Development of a radon-in-water primary standard

HAL Id: cea-05115799 https://cea.hal.science/cea-05115799v1 Submitted on 17 Jun 2025 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Development of a radon-in-water primary standard Benoit Sabot, Philippe Cassette, Marie-Christine Lépy, Sylvie Pierre, Krasimir Mitev To cite this version: Benoit Sabot, Philippe Cassette, Marie-Christine Lépy, Sylvie Pierre, Krasimir Mitev. Development of a radon-in-water primary standard. Metrologia, 2025, pp.1681-7575. �10.1088/1681-7575/addf52�. �cea-05115799� IOP Publishing Metrologia Metrologia XX (XXXX) XXXXXX https://doi.org/XXXX/XXXX xxxx-xxxx/xx/xxxxxx 1 © xxxx IOP Publishing Ltd Development of a radon-in-water primary standard Benoit Sabot1, Philippe Cassette2, Marie-Christine Lépy1, Sylvie Pierre1, Raphaël Martin1, and Krasimir Mitev2 1 Université Paris-Saclay, CEA, LIST, Laboratoire National Henri Becquerel (LNE-LNHB), 91120, Palaiseau, France 2 Sofia University “St. Kliment Ohridski”, Faculty of Physics, 1164, Sofia, Bulgaria E-mail: [email protected] Received xxxxxx Accepted for publication xxxxxx Published xxxxxx Abstract The absence of a certified standard for radon-in-water presents a significant gap in environmental monitoring and water production quality control in compliance with EURATOM directive 2013/51. To address this, we developed a system to produce a radon-in-water primary standard derived from the radon primary standard available at LNHB, which is based on counting in defined solid angle (DSA). The radon certified by DSA counting was dissolved into a known quantity of water using a newly developed system that allows a loss-free transfer with ensured accuracy and reproducibility. To validate the production of this standard, multiple primary measurement methods were employed. Radon activity in water was determined using liquid scintillation counting, specifically the Triple-to-Double Coincidence Ratio (TDCR) method, which provides a direct and highly accurate measurement. Additionally, gamma-ray spectrometry was applied as an independent verification technique. Comparative analysis of these methods was conducted to assess their consistency and reliability in certifying the radon-in-water standard. The results demonstrated the effectiveness of our production method and confirmed the validity of the radon-in-water standard. However, our study also revealed subtle yet significant factors influencing gamma-ray spectrometry measurements, highlighting the need for careful consideration of such effects in future measurements. This work contributes to the establishment of a robust and reliable radon-in-water standard, filling an essential gap in the field and supporting improved traceability chain, environmental monitoring, radioprotection, and calibration of measurement systems. Keywords: 222Rn-in-water, primary standard, TDCR counting, Gamma-spectrometry, LSC counting 1. Introduction Radon (222Rn) is a naturally occurring radioactive gas that is widely studied due to its impact on public health. With a halflife of 3.8232 (8) days, radon decays by alpha transition into a series of radioactive progenies emitting themselves alpha and beta particles associated with gamma transitions. The entire decay chain can contribute to radiation exposure through inhalation or ingestion. The monitoring and regulation of radon concentrations, particularly in water, are crucial to mitigate potential health risks. In this context, the European Union has established specific limits and norms under EURATOM directives 2013/51 [1] to control radon exposure in drinking water. The parametric value for radon in water for human consumption is defined in the directives as 100 Bq·L-1. The ISO standards for radon measurement in water, including ISO 13164-4 for liquid scintillation counting (LSC) and ISO 13164-3 for gamma-ray spectrometry (GS), provide guidance on analytical methods. However, the lack of certified standards for radon-in-water remains a significant challenge for calibration and traceability efforts. Journal XX (XXXX) XXXXXX B. Sabot et al 2 One of the main difficulties in radon-in-water calibration is the interference caused by 226Ra and its progeny, particularly 210Pb, in LSC measurements, as highlighted by [2]. This issue complicates accurate quantification and underscores the necessity of a reliable radon-in-water reference material. Previous interlaboratory comparisons, such as those organized by the Joint Research Centre (JRC) at Geel, Belgium [3] and the Institut de Radioprotection et de Sûreté Nucléaire (IRSN), France [4] have demonstrated a wide spread in the intercomparison results but these were performed without standardized reference value further emphasizing the gap in metrological traceability for radon-in-water analysis. In order to fill the gap we have developed a system to produce a radon-in-water standard derived from the defined solid angle (DSA) radon primary standard developed at LNHB [5]. An