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A method for radiologically evaluating indoor use of dimension stone considering radon exhalation rates

Background: The use of natural radioactive building materials could be a health risk for both dwellers and mining workers. Therefore, a quick and effective method to test batches of rock samples is needed. Nevertheless, there is no reference value for maximum exhalation rates for building materials, except radiological hazard indices that do not measure gas exhalation rates directly. Objectives: This article investigated the correlations between Gamma Index and radon and thoron exhalation rates, and the proportions of radon and thoron in samples. Moreover, the main objectives were to analyze the feasibility of screening problematic samples for indoor use through a portable radiation detector (CoMo 170), which consists of a quick analysis at very low cost, and to simulate indoor concentration of radon using the measured exhalation rates of dimension stone slabs. Design: Best-selling dimension stone slabs were submitted to the following assays: gamma spectrometry, radon and thoron exhalation analysis using scintillation cell, and radioactivity measurement using a portable detector. Univariate and multivariate statistical analyses were conducted using Statistica 13 software. Results: The average activity concentrations measured were 971 ± 58.6 Bq/kg of 40K, 184 ± 9 Bq/kg of 232Th, and 74 ± 3 Bq/kg of 226Ra. The maximum activity concentrations of 40K, 232Th, and 226Ra series were 1,734 ± 100 Bq/kg, 2,667 ± 109 Bq/kg, and 596 ± 2 Bq/kg, respectively. The average exhalation rate of 222Rn was 406 ± 20 Bq/h m2. Conclusions: The main recommendations arising from this study are as follows: a portable radiation detector (CoMo 170) could be used as a screening method for selected samples; Gamma Index limit value = 1 for dimension stone slabs could be adopted when assessing radon and thoron exhalation; and the surface radon exhalation rate should be measured as a basis of recommendation for surface treatment before sales. Finally, thoron exhalations should be considered in radiological assessment, as 57% of the samples had higher thoron exhalation rates than radon.

R adioactive radon gas, present in the environment, is generated by the decay of uranium and thorium found in different quantities in most soils, rocks, and water. Radon and its progeny are wellknown pollutants, and there is considerable public concern about its exhalation from building materials, especially those used for indoor decoration, paving, flooring, or cladding. Thus, dimension stone (natural stone shaped and sized to meet the requirements) used in construction could be a natural source of radon, which could generate indoor concentrations higher than those recommended internationally. Brazil is a leading producer of dimension stone, which is exported mostly to the USA and Europe. While Brazil has no regulations about radon, the results should be presented carefully to avoid unnecessary public alarm, given the economic value of natural stone in international market.
Even though naturally occurring radionuclides are of primordial origin, exposure to them cannot be neglected in an impact assessment (1,2). Radon, for example, occurs naturally in the environment and is one of the most studied carcinogens; several investigations relate carcinogenicity to dose exposure through epidemiological studies on mine workers and case studies with the general population (3)(4)(5)(6)(7)(8)(9)(10)(11). Moreover, there is also sufficient evidence to suggest that reducing radon exposure would benefit public health by decreasing the incidence and mortality of lung cancer (7,12). A study published in the American Journal of Epidemiology, 'The Iowa Radon Lung Cancer Study' (13), states that the likelihood of developing lung cancer increases by 50% for a person exposed to daily concentrations of above 148 Bq/m 3 .
Most of the constructions take place, or covered, with natural stones, and this must be studied to assess indoor concentrations of radon and thoron. The amount of radon exhaled from these materials depends on the following factors: radium concentration in the particles, density, grain size, pore volume, and material moisture (14). The literature distinguishes three main mechanisms of radon transport and penetration in internal environments, namely, convection via cracks and openings in the construction, diffusion, and exhalation from the ground and exhalation from building materials (15). Several international studies have dealt with the radiological assessment of building materials (8,(16)(17)(18)(19)(20), but few of them have also addressed radon and thoron measurements to evaluate radiological impact correctly. Hence, in addition to calculating the radiological hazard index proposed by the European Union (EU; Gamma Index) (21), which considers gamma emissions from 226 Ra, 232 Th, and 40 K, this study also addresses the mass flow exhalation of radon and thoron gas from building materials, specifically dimension stone. The aim is to propose a method to radiologically evaluate the indoor use of dimension stone that includes the screening of problematic samples for indoor use through a portable radiation detector (CoMo 170), which consists of a quick analysis at very low cost; and to simulate indoor concentration of radon using the measured exhalation rates of dimension stone slabs. This method comprises a practical approach to assess whether a specific dimension stone would impose a risk considering an integrated radiological assessment.

