APPLICATION OF LABORATORY BETA RADIOMETRY FOR QUANTITATIVE INDICATION OF RADIONUCLIDE CONCENTRATION IN PLANT SAMPLES

The aim is to improve the beta-radiometric method of quantitative indication of the content of Sr and Cs in the counters of plant samples. Material and methods. In the Chernobyl exclusion zone (ChEZ) in 2017, 2019, leaves of silver birch, black poplar, common reed, sedge were selected, which were dried, crushed, and used as calculating samples for beta radiometry and spectrometry. For measurements, a combined KRK-1 radiometer and a SEB 01-150 spectrometer beta-radiation energy were used. Results. Currently, in plant samples from the ChEZ, the following are widespread: natural K, the concentration of which is usually less than 1 % in relation to the concentration of technogenic radionuclides Sr+Y and Cs, therefore, when measuring Sr and Cs, beta radiation of K can be ignored. The measurements were carried out without a spectral filter and using a thin molybdenum filter. Without filter – show the count rate of Sr+Y and Cs radiation. The filter transmits 2–3.5 % of the low-energy beta radiation of Sr and Cs and more than 95 % of the high-energy Y. The ratio of the count rate of Y pulses with and without filter is 2.14. The Sr concentration in the samples was determined from the results of measurements of Y, and Cs – through the fraction of the counting rate, which remains after deducting Sr+Y. Comparison of the concentration of radionuclides measured by the method of betaradiometry and spectrometry showed no significant difference between the results obtained by the two methods. Conclusions. The beta radiometry method for Sr and Cs provides for measuring the counting rate of beta radiation from counting samples without a spectral filter and using a thin molybdenum filter. Based on the research results, a procedure for calculating the concentration of Sr and Cs in counting samples of plant leaves was developed


Introduction
When conducting radioecological surveys of manmade contaminated areas, there is a need for rapid assessment of the specific activity of 90 Sr and 137 Cs in the counters of plant samples.
Laboratory beta-radiometry is considered to be the most efficient and least expensive method for such measurements. Unfortunately, the existing method involves only the measurement of the total specific activity of beta-emitting radionuclides in the drugs, which significantly narrows the possibilities of its application. To develop and improve beta-radiometry, it is important to develop procedures that allow the identification of certain radionuclides in counting samples.

Literary review
Beta-radiometry is successfully used in the indication of radionuclide contamination of the environment and in biological research. Radiometric methods that are traditional still remain unique for the detection of radionuclides with different half-lives. It is important that methods for determining radionuclides be sensitive, ac-curate, and low cost. Radiometric methods meet these requirements. The peculiarity of these methods is that they do not require large equipment or infrastructure [1].
However, by the method of beta-radiometry it is impossible to selectively determine individual radionuclides by their radiation energy. In addition, there is the problem of self-absorption of low-energy radiation by a counting sample. That is, the determination of radionuclides with low radiation energies is complicated in the presence of radionuclides with high-energy radiation. In order to overcome these problems, various methods are used to increase the sensitivity of the beta-radiometric method. For example, selective extraction of radionuclides from the sample [1], the creation of a thin-layer counting sample [1,2], the use of absorbers of different thickness between the sample and the counter [1]. To simplify the measurement method and increase their expressiveness, when the energy spectrum of the radionuclide mixture of the counting sample allows, the most acceptable is the use of ionizing radiation filters (hereinafterfilters) between the counting sample and the detector. Metal filters with different equivalent radiation thickness are used to cut off radionuclides with lower energies and protect, for example, gamma detectors from high-energy beta radiation [1][2][3].
In the counting samples of vegetation there is a mixture of radionuclides of both man-made and natural origin. The largest powerful source of beta radiation among natural radionuclides is 40 K. In areas with a high content of natural radionuclides in the environment, the specific activity of beta-emitting radionuclides in grassy vegetation can reach significant levels, up to 1800± ±263 Bq/kg, due to both 40 K and decay products of uranium and thorium [4].

