamma rays with different energies emitted by atmospheric radionuclides, and $\varepsilon_{SE}$ is the detection efficiency for gamma rays with different energies emitted by the interfering source. In the simulation, 3.6 cm thick lead was used as the composition material of the ground gamma-ray shielding device. The shielding effect of lead for gamma rays with energies less than 0.975 MeV was greater than 95%, and the shielding effect for 3 MeV gamma rays reached 82.27%; that is, lead can shield most of the gamma rays in nature and meet the requirements for ground gamma-ray shielding. Therefore, only the OAPs for 1 MeV–3 MeV gamma rays with changes in the half-opening angle $\phi_0$ of the ground gamma-ray shielding device were simulated and calculated, and the results are shown in Fig. 5 [FIGURE:5].

Fig. 5 shows that for 1 MeV–3 MeV gamma rays, the optimal half-opening angle of the gamma-ray shielding device is between 20° and 30°. To ensure the detection performance for atmospheric radionuclides, 30° was selected as the half-opening angle of the gamma-ray shielding device; that is, an opening angle of 60° was selected.

A horn-shaped ground gamma-ray shielding device with an opening angle of 60° was subsequently designed and fabricated, with 3.6 cm thick lead used as the filling material and 2 mm stainless steel used as the external support and protection. An XTD-100 digital spectrometer manufactured by Chengdu Newray Technology Co. Ltd. was used. The technical specifications of the detector and the digital spectrometer are shown in Table 1 [TABLE:1].

TABLE 1. Technical specifications of the detector and the digital spectrometer.

Technical index Indicators NaI(Tl) scintillator size 2 in. × 4 in. × 16 in. Energy resolution 7.8% (@¹³⁷Cs 662 keV) Measurable gamma-ray energy range 30 keV–3.0 MeV

To determine whether the NaI(Tl) scintillation detector with a 2 L sensitive volume (2 in. × 4 in. × 16 in.) and the designed ground gamma-ray shielding device meet the MDAC requirements for online atmospheric radionuclide measurement in environments surrounding nuclear facilities, we constructed a sealed lead chamber and measured its background spectrum. The MDAC calculation was performed using Eq. (13), where the detection efficiency $\varepsilon$ was initially estimated using the simulated detection efficiency of a hemispherical radioactive source with a 10 m radius above the ground. The preliminary calculations revealed that the MDACs of the detection system for ¹³⁷Cs and ¹³⁴Cs with a 30-minute measurement time were 6.40 ± 0.24 Bq/m³ and 6.01 ± 0.24 Bq/m³, respectively. These MDAC values are lower than the derived air concentration limits for public radiation exposure in adults under the fast absorption lung absorption category, which are 20.70 Bq/m³ for ¹³⁷Cs and 14.43 Bq/m³ for ¹³⁴Cs. This demonstrates that the design of the detector and the ground gamma-ray shielding device meets the requirements for online measurement of atmospheric radionuclides in environments surrounding nuclear facilities [40].

C. Software Design

The measurement system software adopts a multithreading design to improve data processing efficiency, thus enabling simultaneous execution of measurement, data processing, and data transmission functions. The running process of the measurement system software, which is shown in Fig. 6 [FIGURE:6], is as follows:

1. The corresponding parameters are read. The default parameters include measurement parameters, communication parameters, calculation parameters, and display parameters.
2. When the measurement starts, the software simultaneously creates four threads: a measurement thread; an energy spectrum stabilization thread; a calculation, storage and display thread; and a data transmission thread. These four threads run concurrently, with data transferred between them using a message queue.

The measurement thread serves as the main thread and is responsible primarily for the continuous automated monitoring of atmospheric radionuclide activity concentrations and other meteorological parameters. The energy spectrum stabilization thread monitors the measured spectrum in real time and adjusts the measurement parameters to prevent spectrum drift while also monitoring and adjusting other status parameters. The calculation, storage, and display thread calculates atmospheric radionuclide activity concentrations using the collected spectra and then stores and displays the data. The data transmission thread is responsible for transmitting the measurement data to a designated server or other storage units.

IV. Calibration Experiment

A. Detection Efficiency Simulation

A model of the overall structure of the detection system was constructed using the Geant4 toolkit, as shown in Fig. 7 FIGURE:7. In addition to the simplified PMT and MCA, other related materials and their sizes were represented according to the corresponding parameters provided by the manufacturer. Through the constructed model, a spherical coordinate system was established with the spherical cone vertex of the ground gamma-ray shielding device as the origin. The energy detection efficiencies of different points, layers, and volumes at different atmospheric depths were then simulated. In the simulation of point detection efficiency, based on the central symmetry of the detection system, point sources were uniformly distributed on the spherical surface at each atmospheric depth according to the $\theta$ and $\phi$ angles. A schematic diagram of their projection onto the x–y plane is shown in Fig. 7(b).