amount of 222Rn, certified by the DSA method, is dissolved in a known volume of water using a loss-free procedure, ensuring high accuracy and reproducibility. A second primary method is used in the standardization of the radon-in-water activity concertation, which is the Triple to Double Coincidence Ratio (TDCR) counting method. The two primary methods are systematically compared to assess their reliability in certifying the radon-in-water standard. Gamma-ray spectrometry is also studied as a radon-in-water measurement technique where subtle effects were found to influence GS measurements. To better understand these effects, we conducted Monte Carlo simulations in addition to experimental measurements, which provided insights into their nature and impact. This work represents a significant step toward establishing a robust radon-in-water standard, addressing a critical need in environmental monitoring and radiological protection. 2. Methods and Materials 2.1 Measurement of 222Rn in equilibrium with its short lived progeny. The decay chain of 222Rn can be simplified, as the contribution of 218At, 218Rn and 210Tl can be neglected. At equilibrium the relative activity of these radionuclides vs. the activity of 222Rn are respectively 2.2·10-4, 2.2·10-7 and 2.1·10-4. Thus, the simplified decay scheme considered in this study is presented in Figure 1. The relative activities of the radioactive daughters vs. 222Rn activity at equilibrium can be calculated with the Bateman equations using the DDEP recommended half-lives and associated standard uncertainties [6]. The results are presented in Table 1. The time needed for a closed sample to reach secular equilibrium between 222Rn and its short-lived progeny is 5 hours. This time is governed by the half-life of 214Pb, 26.9 (1) minutes. Therefore, all the measurements in this work started no earlier than 5 hours after the preparation of the corresponding samples. The ingrowth of 210Po is quite slow and the activity of this radionuclide and its radioactive daughters can be neglected in the 222Rn measurement, as, due to the source preparation from gaseous 222Rn, there is no initial 210Po activity. After a delay of 3.8 days from source preparation, the relative activity of 210Pb over the activity of 222Rn is lower than 5·10-4. Thus in our measurement conditions, the activity of 210Pb can be neglected. 2.2 The radon-in-water system General overview The radon-in-water system has been specifically designed to establish a radon-in-water standard and to produce water samples with certified radon concentration (which will be referred to in the following as “radonated water”). This system lays down the basis for a traceability chain for the various radon-in-water measurements used in practice. The main objective is to link a primary standard of radon gas directly to a radon-in-water standard, which is achieved by loss-free dissolution of primary standardized radon in water. The key functional objectives of the design were as follows: i. Enable the transfer of 222Rn certified by the DSA method to the system for production of radonated water; ii. Ensure a secure, airtight system operable from vacuum conditions to overpressure (minimum +1000 hPa); iii. Guarantee excellent, 100% loss free dissolution of radon in water, iv. Design a system which can be thoroughly cleaned after use and restored to a high-quality vacuum state, v. Facilitate sampling of the water or supply it by other means as required to disseminate the unit. Journal XX (XXXX) XXXXXX B. Sabot et al 3 The preliminary concept has been developed through extensive testing over the past three years to achieve the optimal system design. This includes previous versions of the system, which are described in [7] . After this period of testing, we successfully constructed a complete system, shown schematically in Figure 2 and photographically in Figure 3. The entire setup is made of stainless-steel tubing and connectors, with the exception of the pump membrane, made of PTFE, and two glass tubes for visual monitoring of the water to check for absence of gas bubbles. This design choice avoids gas absorption on the system’s walls. The entire system is connected to a reference volume (Vref), a high-precision pressure gauge (CPG2500 from Mensor), a temperature sensor (PT100), and a vacuum pump via volumes V1 and V2. This part of the system is not used for producing radonated water but is essential for precise volume measurement, employing the technique outlined in [7]. Volumes V3 to V19 are designated for radonated water production and are divided into two main sections: one for the LSC sampling process and the other for GS. The circuit can be fully filled with water, the circulation pump enables bi-directional flow and supports vacuum conditions down to 10-⁶ hPa, as well as overpressures up to 1000 hPa. Water temperature is monitored by a PT100 sensor (T1), and pressure by P1 (PTI-S from Swagelok). The circuit is also connected