Gamma index and radon regulations
As more than one radionuclide contributes to the dose, the EU directive No. 112 (22) established a screening tool for building materials based on the maximum gamma-ray dose estimate for a given material, based on the specific activities of 226 Ra, 232 Th, and 40 K. In December 2013, a new directive on ionizing radiation came into force in the EU, laying out uniform basic safety standards for the health protection of individuals exposed to ionizing radiation, both environmentally and occupationally (21,23). This directive also reinforced the Gamma Index proposed in EU directive No. 112. Radon is addressed explicitly in Articles 54, 74, 103, and Annex XVIII. Moreover, Annex XVIII of the directive, which refers to the national radon action plan, introduces the identification of building materials with significant radon exhalation as a tool to prevent radon penetration in new buildings (21,23,24). Indoor radon concentration was set at a reference level of 300 Bq/m 3 with a target concentration of less than 100 Bq/m 3 , in line with the World Health Organization (WHO) recommendation (25,26). The Austrian legislation is slightly different, as it already includes 222 Rn in the screening process (27). This study proposes a novel method, since it includes a fast screening process that can minimize radiological assessment costs. Moreover, the real surficial exhalation rate of each rock is measured and mitigation actions are proposed.
After calculating the Gamma Index, the following comparison, used as a screening tool for discerning the potential risk of specific materials, should be made: the Gamma Index should be less than 1 for a dose of 1 m Sv/year for bulk materials and below 6 for materials strictly used for surface applications (22). The EU regulation follows the same criterion as fixed by the International Atomic Energy Agency (IAEA) Basic Safety Standards (28) that set exemption conditions for radionuclides of natural origin. In the case of bulk material, a case-by-case basis is necessarily considered by using a dose criterion of the order of 1 m Sv/year, commensurate with typical doses due to natural background levels of radiation.

The thoron issue
The only radon isotope mentioned in international legislation is 222 Rn, as it is believed to be responsible for most of the indoor exposure. In this type of environment, it occurs in soil as the soil is seen as the most important source of radon and, in this case, thoron would not have enough time to penetrate the building due to its short half-life (29). However, when considering construction materials as radiation sources, thoron is shown to contribute to the final concentration in the environment, and thoron progeny is inhaled mostly attached to aerosols. Nuccetelli and Bochicchio (30) affirmed that the health risk due to indoor presence of thoron is usually neglected due to its generally low indoor concentration, which is primarily caused by its short half-life. However, in specifically not uncommon situations, such as when thorium-rich building materials are used, 220 Rn may represent a significant source of radioactive exposure. Ishikawa et al. (31) calculated dose conversion factors for short-lived thoron decay products, analyzing a site where the dose from thoron decay products was larger than the dose from radon decay products. Lane-Smith and Wong (32), considering an area of concern close to a thoron source, concluded that the total energy released by alpha emission, inside the lungs, could be seven times greater with the effect of thoron gas instead of thoron progeny alone.
However, since the approach to establish thoron limits is different from that of radon, this study analyzed the exhalation rates of two isotopes differently. For thoron, the effective dose equivalent by inhalation of short-lived thoron daughters as functions of the activity concentration of 232 where A Th 232 − is the activity concentration of 232 Th and A Th 232 − is the activity concentration of 226 Ra, both in Bq/kg.