In this experiment, a radioactive source of ²²⁶Ra that had reached radioactive equilibrium was used. Therefore, in the simulation calculations, gamma-ray energies with relatively high emission probabilities from its decay progeny—specifically, 0.351 MeV (from ²¹⁴Pb), 0.609 MeV (from ²¹⁴Bi), and 1.764 MeV (from ²¹⁴Bi)—were selected [36].

In this simulation calculation, G4EmLivermorePhysics was used to simulate the specific point, layer, and volume detection efficiencies at different atmospheric depths, and the volume detection efficiencies calculated by Eq. (8) and Eq. (10) were compared with the volume detection efficiency obtained by direct simulation.

Fig. 8 [FIGURE:8] (a), (b), and (c) show comparisons between the directly simulated volumetric detection efficiency and the calculated volumetric detection efficiencies (derived from the simulated point detection efficiencies) for different gamma-ray sources at various thicknesses, with $r=120$ cm used as the reference plane. The results demonstrate excellent agreement between the simulated and calculated volumetric detection efficiencies, with relative deviations within ±4%. These simulation results fully validate the correctness and feasibility of the theoretical approach used in this calibration experiment.

B. Detection Efficiency Experiment

The complete experimental platform was composed of the NSAROMS and calibration structural components. The calibration structural components were made of 3D-printed photosensitive resin and carbon fiber materials, which minimized their effects on gamma-ray detection efficiency measurements. Moreover, these materials ensured the required support strength and rigidity of the support rod when radioactive sources were held at greater heights while keeping the overall weight as low as possible. Notably, because the rod had a certain width in the actual measurement, seven fewer radioactive source locations were placed at various heights than in the Monte Carlo simulation. These missing locations were on the circle with the smallest radius at the top.

To avoid the experiment being affected by the construction materials of surrounding tall buildings, the experimental platform was built in an open area more than 50 m away from tall buildings, as shown in Fig. 10 [FIGURE:10]. The activity of the standard source ²²⁶Ra used in this experiment was $1.88 \times 10^7$ Bq (with an uncertainty of 3%). The radioactivity of ²²⁶Ra and its decay products was in equilibrium, and its measured spectrum is shown in Fig. 11 [FIGURE:11]. The tray holding the fixed radioactive source remained perpendicular to the support rod at all times (as shown in Fig. 9 [FIGURE:9]). This ensured that the source consistently faced the detector at the same position, thus minimizing measurement variations caused by the shape of the source, especially at shorter measurement distances.

The point source detection efficiency was subsequently measured. At a measurement distance of 600 cm, significant deformation of the support rod was observed at azimuthal angles $\phi = \pi/6$, which had a considerable effect on the measurement results. Therefore, the data that corresponded to this measurement distance were excluded from the final experimental data.

C. Detection Efficiency and MDAC Discussion

The mean square error of the point source detection efficiencies of each layer obtained by simulation and experiment was calculated, as shown in Fig. 12 [FIGURE:12]. Fig. 12(a) and Fig. 12(b) show that the mean square error of the interlayer point detection efficiencies for gamma rays of different energies, whether simulated or experimentally measured, reached a minimum when the measurement distance was 300 cm, which indicates that the influence of the detector shape on the detection efficiency can be ignored when the measurement distance reaches 300 cm.

A comparison between the experimentally measured detection efficiency calculated by the interpolation integral and the simulated detection efficiency for each layer is shown in Fig. 13 [FIGURE:13]. Within the experimental measurement height, the simulated detection efficiency of each layer was highly consistent with the experimental detection efficiency, and the relative error was within 5%. The main reason for the relative error increasing with increasing measurement height was the slight downward deformation caused by the load-bearing of the carbon fiber rod used for calibration.

When the detection system is simplified to a spherical shape, the total spectrum count rate $M$ of the detector can be expressed as follows [41]:

$$M = K E AC \pi \int_0^{r_1} e^{-\mu_E r} \left(r^2 - r \sqrt{r^2 - r_d^2}\right) dr$$

where $r_1$ represents the gas radius, and $r_d$ represents the radius of the simplified sphere of the detection system.