The purpose and objectives of the study
The aim of the work is to improve the existing method of laboratory beta-radiometry for quantitative indication of the specific activity of radionuclides of manmade origin 90 Sr and 137 Cs in the preparations of plant origins, on the example of ChEZ.
To achieve this goal it was necessary to perform the following tasks: 1) Develop registration procedures for 90 Sr + 90 Y and 137 Cs, which are based on the use of a beta radiation energy filter; 2) To develop procedures for measuring counting samples of plant origin contaminated with a mixture of radionuclides -90 Sr + 90 Y and 137 Cs, and processing the results of the study; 3) Evaluate the value of the relative total uncertainty of the results formed during the quantitative betaradiometric indication, and compare the results with the data of beta-spectrometric measurements of 90 Sr and 137 Cs in counting samples of plant origin.

Materials and methods
The research was conducted in 2017-2019. The leaves of silver birch (Betula pendula Roth.), иlack poplar (Populus nigra L.), common reed (Phragmites australis (Cav.) Trin. Ex Steud) and sedge (Carex acuta) were used for observations, which were collected in the Chornobyl Exclusion Zone in the ecosystems of Azbuchyn, Hlyboke and Daleke lakes, the Chernobyl station cooler reservoir, the Yaniv Bay of the Pripyat River near the city of Pripyat, and the Pripyat River in the vicinity of Chornobyl city. Samples from the last of these ecosystems were considered to be collected in the context of local radionuclide contamination. At least 30 leaves from different plants at each site were selected for the study.
The preparations were air-dried, ground and sent as beta-samples for beta-radiometric and betaspectrometric analysis. The rate of counting beta particles emitted by counting samples of plant leaves was measured using a radiometer combined KRK-1 (Russia). Measurements of the pulse counting rate from beta particles, calculation of the radiometric background and the number of registered pulses were performed according to the existing technical documentation [5]. The relative uncertainty in laboratory beta radiometry did not exceed 30 %. Beta-radiometry of the drugs was performed without a filter and with a radiospectrometric filter made of thin molybdenum (density -10.22 g/cm 3 ) with a thickness of 0.11 mm.
Measurements of some samples of reed plants collected in 2017 were performed on 90 Sr and 137 Cs by spectrometry, using a beta-radiation spectrometer SEB 01-150 (Ukraine) in the laboratory "DSP Ecocenter". Uncertainty in 90 Sr beta spectrometry did not exceed 18 %, 137 Cs -15 %.
The relative measurement uncertainty was calculated according to existing recommendations (JCGM 100: 2008, 2008) as the standard deviation of several consecutive measurements of one sample.

100
, standard deviation of parameters when calculating uncertainty; x is the average value of the measured parameters.
Statistical analysis of measurement results by the Monte Carlo method was performed using the software application Past 3.19. The Monte Carlo permutation test [6] was used to accurately estimate the probability of the following statistical parameters. The Monte Carlo method is based on 99,999 random reassignments of values in a column within each pair and is displayed as probability (p). Spearman's correlation coefficient (rS) was used to estimate the relationship of the sample pairs. The closer p is to 0, the more likely it is that there is no significant difference between the samples being compared. When performing the analysis, the value is taken that p>0.5 means no correlation. The Mann-Whitney (MW) test was used to compare the medians of the two samples. The null hypothesis of this test is: two samples are taken from populations with equal medians. The hypothesis is confirmed when p>0.5. The Kolmogorov-Smirnov (KS) criterion was used to compare the type of statistical distribution of the two samples. The null hypothesis is: two samples are taken from populations with the same distribution. The null hypothesis is rejected if the value of the statistics D>p.
The samples were checked for similarity of correlation coefficients (CV) using the Fligner-Killeen test. Null hypothesis: samples were taken from populations with the same coefficient of variation. The null hypothesis is rejected if p<0.05.