Experimental setup
In this study, we sealed three-dimension stone slabs of each rock with plastic and adhesive tape to ensure the measurement of exhalation from the plate surface only (Fig. 1). The area of each sample was measured to calculate the surficial exhalation rate (the samples were approximately 20 × 20 × 2 cm). Small holes were drilled on the opposite side of air suction to ensure continuous flow and negative pressure in the system. In addition, care was taken to prevent plastic from sticking to the surface and stopping the air from flowing when the pump was connected using narrow silicone tubes glued to the inner surface of the plastic. This measure allowed us to consider that the volume between the plastic and the rock was negligible (distance between the plastic and the rock was less than 0.5 mm). The radon losses due to the use of lowdensity polyvinyl chloride (PVC) plastic and adhesive tape (34) were calculated and experimentally verified, and they were negligible; the results are presented further herein. Nevertheless, there are feasible possibilities to minimize the eventual losses using specific plastics already commercially available for radon dosimetry.
Rock permeability, which is described as the path created by the connectivity of the pores where fluid flows, was measured using PDP-200 CORELAB permeameter, installed in the Basic Petrophysics Laboratory of CENPES in Rio de Janeiro, Brazil. This permeameter is specially designed to measure the permeability of tight rocks using pulse decay and nitrogen gas. Darcy Law was used to calculate matrix flow density (m/s), and the decay constant of 222 Rn and 220 Rn (s -1 ) was used to calculate diffusion lengths. As the average permeability was (1.5 ± 1.17) × 10 -18 m 2 , the diffusion length for 222 Rn was (0.0396 ± 0.0309) µm and (6.52 ± 5.19) × 10 -6 µm for 220 Rn. These data confirm that the exhalation rate of these types of samples is only surficial, and they can be considered radon-tight samples as the thickness is more than three times the diffusion length (35). Radon concentration was measured with RadonMapper (RM) radon monitor manufactured by (TECNAVIA, Lugano, Switzerland) and approved by the Swiss Federal Institute of Metrology (METAS). The operation uses a scintillation cell (Lucas cell) presenting 5% repeatability with built-in pressure, humidity, and temperature sensors. There are USB ports available to connect other types of sensors, for example, differential pressure. The RMs are tested periodically using a radon source, and a gap of a few hours is recommended between measurements to assure the absence of functional contamination in scintillation cell. The persistent contamination is very low, and its value could be estimated, preventing measurement biases. One of the RMs was used in passive mode to control lab concentration, which was considered the background value and subtracted from the measurements. The other two RMs were used in active mode to measure radon and thoron exhalation rates. Moreover, a flowmeter (Vögtlin Instruments, GSM-B4SA-BN00, Aesch, Switzerland) was used to keep the online track of flux during the 4-day measurement campaign for each sample; microfilters were also used to ensure that no solid particles enter the equipment, which could bias the results (Fig. 2).  Figure 3 shows the radon concentration graphic generated by RadonMapper software. Each curve corresponds to one of the three radon monitors used. The diagram was always monitored to verify whether leakage was happening. While small oscillations in the readings are normal due to the pump, they were taken into account because we used a flowmeter integrated all the time.

Measurement procedure for thoron
After the average 4-day measurement, the scintillation cell was closed, and the pump switched off for at least 10 min to verify thoron decay for all assays. Lucas cell used in RM is calibrated for radon only and not for thoron. Thus, its indicated value requires multiplication by a correction factor (CF) to show the real value.    3. Example of radon concentration graphic generated by RadonMapper software, the curve in red (Radon .54) corresponds to the first active radon monitor, the curve in blue (Radon .51) corresponds to the second active radon monitor, and the curve in green (Radon .90) is the passive radon monitor measuring the lab background concentration.
shows the three CFs used to quantify thoron exhalation, and the cell manufacturer (Mi.am, Piacenza, Italy) recommends a CF1 of 0.9 (real value/indicated value). Therefore, there is a trend toward slight overestimation to be taken into consideration. However, other CFs should also be applied, as they correct an underestimation trend due to the rapid decay of thoron in both scintillation cell and path to the cell. This underestimation depends on chamber volume and the flow adopted, since the half-life of thoron is only 55.6 sec. Several authors have recommended the use of two RMs in series, as we did in this study, with a known distance between them to calculate CF2. A known constant flux and chamber volume (0.25 L) allowed to calculate CF. Thus, the challenge in this strategy was to ensure a constant flow to prevent CF2 oscillation during the measurement. For example, for a 0.25 L/min flow, which was adopted in most measurements in this study (average flow of 0.29 L/ min), the underestimation trend would be at least 20%. CF3 depends on the sample length, the flow rate adopted, and the length of the connecting pipes used. One good strategy to calculate this underestimation is to use a tracer gas, such as CO 2 , at the beginning of the plate to calculate the effective time for transiting from gas to the cell. As this technique was not used in this study, only the CF1 was applied to correct the overestimation tendency; hence, the thoron measurements were limited, and the data were underestimated for this isotope.
Activity concentrations (Bq/m 3 ) obtained using RM were then used to calculate the surface exhalation rates (Bq/h m 2 ) using Equation 3.
where C e is the surface exhalation rate (Bq/h m 2 ), C is the radon or thoron concentration (Bq/m 3 ), f is the flow (m 3 /h), and A is the plate area (m 2 ).