The detection efficiency of gamma rays with a specific energy at each layer can be expressed by Eq. (16):

$$\varepsilon_p(r) = \frac{F E K}{4\pi} E e^{-\mu_E r} \left(r^2 - r_d^2\right)$$

where $\varepsilon_p(r)$ represents the layer detection efficiency of gamma rays with energy $E$ at measurement distance $r$. By logarithmically transforming Eq. (16) and adding the corresponding correction coefficient when the measurement distance $r < 300$ cm, Eq. (16) can be expressed as Eq. (17):

$$\ln(\varepsilon_p(r)) = a - \mu_E r + b \ln\left(\frac{r^2 - r_d^2}{r^2}\right) \quad (r < 300 \text{cm})$$

When the measurement distance $r \geq 300$ cm, the influence of the detector shape on the detection efficiency can be ignored, so Eq. (18) is used for fitting:

$$\ln(\varepsilon_p(r)) = c - \mu_E r + \ln\left(\frac{r^2 - r_d^2}{r^2}\right) \quad (r \geq 300 \text{cm})$$

The corresponding coefficients $a$, $b$, and $c$ for gamma rays with different energies can be obtained by fitting the layer detection efficiency change using Eq. (17) and (18). The fitting curve of the experimental measurement data is shown in Fig. 14 [FIGURE:14], and the values of $a$, $b$, and $c$ obtained by fitting are shown in Table 2 [TABLE:2].

TABLE 2. Fitting parameters of the detection efficiency of the 0.351 MeV, 0.609 MeV and 1.764 MeV experiments measured as a function of the measurement distance.

Energy (MeV) a b c 0.351 0.00000 0.00001 0.00002 0.609 0.00003 0.00004 0.00005 1.764 0.00006 0.00007 0.00008

After the formula for the layer detection efficiency change with the measurement distance was obtained, Eq. (10) was used to calculate the volume detection efficiency of the corresponding atmospheric radionuclide in the measurement volume. A comparison between the measured and calculated volume detection efficiencies and the simulated volume detection efficiency is shown in Fig. 15 [FIGURE:15]. The relative error of the volume detection efficiency with different thicknesses calculated by simulation and experimental measurements is within 5%, which indicates that the calibration method adopted in this paper has high feasibility and accuracy.

In actual measurements, determining the maximum detectable distances of gamma rays with different energies is necessary. In this work, the 95% attenuation distance of gamma rays with different energies was used as the maximum detectable distance of the detection system in the air to calculate the detection efficiency and the detectable volume. According to Eq. (5), (6), (18), and the corresponding parameters measured experimentally in Table 2, gamma-ray detection efficiencies of 0.351, 0.609, and 1.764 MeV energy, respectively, were calculated, and the results are shown in Table 3 [TABLE:3]. The uncertainty was synthetic uncertainty, which was caused mainly by standard radioactive source uncertainty.

TABLE 3. System detection efficiencies obtained through fitting calculations on the basis of experimental results.

Energy (MeV) Detection efficiency 0.351 1.45E-08 ± 4.40E-10 0.609 7.03E-09 ± 2.16E-10 1.764 1.36E-09 ± 4.38E-11

By fitting the measured detection efficiencies that were calculated on the basis of the experimental measurements, an expression for the system detection efficiency with energy changes within the measured gamma-ray energy range was established, as shown in Eq. (19):

$$\ln(\varepsilon_E) = -19.56 - 1.476 \times \ln(E) \quad (R^2 = 0.9969)$$

The detection efficiencies of partial atmospheric radionuclide measurements calculated via Eq. (20) are shown in Table 4 [TABLE:4].

TABLE 4. Estimated detection efficiency values for several common atmospheric radionuclides and their 95% confidence intervals.

Nuclide Energy (MeV) Branching ratio Detection efficiency and its 95% confidence interval ²²⁸Ac 0.351 0.00000 3.68E-09 (2.18E-09, 6.20E-09) ¹³⁴Cs 0.609 0.00001 9.52E-09 (5.33E-09, 1.70E-08) ¹³⁷Cs 1.764 0.00002 2.24E-09 (1.17E-09, 4.28E-09) ¹⁰³Ru 0.00003 0.00004 6.74E-09 (4.05E-09, 1.12E-08)

According to Eq. (5), (6), and (13), along with the background spectrum, the corresponding MDACs of ²¹⁴Pb (0.351 MeV), ²¹⁴Bi (0.609 MeV), and ²¹⁴Bi (1.764 MeV) for 30 min measurement were 2.74 ± 0.08 Bq/m³, 2.85 ± 0.9 Bq/m³ and 8.94 ± 0.27 Bq/m³, respectively, and the uncertainty was synthetic uncertainty, which was contributed mainly by the detection efficiency uncertainty and the statistical fluctuations of the gamma rays. The estimated MDACs for several common atmospheric radionuclides, which were calculated on the basis of Table 4, Eq. (5), (6), and (13), and the background spectrum, are shown in Table 5 [TABLE:5].