1. 90 Sr + 90 Y and 137 Cs registration procedures based on the use of a beta radiation filter
The average potassium content in the leaves of reedplants with high ash content, selected in ChEZ, is 940±300 mg/kg, respectively 40 K 30±10 Bq/kg [4]. The leaves of ChEZ plants contain 4 beta emitting radionuclides: natural -40 K, man-made -90 Sr + 90Y, and 137 Cs. According to the results of numerical measurements, in most counting samples of plants taken in ChEZ, the concentration of 40 K is usually less than 1 %, and in the local background of radionuclide contaminationup to 5 % relative to the concentration of man-made radionuclides [7,8], therefore, when measuring 90 Sr and 137 Cs with 40 K beta radiation, it can be neglected. Thus, when measuring beta-emitting radionuclides in the vegetative mass of plants, technogenic 90 Sr and 137 Cs are significant today. The concentration of these radionuclides, for example in higher aquatic plants, which are the most contaminated under ChEZ conditions, varies by 90 Sr from 60 Bq/kg to 8500 Bq/kg and for 137 Cs from 200 Bq/kg to 20,000 Bq/kg, at high values of coefficients of variation of specific activity for both radionuclides, ranging from 60 % to 200 % [7,8]. Required methods of separation of technogenic radionuclides from natural ones. The given data show that in ChEZ conditions, where plants are characterized by low concentration of natural radionuclides and extremely high pollutiontechnogenic, for selective quantitative beta-radiometry of 90 Sr and 137 Cs it is important to use filters.
It is known to use for the separation of radionuclides with lower energies filters made of non-ferrous metals and alloys, such as brass [2]. To cut off lowenergy radiation 90 Sr and 137 Cs with maximum energy values (MeV) -0.54 and 0.52, respectively [9], we used a molybdenum filter. It has been experimentally established on the example of 137 Cs that the applied filter almost completely cuts off the beta radiation of plant sources of contaminated 90 Sr and 137 Cs with a specific activity that occurs in the territory of ChEZ during the last 10 years [10]. Radiation of directly 137 Cs is reliably recorded by laboratory beta radiometry, even at low activities and low-density cellulose matrix (Table 1). From the Table 1 shows that the molybdenum filter passes from 2 % to 3.5 % of beta particles emitted by 137 Cs in the counting sample. This parameter was calculated as the protection factor for low-energy radiation (K le ) on the example of standard IRS 137 Cs, according to the formula: where I imp/spulse counting speed from the IRS (with subtracted background); I Mothe speed of counting the pulses registered using a molybdenum filter (with the background subtracted). The background counting speed was measured and calculated according to the technical documentation of the radiometer [5].
The K le value is established on the basis of multiple measurements of 137 Cs analytical standards, within this work is equal to 0.033 and is used in calculations as a constant. Given the proximity of the maximum radiation energy of 90 Sr and 137 Cs, the result obtained can also be attributed to 90 Sr radiation. Given that the maximum energy of beta radiation 90 Y -2.28 MeV [9], we can assume that the applied molybdenum filter transmits mainly 90 Y radiation.
The effectiveness of protecting a molybdenum filter from beta radiation from counting samples has been empirically established. Radiation sources ( 90 Sr + 90 Y) with activity from 50 Bq to 11100 Bq were used as counting samples ( Table 2).
The measurements show that when using IRS that differ by several orders of magnitude, the value of the protection factor varies within the statistical error. Accordingly, within all possible values of the specific activity of the counting vegetation samples that can occur in ChEZ, when using a molybdenum filter, only highenergy radiation 90 Y is measured. When measured without a filter, the beta particle flux consists of low-energy 90 Sr radiation and highenergy 90 Y radiation (Table 2).
In order to take into account the difference in the efficiency of pulse recording from high (Е hе ) and lowenergy (Е lе ) radiation, the values of relative units of registration efficiency given in the technical documentation to the laboratory beta radiometer KRK-1 were used. The calculated 90 Sr, 90 Y and 137 Сs fractions were multiplied by correction factors of 0.46, 0.95 and 0.44, respectively [5].
Calculation of the proportion of beta radiation 90 Y in standard samples of IRS was performed by the formula: where Е ihethe share of registered pulses from radiation Y; Е hеthe efficiency of registration of pulses of highenergy radiation, in this case 90 Y in relative units from 0 to 1 [5]; Е lеthe efficiency of registration of pulses of low-energy radiation, in this case 90 Sr.
To find the proportion of high-energy beta radiation recorded from experimental counting samples, the ratio of 90 Y pulses to pulses recorded using a molybdenum filter was calculated from the results of measurements of standard IRS samples. The calculations were performed according to the equation: K ІВЕ calculations performed for all measured standard IRS samples ( Table 2) showed that the average K ІВЕ value=2.14, with an uncertainty of 26 %. The share of low-energy radiation in the calculation rate from the IRS was calculated by the equation: The application of correction factors equalized the values of the fractions of the rate of calculation of the measured radionuclides (І Е ), and these data calculated the sensitivity of the registration of radiation IRS (Е А(rn) ): where А rn , Bq -IRS activity on the corresponding radionuclide; I rn , imp.the fraction of the rate of calculation of the corresponding radionuclide According to the results of calculating the efficiency of registration of IRS radiation given in Table 1 found that the average value of Е А =12 Bq/imp, with uncertainty -27 %.
The deviation of the measured specific activity of 137 Cs from that prescribed for BS and TSMP-1 is less -1 %. The sensitivity of the analysis decreases by about a third as the density of the sample increases. For IRS with a matrix of 0.1 g/cm 3 , the sensitivity value calculated by formula 5 is 26 Bq/imp, and for IRS with a density of 1 g/cm 3 -36 Bq/imp. Accordingly, for the method of radiometric indication of 90 Sr and 137 Cs in samples of vegetative mass of plants with low density, which differ from denser samples of wood, forest litter, and soil, the values of Е а =21.4 Bq/imp.
The proposed method of laboratory radiometric measurement of high-energy and low-energy radionuclides using a molybdenum filter showed that it makes it possible to estimate the proportions of recorded pulses generated by radiation with different energy from different radionuclides. The calculated ratio of the pulses 90 Y to the pulses recorded using the molybdenum filter must be recalculated when changing the radiometer, or changing the filter, or when performing metrological verification. The value of the coefficient must also be checked and clarified at each subsequent calibration of the measuring equipment. The efficiency coefficient of IRS radiation registration for 90 Sr+ 90 Y is also established, which allows to calculate the activity of the radionuclide in the radiation source based on the results of the adjusted pulse counting calculation. In the case of a pulse ratio of 90 Y to pulses recorded using a filter, this ratio must also be specified for each individual measuring instrument and during their verification.
Thus, it is possible to determine the activity of 90 Y in the counting sample by taking into account the difference in the efficiency of recording pulses from high and low energy radiation when using a filter. The method allows to determine 90 Sr and 90 Y with a relative uncertainty of not more than 30 %.
The method is based on an empirically established coefficient. The molybdenum filter used transmits from 2 % to 3.5 % of low-energy beta particles emitted by 137 Cs in the counting sample. Given the proximity of the maximum radiation energy of 90 Sr and 137 Cs, the result obtained can also be attributed to 90 Sr radiation.