to two additional volumes: V20, through which the system is provided with dry and clean air (relative humidity below 3%), and V21, which supplies the circuit with degassed water, ensuring that no gas is absorbed during the procedure described in Section 3.1. The gamma-ray spectrometry branch The GS sampling branch of the system comprises a set of five stainless steel volumes: four of 100 cm³ and one of 50 cm³ (GAZ 11). The GS branch is indicated in Figure 2 and the positions of the GAZ volumes can be seen in Fig. 3. These volumes are interchangeable at any time via VCR® connectors, which ensure an exceptionally tight and reproducible connection, enabling flexible geometries, provided that stainless steel containers are used. A close-up of the GAZ volumes is shown in Fig. 4. A key feature of this setup is that any GAZ volume can be directly connected to the primary radon standard system for cryogenic radon transfer. Each volume is precisely measurable and can be disconnected as required to calibrate various gammaray spectrometers. The Liquid Scintillation Counting branch The Liquid Scintillation Counting (LSC) sampling branch of the system is specifically designed to provide over 100 mL of radonated water for the preparation of liquid scintillation vials. The setup includes approximately 9 meters of narrow tubing (4 mm internal diameter), which enables precise sampling. This circuit can be isolated from the rest of the system and is connected to a Dispensette®, which pushes pre-selectable amount of clean water through the tubing. Pushing with the Dispensette® allows high reproducibility and accuracy of the amount of the pushed water per push, which enables precise water sampling with the system. The narrow diameter of the tubing minimizes exchanges between the radonated water and the clean water used for sampling into the LSC vial (examples of the LSC sampling are shown in [7]). During the LSC sampling process, the needle is carefully inserted into the liquid scintillation vial and water is dispensed in the selected volume well below the surface of the liquid scintillator, in order to ensure no water reaches the air above the liquid level. Once sampling is complete, the mass of the sampled water is measured, and the vial is then topped up with scintillator to ensure no air bubbles remain when the vial is sealed. Note that as the water is denser than the organic liquid scintillation cocktails used, it stays below the cocktail and no radon escapes during the mass measurement step. Standardization of the radon-in-water concentration By design, the radon-in-water concentration is directly linked to the DSA primary standard of radon gas but can also be standardised by the Triple-to-double coincidence ratio (TDCR) counting method. In the standardisation by the defined solid angle measurement, the activity per unit of volume of 222Rn in the water (AV) is given by: where A  is the radon activity transferred to the system, which is certified by the DSA measurement, Vsys is the volume of the system filled with water and kV is a corrective factor accounting for the condition of the water during the filling of the system and the transfer of the radon to the water (e.g. temperature gradient in the water filling the system, potential existence of miniature bubbles, etc.). The relative standard uncertainty of AV is given by: 𝐴𝑉=𝐴  𝑉𝑠𝑦𝑠𝑘𝑉 (1) Journal XX (XXXX) XXXXXX B. Sabot et al 4 𝛿𝐴𝑉=√𝛿𝐴  2+𝛿𝑉𝑠𝑦𝑠 2+𝛿𝑘𝑉 2 (2) where δA  , δVsys and δkV are the relative standard uncertainties of A  , Vsys and kV , respectively. With this configuration, it is possible to calculate the volume activity in Bq·L-1, fully complying with EURATOM directive [1]. Additionally, by considering the water density under the experimental conditions, the mass activity can be determined in Bq·g-1. This method, therefore, provides two distinct measurement parameters for the same experiment. In the standardization by TDCR counting, the massactivity of 222Rn in the water is given by: 𝐴𝑚=𝐴𝑇𝐷𝐶𝑅 𝑚 (3) where ATDCR is the activity of 222Rn in the water sampled in a LSC vial, which is standardized by TDCR counting, and m is the mass of the water sampled (i.e. poured) in the LSC vial. The relative standard uncertainty of Am, δAm, is given by: 𝛿𝐴𝑚=√𝛿𝐴𝑇𝐷𝐶𝑅 2+𝛿𝑚 2 (4) where δATDCR and δm are the relative standard uncertainties of ATDCR and m, respectively. It should be noted here that no measurement is shared between the standardization of the volume activity (AV) and the mass activity (Am). In this sense it is claimed that AV and Am standardizations are completely independent. This allows for a crosscheck of the production of a radonated water standard with the new system. The criterion for the cross check is to compare whether AV and Am give coherent results taking into account the conditions of the filling the system with water. Quantitatively, a production of a radonated water standard is considered successful when the following equation is satisfied within the estimated uncertainties: 𝐴𝑉=𝜌𝐴𝑚 (5) where AV and Am are determined according to Equations 1 and 3 𝜌 is the density and their uncertainties are determined according to Equations 2 and 4, respectively. 