TABLE 5. Estimated MDACs (30 min) and 95% confidence intervals for several common atmospheric radionuclides.

Nuclide Detectable volume (m³) 30 min MDAC (Bq/m³) and its 95% confidence interval ²²⁸Ac 1.47E+07 3.68E-09 (2.18E-09, 6.20E-09) ¹³⁴Cs 6.16E+06 9.52E-09 (5.33E-09, 1.70E-08) ²¹⁴Pb 2.42E+07 2.24E-09 (1.17E-09, 4.28E-09) ²¹⁴Bi 8.31E+06 6.74E-09 (4.05E-09, 1.12E-08)

TABLE 6. DACs of various common atmospheric radionuclides under several lung absorption classes for adults.

Nuclide Physical half-life Lung absorption category Committed effective dose e(g) (Sv/Bq) DAC (Bq/m³) ²¹⁴Pb 6.13 h F 5.30E-09 1.89E+04 ²¹⁴Bi 19.9 min F 1.30E-08 7.69E+03 ¹³¹I 8.04 d F 1.10E-08 8.77E+03 ¹³⁴Cs 2.06 a F 6.80E-09 1.47E+04 ¹³⁷Cs 30.0 a F 4.60E-09 2.17E+04

China has established a national standard (GB18871-2002) that specifies dose limits for workers and the public (20 mSv·a⁻¹ and 1 mSv·a⁻¹, respectively), as well as the committed effective dose per unit intake e(g) for the corresponding radionuclides, but does not directly provide the derived air concentration (DAC) [42]. We refer to the Chinese national standard (GB18871-2002) and ICRP publications 30, 60, and 103 and assume that the human respiratory rate is 20 L/min and that the annual volume of inhaled air is $1.05 \times 10^4$ m³. The DACs of various common atmospheric radionuclides for adults in several lung absorption categories were derived according to the maximum yearly dose limit of 1 mSv for the public, as shown in Table 6 [42–45].

A comparison of Table 5 and Table 6 reveals that the MDACs of all the common atmospheric radionuclides, except for ²²⁸Ac, that were measured by the NSAROMS for 30 minutes are lower than the required public DACs. This shows that the NSAROMS can be applied for daily and emergency monitoring around nuclear facilities and can obtain monitoring results faster than traditional monitoring methods can.

V. Preliminary Application Results and Analysis

The NSAROMS was installed in several regions of Sichuan Province, China, including Mianyang, Leshan, Yibin, and Guangyuan. It was used to measure atmospheric radionuclides under natural environmental conditions. The gamma energy spectra obtained from these measurements are shown in Fig. 16 [FIGURE:16]. As shown in Fig. 16, the NSAROMS is capable of measuring the activity concentrations of radon progeny, specifically ²¹⁴Pb (0.351 MeV) and ²¹⁴Bi (0.609 MeV, 1.764 MeV), in the ambient atmosphere. Therefore, the system was preliminarily applied to measure atmospheric radon concentrations to evaluate its accuracy and stability.

The concentration of radon in the atmosphere can be represented by the activity concentrations of ²¹⁴Pb and ²¹⁴Bi [46, 47]:

$$C_{Rn} = m(0.515C_{^{214}Pb} + 0.380C_{^{214}Bi}) + n$$

where $C_{Rn}$ represents the radon concentration in the atmosphere, $C_{^{214}Pb}$ represents the activity concentration of ²¹⁴Pb in the atmosphere, $C_{^{214}Bi}$ is the activity concentration of ²¹⁴Bi, and $m$ and $n$ are calibration factors. The radon concentrations measured by the NSAROMS were calibrated using the RDA7 radon monitor from Durridge Company, and the obtained calibration coefficients are as follows:

$$C_{Rn} = 1.15(0.515C_{^{214}Pb} + 0.380C_{^{214}Bi}) + 1.25 \quad (R^2 = 0.74)$$

The atmospheric radon concentration measurements obtained by the NSAROMS in Mianyang, Leshan, Yibin, and Guangyuan from September 7 to October 7, 2024, with a measurement interval of 30 minutes are shown in Fig. 17 [FIGURE:17].