Indoor concentrations from surface exhalation rates
Monitoring the buildup of radon concentration at regular time intervals in the chamber, where the sample is enclosed, is required to measure the mass exhalation rate. We used Equation 4 (36) to calculate the time needed for concentration in a room, with a volume of 56 m 3 and 20 m 2 of the floor covered with sampled material, to reach 100 Bq/m 3 and 300 Bq/m 3 using different air exchange rates: where C(t) is the radon concentration (Bq/m 3 ) in the room at time t; J m is the exhalation mass rate (Bq/kg h -1 ); M is the total dry mass of the sample (kg); C 0 (Bq/m 3 ) is the initial amount of radon in the room (t = 0); V is the effective volume (m 3 ); and (s -1 ) is the effective decay constant, which can be determined by the following formula: where Q/V is the leak rate (LR), obtained from the ratio of airflow (Q) and the volume of room (V), and λ Rn−222 is the decay constant of 222 Rn (s −1 ). In these simulations, we did not consider the back diffusion of radon gas.

Gamma spectrometry
Radioisotopes activities were determined using gamma-ray spectrometric measurements. Before the application of gamma spectrometry, the sample was crushed and screened to reach a particle size of below 2 mm. Then it was sealed in a metal can for 30 days to ensure equilibrium between 226 Ra and 222 Rn. Specific sample activities were then determined using a Ge-hyper-pure detector (HPGe -CANBERRA Industries Inc., model GX 2020, relative efficiency of 20% and resolution of 1.9 keV for the 60 Co photopeak) located at the Poços de Caldas Laboratory (LAPOC) of the National Nuclear Energy Committee (CNEN). The reference materials RGU, RGTh, and RGK from IAEA were used for efficiency calibration, and calibrated sources of 60 Co, 137 Cs, 152 Eu, and 241 Am, were used for energy calibration. Potassium, Th, and Ra activity concentrations were calculated using the Canberra Genie 2000 software. The equilibrium was determined by taking the mean value of three photo peaks of their progeny: 214 Pb (295.2 keV and 351.9 keV) and 214 Bi (609.3 keV). 228 Ra was determined by measuring the intensity of 911-keV and 968-keV peaks of 228 Ac, assuming that they were in radioactive equilibrium, and the 40 K was determined directly by its photo peak with 1,460-keV energy.

Portable contamination monitor
A portable contamination meter (CoMo 170 manufactured by GRAETZ) was used to analyze the counting (cps) of dimension stone samples. The aim was to verify whether this type of equipment is suitable to screen samples that could be problematic for indoor use. This equipment has an auto-calibration with an open area of 170 cm 2 , which provides a very sensitive means of locating radionuclides and quantifying contamination levels by alpha, beta, and gamma emitting radionuclides. This type of equipment is designed to detect high levels of radioactivity associated with contamination problems in case of accidents or equipment malfunctioning. Hence, the efficiency must not be high (and it is not), but rather the equipment response time should be fast. Therefore, this method is semi-quantitative, since it does not aim to quantify isotopes in the samples or measure the associated radioactive dose. The equipment also has a thin ZnScoated plastic film, which is a scintillation detector protected by a grid, and was used in this study to detect 238 U alpha activity (26% efficiency) (37) and 40 K beta and gamma activity (30% efficiency) (37) present in natural rocks. This equipment was acquired to perform this study, so the film had no previous contamination. The background value was measured before each analysis and subtracted from the assay results. The net counting rate is reported in Table 1.