2.3 The defined solid angle standard The radon primary standard was initially developed at LNHB in 1996 [5], recently upgraded [8], and is utilized in numerous international comparisons [9] [10]. This system operates based on the defined solid angle method [11] with a cryogenic radon source. Through a high vacuum and a cold finger maintained at 80 K, 222Rn, produced from a 226Ra source, is frozen in front of a collimated silicon detector. By precisely measuring the collimator size and the source-collimator distance, we can calculate the solid angle and, subsequently, derive the detection efficiency of the system, which is 2.019(6)·10-3. This setup allows radon standardization with a typical relative standard uncertainty as low as 0.3 %, subject to the counting statistics during measurement. Once the measurement is completed, the radon standard is transferred using a cryogenic bath into a metal container, such as the one directly connected to the radonated water system (GAZ 11 in Figure 2). 2.4 TDCR and LSC counting methods. Measurements devices The Triple to Double Coincidence Ratio (TDCR) method requires the use of a three photomultipliers tubes working in coincidence. The TDCR counters employed in these experiments include the mini-TDCR and micro-TDCR, both developed at LNE-LNHB and validated through multiple comparisons [12]. For the mini-TDCR a custom power supply set to a positive voltage of 900 V, the maximum rated voltage for the photomultiplier tubes (PMTs) was used. The TDCR acquisition is performed with a nanoTDCR module from Yantel® [13] , which enables simultaneous data acquisition with two different dead times. Consequently, measurements were repeated twice, producing a minimum of four results with dead times of 20 µs, 50 µs, 100 µs, and 150 µs, allowing for the application of the extrapolation method detailed in Section 3.2. Journal XX (XXXX) XXXXXX B. Sabot et al 5 For the micro-TDCR setup, the PMTs were supplied with a positive voltage of 1000 V through a custom high-voltage power supply. Pulses were then amplified using a fast amplifier CAEN N978 and subsequently connected to a CAEN DT5751 digitizer, featuring four channels with 1 GS·s⁻¹ sampling rate and 10-bit resolution. This configuration enables list-mode data analysis using Rust software developed in previous studies [14]. The data are analysed with an automatic Python software developed to run the Rust software with a broad range of dead-time analysis variations from 10 µs to 500 µs (value above 500 µs are possible but not relevant in this study); the results are then directly corrected for accidental coincidences [15] and radon half-life decay. The commercial liquid scintillation counting (LSC) system is the RackBeta 1214 by LKB (manufactured in 1986), operating with coincidence counting using two PMTs. Calibration was performed with liquid scintillation vials containing radon in water, using TDCR measurements from the mini-TDCR. Samples were measured individually to avoid interference from other radonated water vials in the sample changer system of RackBeta. This is essential due to the limited shielding of the LSC counting system, which was originally designed for pure beta emitters. All liquid scintillation measurements were conducted using 20 mL liquid scintillation vials completely filled with UltimaGold™ AB and the sampled water. The selected vials were made of polyethylene, coated with PTFE, as they demonstrated good stability over time compared to glass vials. The vial caps are lined with aluminium foil, ensuring a secure seal and effectively retaining radon in the cocktail. Measurements analysis for TDCR without extrapolation We consider an homogeneous mixture of radonated water with a water-miscible liquid scintillation (LS) cocktail. The measurement of the LS source starts 5 hours after preparation in order to reach secular equilibrium between radon and its shortlived progeny (i.e. not considering 210Po and its daughters). The total activity of the source at secular equilibrium is calculated by: Thus, using the data of Table 1, the global counting rate of the source is: The detection efficiency of 222Rn and 218Po is equal to one, as both nuclides are alpha emitters. The detection efficiency of 214Po is 100% when it’s decay does not occur during the dead-time of the counter. If 214Bi is detected, the probability of detection of 214Po is (1−exp(−𝜆𝜏)), where  is the decay constant of 214Po and  is the dead-time duration. Thus, the detection efficiency of 214Po is: Where 𝜀𝐵𝑖−214 ∗ is the probability that the decay of 214Bi starts the dead-time of the counter. For the nanoTDCR acquisition system based on the MAC3 logic [13], [16], the dead-time is triggered when the decay is detected in any PMT, i.e. not necessarily in