The atmospheric radon concentrations measured at the four monitoring sites exhibited diurnal periodic variations on non-rainy days. As shown for the period from September 23 to 25, 2024, in Fig. 17, the concentration peaked around sunrise when the temperature was at its lowest, then gradually decreased until reaching a minimum in the late afternoon when the temperature was the highest, and subsequently began to rise again. The diurnal variation in atmospheric radon concentration is caused primarily by the formation and dissipation of a temperature inversion layer. After sunset, a temperature inversion forms and gradually thickens throughout the night until reaching its maximum just before sunrise. This inversion suppresses atmospheric turbulence and reduces vertical mixing near the ground, thus allowing radon gas to accumulate, which results in the highest concentrations around sunrise when the ground surface temperatures are at their lowest. After sunrise, solar radiation rapidly warms the ground surface compared with the air above, which disrupts the inversion layer. This enhances atmospheric turbulence and vertical convection, thereby leading to increased dispersion of radon and, consequently, the lowest ground-level radon concentrations in the late afternoon when temperatures peak [48, 49].

During rainfall or strong winds, the typical diurnal variation pattern of atmospheric radon concentration is disrupted. Taking the Guangyuan monitoring site as an example, owing to the difference between this measurement method and traditional enrichment-based techniques, the scavenging effect of rainfall on radon progeny in the atmosphere caused more radon decay products to enter the detection volume with rainwater or settle on the surface of the measurement system. This led to elevated atmospheric radon concentrations in the NSAROMS, as shown in Fig. 18 [FIGURE:18] [50]. On September 11, the elevated atmospheric radon concentration observed in Fig. 18 was not accompanied by detected optical rainfall because the precipitation did not exceed the detection limit of 0.01 mm per minute for the small integrated weather station.

Under strong wind conditions, radon tends to disperse over a broader area and to greater heights, which leads to a minimum atmospheric radon concentration. This is demonstrated by the radon concentration and wind speed measurements that were obtained on September 22, as shown in Fig. 19 [FIGURE:19] [48].

The diurnal variation in atmospheric radon concentration under non-rainy conditions and the decrease observed during strong wind events, as measured by the nonsampling online monitoring system for atmospheric radionuclides, are consistent with the findings reported by Kumar K. C. et al. However, during rainy weather, the wet deposition of radon progeny leads to overestimated measurements by the nonsampling online monitoring system for atmospheric radionuclides. The extent of this overestimation is influenced by factors such as the atmospheric aerosol concentration, rainfall intensity, and duration of precipitation. To address this phenomenon, future research will utilize the atmospheric radionuclide activity concentration data measured by the NSAROMS, along with meteorological data such as PM2.5, PM10, and optical rainfall measurements, to further investigate the wet deposition of atmospheric radionuclides. A deposition model will be developed to characterize the effects of rainfall on radonuclide activity concentrations, thereby enabling correction of the measured concentrations of various atmospheric radionuclides during rainy conditions.

After excluding the measurement results during rainfall, the atmospheric radon concentration ranges in Mianyang, Leshan, Yibin, and Guangyuan were <3.91–13.67 Bq/m³, <3.91–9.91 Bq/m³, <3.91–9.90 Bq/m³, and <3.91–19.95 Bq/m³, respectively. The minimum values at all locations were below the MDAC for atmospheric radon (3.91 Bq/m³) of the NSAROMS. The average atmospheric radon concentrations in Mianyang, Leshan, Yibin, and Guangyuan were 7.87 ± 0.23 Bq/m³, 4.48 ± 0.15 Bq/m³, 4.30 ± 0.13 Bq/m³, and 9.90 ± 0.29 Bq/m³, respectively. All the values were lower than the typical outdoor concentration of 10 Bq/m³ reported by the UNSCEAR in 2000 [51]. This was primarily because all the measurement sites were located in suburban areas, far from densely built-up zones—buildings are among the major sources of radon emissions. The NSAROMS can accurately measure atmospheric radon concentrations and reflect their variation patterns. In contrast to traditional radon measurement methods, this system does not require enrichment or sampling steps, is less affected by air humidity, and enables long-term continuous online monitoring of atmospheric radon concentrations. Moreover, the NSAROMS is also capable of measuring other atmospheric radionuclides, thus providing reliable measurement data for routine monitoring of various nuclear facilities and early warning in the event of nuclear accidents.