Results and discussion
The experimental results obtained by the contamination monitor, gamma spectrometry, and scintillation cell are presented in Table 1 for 21 of 35 samples analyzed, and the full dataset is available for consultation. Importantly, the samples that showed alpha activity detected by the contamination monitor were also the ones with the highest Gamma Index and total radon exhalation rates. Moreover, Gamma Index only helps to discern the potential risk and cannot be used to predict radon exhalation from dimension stone. While Gamma Index = 6 is recommended for surface rocks by the EU regulation, it did not correlate at all with hazardous exhalations, leading to the adoption of Gamma Index = 1. The average activity concentrations measured were 971 ± 59 Bq/kg for 40 K, 184 ± 9 Bq/kg for 232 Th, and 74 ± 3 Bq/kg for 226 Ra. The maximum activity concentrations of the 40 K, 232 Th, and 226 Ra series were 1,738 ± 100 Bq/kg, 2,667 ± 109 Bq/kg, and 596 ± 2 Bq/kg, respectively. When comparing the results with other granite analyses, for example, in the USA, these values show that the Brazilian dimension stone are enriched in thorium in their formation (38). From the analysis of 39 granite countertops, Myatt et al. (38) reported the value of 231 Bq/kg for the maximum activity concentration of 232 Th and an average value of 72 Bq/kg. Therefore, the radiological assessment of the rocks addressed in this research must be different because the thoron participation in the individual dose rate is much higher than the one reported commonly in the literature. The average exhalation rate of 222 Rn was 406 ± 20 Bq/h m 2 , which is much higher than the result reported by Allen et al. (39) for 39 granite countertops in the USA. This difference could be interpreted by the influence of geological genesis factors in the sample radioactivity and it highlights the importance of assessing each lot of dimension stone sold for indoor use. 222 Rn exhalation rates were calculated using Equation 4, and these would reach the limits of 300 Bq/m 3 and 100 Bq/m 3 in 1 h for different scenarios in a room of 56 m 3 with 20 m 2 of rock used as floor coverage. This approach was only used for 222 Rn, as the concentration due to thoron builds up very slowly, resulting from the much shorter 220 Rn half-life, which would be disturbed by any leakage rate in the room. Table 2 presents the results obtained for this simulated room. This calculation is only an example but could help in the radiological assessment of radon concentration in a room when someone is interested in buying a new floor or a countertop for house. It is also helpful when verifying whether a room needs to increase air exchange or whether the area covered with a particular rock should be restricted. Therefore, the J m exhalation limit could be updated, depending on the real scenario of a room in a dwelling, and it hinges on the ventilation rate and the time spent in this room.
When comparing the values of Gamma Index with total radon exhalations, 12 samples, one sample with Gamma Index = 1 and 11 samples with Gamma Index > 1 showed 222 Rn exhalation rate higher than 140 Bq/h m 2 , which is the strictest scenario. On the other hand, only

Simulation of indoor radon concentrations
As a way of verifying compliance with the legislation in force in the EU and the WHO recommendations, exhalation values, presented in Table 3, were calculated based on the 222 Rn surface exhalation rate. Table 3 shows the results obtained from Equation 4 for 21 of the 35 samples analyzed, and the full dataset is available for consultation. We conclude that 11% of the samples would reach the EU-recommended concentration in less than 1 h, 23% in less than 2 h, and 80% of the samples reach the limit in less than 24 h. Considering the target concentration recommended by the WHO, 100% of the samples would reach this limit in 24 h. These results were obtained considering C 0 (background concentration) and LR (leakage rate or air renewal rate) equal to zero, which is an unrealistic scenario. Table 3 presents simulations with a realistic air renewal rate. Time to reach the limits of 100 Bq/m 3 and 300 Bq/m 3 is considerably higher when fresh air is added into the environment (air renewal rate [LR] in s -1 ). However, samples with high exhalation rates could be dangerous for human health, even in case of air exchange, especially in places  with low air renewal rates, such as cold weather countries. Therefore, alternative uses of these rocks should be investigated, either by limiting the area covered by this rock or using complementary surface treatment. The average indoor concentration found in researches worldwide varies between 21 Bq/m 3 and 80 Bq/m 3 (12,25), mainly from soil and almost exclusively from 222 Rn. By adding this initial concentration value C 0 , the time to reach the stipulated limits drops significantly (98.3%), as observed in the last two columns of Table 3. This fact reinforces the need for calculating the exhalation rate value acceptable to be used for sample screening. If a problematic sample is found, surface treatment could be applied. For example, 20 m 2 of a dimension stone in a 56 m 3 room with an exhalation rate of 140 Bq/h m 2 would build up the 222 Rn concentration to 100 Bq/m 3 and 300 Bq/m 3 in less than 1 and 4 h, respectively, with an LR of 2 m 3 /h/person (0.37 h −1 ) and background equal to 50 Bq/m 3 .
Using an exhalation rate of 140 Bq/h m 2 for 222 Rn as a criterion, 39% of the samples tested in this study would need to be submitted to an additional polishing or waterproofing treatment. If surface treatment is not used, care should be taken in the indoor use of these rocks. The limiting criteria to be followed in these cases could be to restrict the covered area, limit the use of this material to a few square meters in well-ventilated sites or in places where people do not remain for an extended time such as corridors and laundries. Figure 5a shows the setup used to assess radon losses through plastic membrane and adhesive tape. RadonMapper 1 receives the flow from radon source, it then passes through the first plastic membrane and goes into RM 2 before going outdoor. As a double check mechanism, we used a second plastic membrane of 0.5 mm above the first one to check eventual losses using two RMs in a closed circuit. A fifth RM was also used in passive mode to check the background of the room, but it is not presented in Fig. 5a. Figure 5b shows average concentrations for the 36 h of measurement, which were as follows: 382 ± 23 Bq/m 3 for RM1, 377 ± 25 Bq/m 3 for RM2, 40 ± 8 Bq/m 3 for RM3, and 41 ± 8 Bq/m 3 for RM4. The background of the lab was 41 ± 9 Bq/m 3 . Therefore, since radon losses are within the detection limit of equipment, it could be considered negligible.