coincidence. Strictly speaking, the dead-time duration to consider is not the base dead-time duration, but a mean dead-time extended by any pulse occurring during the dead-time. This only concerns the radionuclides of the decay chain of 222Rn uncorrelated with the decay of 214Bi. Thus this contribution, depending of the count rate, is evaluated considering a Poisson distribution of the pulses during the dead-time duration (see below). The global detection efficiency of the radonated water by the TDCR method is calculated by a locally developed FORTRAN code, Rn222TDCR, using the acquisition data (single, double and triple counting rates), the dead-time base duration and the half-life of 214Po. The detection efficiency of alpha emitters are supposed to be unity and the detection efficiency of the two beta emitters are calculated using the free parameter model in TDCR counting. It is worth noticing that the distribution of the energy deposited in the scintillator is determined by Monte Carlo simulation with the PENELOPE [17] code. This is necessary in this case, as, for such high-energy beta emitters, electrons can escape from the scintillator and do not contribute to the detection efficiency. In the case of 214Bi, Figure 5 shows the significant difference between the theoretical beta spectrum and the deposited energy distribution in the scintillator. The theoretical spectra considered are linear combinations of beta spectra 𝐴𝑡𝑜𝑡𝑎𝑙 =𝐴𝑅𝑛−222+ 𝐴𝑃𝑜−218 + 𝐴𝑃𝑏−214+ 𝐴𝐵𝑖−214+ 𝐴𝑃𝑜−214 (6) 𝑁𝑡𝑜𝑡𝑎𝑙 =𝐴𝑅𝑛−222 (𝜀𝑅𝑛−222+1.00056×𝜀𝑃𝑜−218+1.00547×𝜀𝑃𝑏−214+1.0091×𝜀𝐵𝑖−214+ 1.0091×𝜀𝑃𝑜−214) (7) 𝜀𝑃𝑜−214 =1.0091 × ((1− 𝜀𝐵𝑖−214 ∗)+ 𝜀𝐵𝑖−214 ∗ ×(1 − exp(−𝜆𝜏))) (8) Journal XX (XXXX) XXXXXX B. Sabot et al 6 calculated with the BETASHAPE code [18] after neglecting the beta transitions with probabilities lower than one percent and after normalization of the global beta decay to unity. As the energy of the beta electrons is high, the contribution of gamma-ray absorption to the detection efficiency is neglected. The contribution of Cerenkov emission to the detection efficiency is also neglected, as the PENELOPE model does not include this effect. Therefore, the global detection efficiency calculated is slightly underestimated but this bias is taken into account in the uncertainty evaluation. This type of TDCR determination of radon activity is termed “Rn-222 code” and has to be distinguished from the determination by extrapolation to zero dead-time, presented later. The main components considered for the relative standard uncertainty evaluation are: i. Experimental standard deviation of the double (D) and triple (T) counting rates and standard uncertainty of the TDCR value (depending on the experiment); ii. Influence of the kB value in the TDCR model. Even considering a large kB interval from 0.007 cm·MeV-1 to 0.015 cm·MeV1, the influence of this factor is less than 0.001%, due to the high energy of the beta particles depositing energy to the scintillator; iii. The influence of the 214Po half-life was evaluated considering the DDEP half-life evaluation of 162.3 (12) µs. For a deadtime base duration of 50 µs, the contribution of the 214Po half-life uncertainty to the relative standard uncertainty of the detection efficiency is 0.04%; iv. The contribution of the uncertainty of the spectrum calculation is evaluated to 0.6% (taking into account beta shape spectra, gamma absorption, Monte Carlo simulation of the electron energies absorbed by the scintillator, simplification of the decay scheme and no consideration of the Cerenkov effect). Measurements analysis for TDCR with extrapolation The extrapolation to zero dead time is performed using data from the CAEN module by varying the dead time value and analysing the corresponding data. A Python-based software tool enables fitting the results using the following function: D(𝜏)= a + b * exp(-ln(2)/c * 𝜏) (9) Where τ is the dead-time base duration and a, b and c are fitting parameters. An example for two different samples is presented in Figure 6; the results include the corrections for accidental coincidences, decay during measurements and decay to a reference date. In the case of the nanoTDCR measurements the same extrapolation is used however with only 4 points. The obtained results are then used with the Rn222TDCR code considering zero dead time. 2.5 Gamma-ray spectrometry method Four high-purity germanium (HPGe) spectrometers were used for the measurement of the radonated water samples. Their main characteristics are summarized in Table 2. The samples activity is measured following the process described below with the corresponding uncertainties calculated according to [19]. Efficiency calibration The efficiency calibration of the spectrometers is established for different geometrical conditions (point and volume sources) and source-to-detectors distances, as specified in Table 2. Calibration is carried out using standard sources prepared at the LNELNHB, from radioactive solutions whose mass