VI. Conclusions

This study developed a nonsampling atmospheric radionuclides online measurement system based on a NaI(Tl) scintillation detector for routine and emergency monitoring of atmospheric radionuclides around nuclear facilities. In addition, a calibration model and method for determining the detection efficiency of this online monitoring system were established. The experimental results for the detection efficiency show that, within the measured distance range, the relative errors between the experimentally measured and calculated detection efficiencies for each layer, as well as the volumetric detection efficiencies at different depths, were all within ±5% of the simulated values. This finding indicates that both the online measurement system and the calibration method are highly feasible and accurate. The layer detection efficiencies for different gamma-ray energies at various measurement distances were analyzed. The results indicate that in this measurement system, when the measurement distance exceeds 300 cm, the influence of the detector shape on the detection efficiency becomes negligible. The MDACs for gamma rays with energies of 0.351 MeV (²¹⁴Pb), 0.609 MeV (²¹⁴Bi), and 1.764 MeV (²¹⁴Bi), calculated from the calibration experiments for a 30-minute measurement by the system, were 2.74 ± 0.08 Bq/m³, 2.85 ± 0.09 Bq/m³, and 8.94 ± 0.27 Bq/m³, respectively. Based on the existing experimental results, the MDACs for several common atmospheric radionuclides—such as ⁷Be, ²²Na, ¹³⁴Cs, ¹³⁷Cs, ¹³¹I, and ⁴⁰K—were calculated for a 30-minute measurement using the NSAROMS. A comparison reveals that the majority of these MDACs meet the DACs that correspond to the public dose constraints. Finally, one-month continuous atmospheric radon concentration measurements were conducted at four locations—Mianyang, Leshan, Yibin, and Guangyuan—using the NSAROMS. The results revealed that the average radon concentrations at these four sites were 7.87 ± 0.23 Bq/m³, 4.48 ± 0.15 Bq/m³, 4.30 ± 0.13 Bq/m³, and 9.90 ± 0.29 Bq/m³, respectively, all of which were below the typical outdoor concentration value reported by the UNSCEAR in 2000. Therefore, the NSAROMS not only meets the requirements for routine and emergency monitoring around nuclear facilities but also proves suitable for daily monitoring of atmospheric radon concentration. Compared with traditional measurement methods, it significantly improves the timeliness of atmospheric radioactivity surveillance and provides fast and reliable data for both routine and emergency monitoring of atmospheric radioactivity levels.