Leakage and reproducibility tests for radon measurements
Six samples were measured in two labs by independent teams to check the reproducibility of radon measurements, and the results are presented in Table 4. The average standard deviation between labs was 9%, which shows a good level of reproducibility of this method (40,41). However, we did not perform direct repeatability testing of the method, which should be done in further studies. Table 5 shows the overall inhalation dose equivalent and the effective dose equivalent for short-lived 220 Rn daughter's results. They allow us to conclude that 220 Rn cannot be neglected for the samples studied in this research since 61.7% of the total average dose is due to 220 Rn contribution. This assessment is limited because we include only the thoron progeny dose, not the thoron gas itself. The dose was calculated using Equations 1 and 2 as proposed by Keller et al. (33) since not all the biases of thoron exhalation rates were solved in the campaign. However, the results were consistent with the exhalation rates measured. The purpose of thoron measurements was to show how important it could be when assessing some types of thorium-enriched samples. For all further analyses in this study, only 222 Rn exhalation rates were considered. Table 6 presents Spearman correlation coefficients calculated for alpha, beta, and gamma counting (cps), Gamma Index, and 222 Rn-and 220 Rn-exhalation rates. The results show significant correlation, with 95% confidence level (P < 0.01) between the following variables: alpha count and beta and gamma count (0.703); alpha count with Gamma Index (0.667); alpha count and 222 Rn (0.802); alpha count and 220 Rn (0.784); beta and gamma count and Gamma Index (0.911); beta and gamma count and 222 Rn (0.715); beta and gamma count and 220 Rn (0.678); Gamma Index and 222 Rn (0.772); Gamma Index and 220 Rn (0.736); and 222 Rn and 220 Rn (0.879). Figure 6 presents the linear regression equation for Gamma Index and beta and gamma variables. For 95% confidence level, the value of r (Pearson correlation coefficient for samples) represents, in the exact hypothesis test, the rejection of null hypothesis, that is, H 0 : | ρ| = 0. Hence, there is statistical evidence of a linear correlation between Gamma Index and beta and gamma variables. The confidence interval for ρ (Pearson's population correlation coefficient) using Fisher's Z-approximation is 0.940 ≤ ρ ≤ 0.985.

Statistical analysis regarding the screening method
For the one-tailed test, 0.946 ≤ ρ indicates a robust positive correlation (above 0.9), and the population R 2 (coefficient of determination) ≥ 0.894, which shows that the variables explain its variation in 89.4% for a sample of 35 elements. Figure 7 shows the distribution of residuals for beta and gamma count and the Gamma Index. It is possible to conclude that the data follow a normal distribution with a strong correlation between them, which corroborates the analysis shown in Fig. 6. Figure 8 shows the representation of confidence interval in dashed lines for the same linear regression presented in Fig. 6 to predict the dependent variable. For Gamma Index ≥ 1, all samples present values for beta and gamma  Fig. 6. Linear regression -beta and gamma count and gamma index.
greater than or equal to 13.7 cps. Therefore, the Gamma Index can indirectly be inferred by measurements with portable radiation detector. Consequently, it is possible to conclude that non-zero alpha count and/or beta and gamma counts equal to or higher than 10 cps are the recommended values used for this primary screening. The value of 10 cps is considered conservative in this case. A security factor of 1.37, which is a coefficient employed to prevent uncertainties, was applied to have a stricter screening value to avoid false negatives. However, by decreasing the security factor, values higher than 10 are obtained but are less security-friendly. By this method, 26% of the samples of this study would be approved for indoor use without a need for additional exhalation assessments and radiological hazard indices. More data could decrease this value.