activity has been accurately determined by different primary methods. For each geometrical condition and each energy, E, the full-energy peak (FEP) efficiency, 𝜀(𝐸), is derived from the peak area (net counting), according to: 𝜀(𝐸)=𝑁(𝐸) 𝐴∙𝐼(𝐸)∙𝑡∏𝐶𝑖 𝑖 (10) where 𝐴 is the activity of the standard radionuclide (Bq), 𝐼(𝐸) is the emission intensity of the line with energy E taken from the DDEP recommended data [6], 𝑡 is the acquisition duration (live time) (seconds), 𝐶𝑖 stands for different correction factors accounting for: i. the radioactive decay between the reference time and acquisition start time: Journal XX (XXXX) XXXXXX B. Sabot et al 7 𝐶𝑇=𝑒𝑥𝑝(−ln(2)∙(𝑇𝑚−𝑇0) 𝑇1/2 ) (11) where 𝑇𝑚 is the acquisition start time (when the measurement is carried out), 𝑇0 is the reference time (when the reference activity is known), 𝑇12 ⁄ is the 222Rn half-life, as measurements are performed once radon and its daughters have reached equilibrium. ii. the decay during measurement: 𝐶𝐷𝑒𝑐 =ln(2)∙𝑇𝑟 𝑇12 ⁄ 1−𝑒𝑥𝑝(−ln(2)∙𝑇𝑟 𝑇12 ⁄) (12) where 𝑇𝑟 is the real acquisition time (total duration of acquisition), iii. the true coincidence summing effect: Contrary to the first two corrective factors, which are the same for a specific standard radionuclide, the coincidence-summing effect is due to the decay scheme of the measured radionuclide and associated corrective factors depends on each energy. Here these are computed using the ETNA software [20, 21]. For practical use, to derive the efficiency for any energy, the set of experimental data (energies and efficiencies) are processed to obtain an efficiency curve as a function of photon energy. ACORES is a software, developed by the LNE-LNHB, used to get the calibration curve as a polynomial function by applying the chi-2 minimisation method [22]. A key feature is the ability to take into account correlations between input data through a covariance matrix. Here, for each radionuclide, the correlation factor corresponds to the source activity uncertainty, which is a common uncertainty parameter. An example of the experimental data and the resulting calibration curve in the range from 100 keV to 2 000 keV for detector G8 is plotted in Figure 7. It was obtained using seventeen standard radionuclides and the resulting relative uncertainty on the fitted values is about 0.5 %. The fitted calibration curves versus the energy for several geometrical conditions for detector GEHP1C are compared in Figure 8. Activity measurement Once the calibration curve is available, one can derive the activity of a sample as: 𝐴= 𝑁(𝐸) 𝜀(𝐸)∙𝐼(𝐸)∙𝑡∏𝐶𝑗 𝑗 (13) Only selected source-detector geometries have been used for the efficiency calibration of spectrometers (Table 2). If one wishes to measure samples with a different shape or position, it is necessary to calculate a corrective factor to account for the geometry change. This is computed using the software ETNA [21]. The calculation is based on the assumption that the detector efficiency is a combination of the intrinsic efficiency of the detector, which depends only on the energy, and of geometric factors depending on both the photon energy and the measurement geometry. This geometric factor is calculated by including the solid angle of detection and any attenuation effects in the source and container material. As presented in section 2.2, the samples are conditioned either in a 50 cm3 or 100 cm3 volume. To ensure that the geometry correction factor between calibration and measurement is as close as possible to 1, the 50 cm3 gas container has been designed with the same dimensions as the so-called “SG50” calibration volume, with the exception of the container walls which are made of 0.5 mm stainless steel instead of 1.2 mm polyethylene. For example, at 10 cm from the detector window, the geometry correction factors are1.02 and 1.03 for 352 keV and 609 keV, respectively. For each detector, the measurement sequence includes recording a background spectrum (240 000 s) without any containers, before measuring the samples. It is subtracted from the counting spectrum (proportionally to the counting live time) before determining the net peak areas, with the dedicated deconvolution software COLEGRAM [23] being used for overlapping peaks. The correction factors, efficiency transfer from Journal XX (XXXX) XXXXXX B. Sabot et al 8 calibration geometry (SG50 10 cm) to measurement geometry and coincidence summing in the measurement conditions, are calculated using ETNA. The activity of 222Rn cannot be directly measured through its gamma-ray emission (E = 510 (2) keV), whose emission is questionable. However, it can be derived via the activity of its two progenies, 214Pb and 214Bi, which are quickly in equilibrium with the parent nuclide. Both are multi-gamma emitters and they can easily be quantified using their most intense peak, respectively 351.932 (2) keV (intensity: 35.60 (7) %) and 609.312 (7) keV (intensity: 45.49 (19) %) for 214Pb and 214Bi. To derive the activity of 222Rn, the resulting activity of each daughter must be multiplied by an additional corrective factor to account for the activity ratio between 222Rn and its progenies when the radioactive equilibrium is reached (see Table 1) The GS measurements were conducted with several objectives: i. Checking the homogeneity of sampling by measuring several containers at the same sample-to detector distance, ii. Measuring the activity of individual containers at different source-to detector distances, to define the most suitable measurement conditions, iii. Measuring any residual activity when the container is emptied; iv. Demonstrating the deposition of solid daughters on the container’s walls. 