References

[1] J. Masarik. Origin and Distribution of Radionuclides in the Continental Environment. Elsevier; 2009. p. 1-25.
[2] S. Pulinets, I. Mironova, P. Miklyaev, et al. Radon Variability as a Result of Interaction with the Environment. Atmosphere;15:167. 2024. doi: 10.3390/atmos15020167.
[3] L. J. R. Nunes, A. Curado, S. I. Lopes. The Relationship between Radon and Geology: Sources, Transport and Indoor Accumulation. Applied Sciences;13. 2023. doi: 10.3390/app13137460.
[4] S. S. Al-Dargazelli. Bismuth radionuclides in the natural background gamma radiation spectrum. Journal of Radioanalytical and Nuclear Chemistry;116:3-12. 1987. doi: 10.1007/BF02037206.
[5] X. L. Wang, J. D. Zhou, K. J. Su, et al. Atmospheric radioactive nuclide deposition on the coast of the Maowei Sea, northern Beibu Gulf, China. Front Mar Sci;10. 2023. doi: 10.3389/fmars.2023.1196906.
[6] D. Lal, B. Peters. Cosmic Ray Produced Radioactivity on the Earth. In: Sitte K, editor. Kosmische Strahlung II / Cosmic Rays II. Berlin, Heidelberg: Springer Berlin Heidelberg; 1967. p. 551-612.
[7] R. Jasiulionis, H. Wershofen. A study of the vertical diffusion of the cosmogenic radionuclides, ⁷Be and ²²Na in the atmosphere. J Environ Radioactiv;79:157-169. 2005. doi: 10.1016/j.jenvrad.2004.06.003.
[8] R. Prăvălie. Nuclear weapons tests and environmental consequences: a global perspective. Ambio;43:729-744. 2014. doi: 10.1007/s13280-014-0491-1.
[9] K. Hirose. Review of the sources and behaviors of plutonium isotopes in the atmosphere and ocean. J Environ Radioactiv;277. 2024. doi: 10.1016/j.jenvrad.2017.11.009.
[10] P. P. Povinec, M. Gera, K. Holý, et al. Dispersion of Fukushima radionuclides in the global atmosphere and the ocean. Applied Radiation and Isotopes;81:383-392. 2013. doi: 10.1016/j.apradiso.2013.03.058.
[11] I. R. Bartol, M. S. Graffigna Palomba, M. E. Tano, et al. Computational multiphysics modeling of radioactive aerosol deposition in diverse human respiratory tract geometries. Communications Engineering;3:152. 2024. doi: 10.1038/s44172-024-00296-z.
[12] K. G. Andersson, C. L. Fogh, M. A. Byrne, et al. Radiation dose implications of airborne contaminant deposition to humans. Health Phys;82:226-232. 2002. doi: 10.1097/00004032-200202000-00011.
[13] B. Yang, F. Tuo, Q. Zhou, et al. Dietary exposure of radionuclides and heavy metals in adult residents in a high background natural radiation area using duplicate diet method. Scientific Reports;12:16676. 2022. doi: 10.1038/s41598-022-19979-8.
[14] Y.-l. Zhao, G.-j. Ma, B. Xie, T. Song, X. Liu. Preliminary Exploration of Aerosol Capturing. Journal of Nuclear and Radiochemistry;38:91-96. 2016. doi: 10.7538/hhx.2016.38.02.0091. (in Chinese)
[15] Z. Tan, L. Chen, W. Cheng, et al. Design and implementation of a porous impingent sampler for radon progeny aerosol. Nuclear Techniques;46. 2023. doi: 10.11889/j.0253-3219.2023.hjs.46.050401.
[16] M. E. Moore, M. E. Keillor, D. M. Kasparek, et al. Electrostatic precipitator collection efficiency studies using atmospheric radon progeny as aerosol analogs for nuclear explosion radionuclides. J Environ Radioactiv;270:107306. 2023. doi: 10.1016/j.jenvrad.2023.107306.
[17] F. Zhou, X. Chen, H. Liu, et al. Characteristics of radioactive aerosols during the pre-decommission phase of the experimental shielding reactor. Journal of Hazardous Materials;476:135120. 2024. doi: 10.1016/j.jhazmat.2024.135120.
[18] Q. Li, G. Zeng, J. Cai, et al. Instrument design for radioactive aerosol continuous monitoring. Nuclear Techniques;38:030401. 2015. doi: 10.11889/j.0253-3219.2015.hjs.38.030401. (in Chinese)
[19] G. Dougniaux, G. Hoarau. Detection limit variation against coarse aerosol during airborne contamination measurement with continuous air monitor. Radiation Protection Dosimetry;199:2229-2232. 2023. doi: 10.1093/rpd/ncad147.
[20] Z. Wang. Natural radiation environment in China. International Congress Series;1225:39-46. 2002. doi: 10.1016/S0531-5131(01)00548-9.
[21] RMTCE. 2022 ANNUAL REPORT OF THE NATIONAL RADIATION ENVIRONMENT QUALITY. 2023.
[22] L. Qu, D. Yao, P. Cong, et al. Radioactivity Concentrations in Soils in the Qingdao Area, China. Annals of the New York Academy of Sciences;1140:308-314. 2008. doi: 10.1196/annals.1454.038.
[23] Z.-Q. Pan, Sen-Lin. Radiation Levels in China: ATOMIC ENERGY PRESS; 2010. p. 25.
[24] D. Glavič-Cindro, D. Brodnik, T. Petrovič, et al. Compact radioactive aerosol monitoring device for early warning networks. Applied Radiation and Isotopes;126:219-224. 2017. doi: 10.1016/j.apradiso.2016.12.036.
[25] Q. Guoxiu, X. Chen, Y. Xu, et al. Measurement of filtering efficiency of artificial radioactive aerosol filter membrane. Journal of Radioanalytical and Nuclear Chemistry;331:3545-3550. 2022. doi: 10.1007/s10967-022-08344-8.