Surface treatment
Techniques to reduce and control the effects of radon pollution indoors have been studied, and even an anti-radon coating was developed and patented (42). However, for dimension stone slabs, a much simpler and cheaper technique, namely polishing, could be used to decrease radon exhalation rates. Thus, this study investigated this technique by analyzing rough and polished surfaces of each sample. Table 7 shows that there is an average decrease of 25% in total Rn exhalation for the studied samples when the surface of the dimension stone is polished. While the reduction is present in almost all samples studied due to less exhalation of 222 Rn, it was not consistent for 220 Rn. However, when narrowing down the samples to those that exhale more than 140 Bq/h m 2 , the thoron reduction is consistent. This technique could be used as a surface treatment to enable safe indoor use of dimension stone slabs. After polishing, if the samples still present high exhalation rates, an oil/water-phobic substance could be applied to decrease the exhalation rate. The commercial substance tested in this study is called PEK Bio, which is designed to avoid stains in dimension stone, preserving the natural beauty of the rock. Using this substance caused an additional 30% decrease in exhalation rate (relative decrease of 29% for 222 Rn and 31% for 220 Rn). While the long-term efficiency of the surface treatment was not monitored, the promising results recommend this analysis for the future studies. Figure 9 presents the method proposed for indoor use of a batch of dimension stone. In principle, the approval of a particular material cannot occur only once per mine because even for an apparently homogeneous  mineral body there is an intrinsic heterogeneity in the material that cannot be neglected. Homogeneity is an unachievable condition of zero heterogeneity (43). Therefore, each batch of marketed material must be evaluated by the proposed method. Batch sampling must be non-bias (accurate samples) and provide reproducible (precise) samples, thus making them representative of the batch (44).

Proposed method
Samples taken from a batch should be analyzed employing a portable contamination monitor. If the mean value of beta and gamma counts, discounted from the background, is higher than 10 cps and/or the alpha count is different from zero, then the 222 Rn and 220 Rn exhalation rates and the Gamma Index should be assessed. If the 222 Rn exhalation rate is higher than the value considered acceptable for a specific room, the sample should be submitted for surface treatment before being released for indoor use. Batches approved according to the limit criteria could be used for indoors if they meet mass and location specifications. The use of such batches in the floor covering of a bedroom or institutional dormitory should be avoided, since a human being spends, on average, 33% of their time sleeping, which results in a very high exposure time.

Conclusions
This research is based on case studies of radiometric analysis of building materials, notably dimension stone. The objective of this research was to provide concrete, practical, and economical quantification procedure that aims at the health protection of people who might be exposed to these materials.
In particular, the research highlighted the following points: 1. The primary natural alpha radiations from building materials are due to radon ( 222 Rn) and thoron ( 220 Rn). While the first one is the object of various national regulations and international recommendations from the WHO, the second one, although in no way less critical than the first one, is often disregarded, and, in our opinion, it does not receive enough coverage by policymakers. Quantified radiometric analysis of indoor use of dimension stone 2. Radon and thoron exhalations do not always correlate with the Gamma Index as the gas exhalation rate depends on physical parameters of the rock, such as humidity, permeability, density, and the roughness of the surface. This work demonstrated that radon and thoron exhalations could be significantly impacted when the surfaces of materials are polished. 3. The present research verified the feasibility of quantifying radon and thoron exhalations and proposed an analytical procedure that could define limits for the application of materials, particularly in the case of indoor applications of dimension stone.
Summing up, setting a new regulation for radon and thoron exhalations could be useful, thus complementing the one commonly defined as Gamma Index. This regulation could also be applied as a quality label for products in the case of import/export materials as well as for private sales.