3. Results 3.1 Production of radon in water standard with the new system Production of radonated water Producing radonated water is particularly challenging due to the necessity of avoiding any gas phase in the circuit, as this could lead to radon desorption from the water into air gaps. The following preparatory steps are therefore essential and must be completed before the preparation of radonated water. Strict adherence to this protocol is required: i. The radon standard, produced under vacuum in volume GAZ11, is connected to the system. All valves on the standard and in the circuit are initially closed. ii. The entire system is evacuated to a vacuum of 10-⁶ hPa. iii. The degassed water tank is filled with enough water to supply V21, and the water is degassed by pumping. ii. Once degassed, V21 is isolated, and B30 is opened, allowing degassed water to fill V21. Clean water is then dispensed through the tubing by opening either B31 and B24 or B30, ensuring all required tubing, including the Dispensette®, is entirely filled with water. iii. B21 and B24 are then closed while B30 remains open to enable further degassing of the water tank, ensuring that no gas remains in the small tubing within V21. iv. After this, the tank is filled fully with water, and degassing is completed by pumping. After these steps, the remaining system, held under vacuum at 10-⁶ hPa, is ready for water injection. Trials have shown that omitting any of these steps jeopardizes the preparation of radon in water samples. To transfer radon into water, the gaseous radon standard must first be frozen in the gas volume, using a liquid nitrogen bath. The partial pressure of radon at the temperature of liquid nitrogen is negligible, i.e. at this temperature radon is 100% frozen on the walls in contact with the bath. Once frozen, and after ensuring the system maintains an optimal vacuum, all valves are closed except B30. Sequentially, each B valve is then opened from the top of the system down to B11 and B10, the valves on the frozen standard. It is essential to wait until each opened volume is filled with water before proceeding to the next valve, allowing water to gradually fill each section. When the water reaches the radon standard valves (i.e. GAZ11 valves), these are opened one by one. The water fills the vial, immediately freezing, after which the nitrogen bath is removed. The frozen water is then allowed to thaw back into liquid form, with B30 open to maintain pressure equilibrium in the circuit. Under these conditions, radon fully dissolves into the water in GAZ11. To isolate the water supply volume, B24 is then closed, and the water is circulated with the entire system with the pump in both directions for at least 30 minutes to ensure thorough mixing. The pump flow rate is set to 1 L·min-¹, while the total volume is less than 1 L. Journal XX (XXXX) XXXXXX B. Sabot et al 15 [20] M.-C. Lépy, L. Ferreux and S. Pierre, “Coincidence summing corrections applied to volume sources,” Applied Radiation and Isotopes, vol. 70, pp. 2137-2140, 2012. [21] F. Piton, M.-C. Lépy, M.-M. Bé and J. Plagnard, “Efficiency transfer and coincidence summing corrections for γ-ray spectrometry,” Applied Radiation and Isotopes , vol. 52(3), pp. 791-795, 2000. [22] B. Boyer and M.-C. and Lépy, “ACORES, a software for fitting efficiency calibration curves,” 2025. [23] Y. Ménesguen and M.-C. Lépy, “COLEGRAM, a flexible user-friendly software for processing of ionizing radiation spectra,” Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol. 1003, p. 165341, 2021. [24] M. Tanaka, G. Girard, R. Davis, A. Peuto and N. Bignell, “Recommended table for the density of water between 0 °C and 40 °C based on recent experimental reports,” Metrologia, vol. 38, no. 4, p. 301, 2001. [25] B. Sabot, M. Rodriguez and S. Pierre, Experimental facility for the production of reference atmosphere of radioactive gases (Rn, Xe, Kr, and H isotopes), Applied Radiation and Isotopes 155, 108934, 2020. Journal XX (XXXX) XXXXXX B. Sabot et al 16 FIGURES Figure 1. Complete decay scheme of 222Rn, the light colored isotopes are negligible due either to their very low branch ratio or to their long half-life. Decay scheme extracted from Laraweb based on DDEP data [5]. Figure 2. Diagram of the radon-in-water setup with