[26] Z.-Q. Li, D.-T. Xiao, G.-Z. Zhao, et al. Rapid determination of radon monitor's calibration factors. Nuclear Science and Techniques;27:116. 2016. doi: 10.1007/s41365-016-0118-2.
[27] G. Qin, Y. Xu, X. Chen, et al. Design of a calibration system for radioactive aerosol monitor. Journal of Radioanalytical and Nuclear Chemistry;322:367-375. 2019. doi: 10.1007/s10967-019-06557-3.
[28] J. C. Liang, P. H. Zheng, Z. J. Yang, et al. Development of calibration facility for radon and its progenies at NIM (China). Radiation Protection Dosimetry;167:82-86. 2015. doi: 10.1093/rpd/ncv222.
[29] Hubbell JH, Seltzer SM. Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients from 1 keV to 20 MeV for Elements Z = 1 to 92 and 48 Additional Substances of Dosimetric Interest. 2004.
[30] G. Cho, H. K. Kim, H. Woo, et al. Electronic dose conversion technique using a NaI(Tl) detector for assessment of exposure dose rate from environmental radiation. IEEE TRANSACTIONS ON NUCLEAR SCIENCE;45:981-985. 1998. doi: 10.1109/23.682692.
[31] X.-B. Tang, J. Meng, P. Wang, et al. Simulated minimum detectable activity concentration (MDAC) for a real-time UAV airborne radioactivity monitoring system with HPGe and LaBr₃ detectors. Radiation Measurements;85:126-133. 2016. doi: 10.1016/j.radmeas.2015.12.031.
[32] G. Gilmore. Practical Gamma-ray Spectrometry. 2nd ed: John Wiley; 2008.
[33] L. Rinaldi, F. Ambrosino, V. Roca, et al. Study of ²²²-²²⁰Rn Measurement Systems Based on Electrostatic Collection by Using Geant4+COMSOL Simulation. Applied Sciences 12. 2022. doi: 10.3390/app12010507.
[34] D. N. Grozdanov, N. A. Fedorov, Y. N. Kopatch, et al. Semi-empirical gamma-ray response function of BGO, NaI(Tl) and LaBr₃(Ce) scintillation detectors. Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment;1014. 2021. doi: 10.1016/j.nima.2021.165741.
[35] E. Ye, H. Nan, C. Shen, et al. Study on point source efficiency function of LaBr₃(Ce) detector. Nuclear Techniques;45. 2022. doi: 10.11889/j.0253-3219.2022.hjs.45.090202. (in Chinese)
[36] Knoll GF. Radiation Detection and Measurement. 4 ed: John Wiley & Sons, Inc.; 2010.
[37] Dorenbos P, de Haas JTM, van Eijk CWE. Non-proportionality in the scintillation response and the energy resolution obtainable with scintillation crystals. IEEE Transactions on Nuclear Science;42:2190-2202. 1995. doi:10.1109/23.489415.
[38] Shah KS, Glodo J, Klugerman M, et al. LaBr₃:Ce Scintillators for Gamma Ray Spectroscopy. 2002 IEEE Nuclear Science Symposium Conference Record;1:92-95. 2002. doi:10.1109/NSSMIC.2002.1239275.
[39] Moszynski M, Kapusta M, Wolski D, et al. Energy resolution of scintillation detectors readout with large area avalanche photodiodes and photomultipliers. IEEE Transactions on Nuclear Science;45:472-477. 1998. doi:10.1109/23.682429.
[40] Cheng Z, Qi-Hong Z, Yun-Ping W, et al. Evaluation of nuclear accident radioactive aerosols ation monitoring. Nuclear Techniques;34:866-871. https://d.wanfangdata.com.cn/periodical/hjs201111014.
[41] GONG Y-W, JIA M-C, GUO Z-R, et al. The Study of a Non-Sampling Atmospheric Radioactivity Monitoring Method. Nuclear Electronics & Detection Technology;34. 2014. doi:10.3969/j.issn.0258-0934.2014.04.015.
[42] AQSIQ. Basic standards for protection against ionizing radiation and for the safety of radiation sources. 2002.
[43] ICRP. Limits for Intakes of Radionuclides by Workers: Annals of the ICRP; 1979.
[44] ICRP. 1990 Recommendations of the International Commission on Radiological Protection. Oxford: Pergamon Press; 1991.
[45] ICRP. The 2007 Recommendations of the International Commission on Radiological Protection. Oxford: Annals of the ICRP; 2007.
[46] M. Kümmel, C. Dushe, S. Müller, et al. Outdoor ²²²Rn-concentrations in Germany – part 1 – natural background. J Environ Radioactiv;132:123-130. 2014. doi: 10.1016/j.jenvrad.2014.01.012.
[47] A. Baeza, J.M. Caballero, J.A. Corbacho, et al. Response of an automatic air monitoring gamma-spectrometry station based on sample retention to rainfall-caused dosimetric alterations and to environments with a wide range of radon levels. Radiation Measurements;134:106324. 2020. doi: 10.1016/j.radmeas.2020.106324.
[48] L. Sesana, E. Caprioli, G.M. Marcazzan. Long period study of outdoor radon concentration in Milan and correlation between its temporal variations and dispersion properties of atmosphere. J Environ Radioactiv;65:147-160. 2003. doi: 10.1016/S0265-931X(02)00093-0.
[49] K.C. Kumar, K. Nagaraja. Time-series analysis of radon concentrations for Bengaluru's atmosphere. Radiation Protection Dosimetry;200:1003-1006. 2024. doi: 10.1093/rpd/ncad272.
[50] R. Dabrowski, H. Dombrowski, P. Kessler, et al. Detection of rain events in radiological early warning networks with spectro-dosimetric systems. Journal of Instrumentation;12:P10005. 2017. doi: 10.1088/1748-0221/12/10/P10005.
[51] UNSCEAR. SOURCES AND EFFECTS OF IONIZING RADIATION; 2000.