all components. "B" refers to the valve numbers and "V" to the volumes between the valves. Two lines are visually identified: one corresponds to the sampling for GS (in yellow), and the other for LSC sampling (in grey). Journal XX (XXXX) XXXXXX B. Sabot et al 17 Figure 3. A photograph of the radon-in-water standard production system at LNE-LNHB. The GS sampling part is on the left side and the LSC sampling part is on the right side (see also Fig. 2) Figure 4. The GS volumes with the VCR® connectors. Journal XX (XXXX) XXXXXX B. Sabot et al 18 Figure 5. Difference between BetaShape spectra emitted and the absorbed spectra in the liquid scintillator simulated with PENELOPE in plastic liquid scintillation vial filled with Ultima Gold™ AB with 5 mL of water. Journal XX (XXXX) XXXXXX B. Sabot et al 19 Figure 6. Example of D counting rate as a function of dead time from 10 µs to 500 µs used for the analysis of the data from the digitizer. Figure 7. Experimental efficiency calibration of detector G8 for point sources at 10 cm. The lower panel displays the relative residuals between the fitted values and the experimental ones. Journal XX (XXXX) XXXXXX B. Sabot et al 20 Figure 8. Experimental efficiency calibration of detector GeHP1C for the three different experimental conditions using the same standard SG50 (liquid solution with 50 mL volume in plastic container). Typical relative standard uncertainties are about 1.5%, 1.2% and 0.8% for the measurement distances: contact, 10 cm and 20 cm, respectively. Figure 9. Calculated mass activity of sample 5 from experiment #2 as a function of dead time with Rn-222 code, validation. Journal XX (XXXX) XXXXXX B. Sabot et al 21 Figure 10. Evolution of D (upper panel) and T/D (lower panel) counting rates corrected for radon decay and T/D over time. Figure 11. Comparisons between the results of the different methods obtained in the first experiment. The error bars indicate the overall estimated standard uncertainties. Journal XX (XXXX) XXXXXX B. Sabot et al 22 Figure 12. Comparisons between the results of the different methods obtained in the second experiment. The error bars indicate the overall estimated standard uncertainties. Journal XX (XXXX) XXXXXX B. Sabot et al 23 TABLES Table 1. Relative activities of radon daughters vs. 222Rn activity at equilibrium. Radionuclide Relative activity vs. 222Rn 222Rn 1.0 218Po 1.00056 (30) 214Pb 1.00547 (37) 214Bi 1.00910 (43) 214Po 1.00910 (48) Table 2. Main characteristics of the gamma-ray spectrometers. Detector identification G8 G9 GeHP1C GeHP2b Type Coaxial N Coaxial N Coaxial N Coaxial N Crystal diameter 49.5 mm 48.7 mm 84.8 mm 68.5 mm Crystal thickness 47.8 mm 55.4 mm 31.9 mm 71.2 mm Ge dead layer thickness 300 µm 300 µm 200 µm 300 µm Windom material Be Be Carbon-epoxy Al Window thickness 500 µm 500 µm 1 mm 2 mm External shielding Passive: 5 cm of lead – 2 mm of cadmium - 2 mm of copper Passive: 5 cm of lead – 2 mm of copper Passive: 10 cm of lead - 3 mm Stainless steel Active: Anti-cosmic Passive: 10 cm of lead and 5 mm of copper Energy resolution (Full Width at Half Maximum at 122 keV) 0.82 keV 0.92 keV 0.70 keV 1.20 keV Energy resolution (Full Width at Half Maximum at 1 332 keV) 1.82 keV 1.92 keV 1.86 keV 1.90 keV Point source calibration distance(s) 10 cm and 19 cm 10 cm 10 cm 10 cm Liquid source (50 cm3) calibration distance(s) 10 cm and 18 cm 8 cm Contact and 10 cm and 20 cm Contact and 10 cm Software Maestro Maestro Interwinner Interwinner Acquisition Ortec 926 Ortec 926 Itech QuadADC Itech QuadADC Journal XX (XXXX) XXXXXX B. Sabot et al 24 Table 3. Results of measured volumes of the circuit with associated standard uncertainties. Name of the sample Volume (cm3) VTotal 672.7 (7) VGaz11 49.32 (14) VGaz9 105.45 (20) VGaz7 105.08 (27) VGaz5 104.28 (25) VGaz1 106.06 (15) V1 + V2 29.30 (17) V3 4.17 (7) V4 3.01 (30) V6 5.72 (8) V8 4.39 (15) V9 9.90 (14) V10 13.55 (9) V12 5.41 (8) V14 4.94 (18) V16 13.25 (15) V17 5.53 (19) V18 12.44 (16) V19 120.55 (6) V20 5.03 (27) Table 4. Average masses of the water in the gas volumes estimated on the basis of different experiments. Volume No of experiments Average mass of the water in the GAZ volumes Estimated average density of the water in the GAZ volumes Mass and standard uncertainty, g Relative standard uncertainty, % Density and standard uncertainty, g/cm3 Relative standard uncertainty, % GAZ1 4 105.28(18) 0.17 0.9927(16) 0.17 GAZ5 4 103.72(26) 0.25 0.9947(25) 0.25 GAZ7 2 104.48(40) 0.38 0.9953(38) 0.38 GAZ9 3 104.60(10) 0.10 0.9920(87) 0.09 GAZ11 4 48.999(69) 0.14 0.99422(67) 0.07 Table 5. Uncertainty budget for measurements with RackBeta LS counter. Variable Typical relative standard uncertainty, % Efficiency 1.5% Mass, taking into account drop on the sampling needle 0.4% Variability across samples 0.5% Counting statistics and background correction 0.4% Decay correction with half-life of 222Rn 0.003% Decay correction during measurement 0.04% Combined relative standard uncertainty 1.7%