2. Procedure for measuring counting samples of plant origin contaminated with a mixture of radionuclides -90 Sr + 90 Y and 137 Cs and calculating the results of the study
The main beta contaminating radionuclides -90 Sr and 137 Сs are always found together in vegetation samples with ChEZ, although in different proportions. Due to the high energy beta radiation of 90 Y, direct measurement of 90 Sr and 137 Сs using laboratory beta radiometry is not possible, but the specific activity of 90 Sr in the counting samples can be calculated from the measurement results of 90 Y. The concentration of 137 Сs is calculated as a fraction of the counting rate, minus 90 Sr+ 90 Y.
Conducted experiments to determine the correction for backscattering (q) from IRS 90 Sr+ 90 Y and 137Cs radiation showed that 90 Sr+ 90 Y give virtually no statistically significant backscattering, and 137 Cs backscattering averages 1.15 [2]. Accordingly, this figure was taken into account when calculating the beta radiation with low energy.
Measurements of the specific activity of 90 Sr and 137 Сs were performed in two stages: in the firstthe measurement of the total rate of beta radiation counting of the counting sample was performed. The second is the measurement of the counting speed using a molybdenum filter.
The calculation was performed in 7 stages: In the first stage, the fraction of low-energy beta radiation 90 Sr and 137 Cs transmitted by the molybdenum filter (K SrСs ) was calculated. Values (K SrСs ) were calculated by the formula In the second stage of calculations set the value of the actual efficiency of registration of the counting sample (E prb ), according to the formula: E prb =(I MO •(Е he +Е le )) •I imp/s -1 (7) In the third stage of calculations set the share of 90 Y in the total counting speed (І Y E) by the formula: where K ІВЕ =2.14, as shown above; E Y =0.95energy recording efficiency 90 Y on KRK-1, set according to the technical documentation of the radiometer [8]. In the fourth stage, the calculation of the total counting rate of 90 Sr and 137 Сs (І SrCs ) in the counting sample of the herbal preparation according to the formula: where E SrCsaverage registration efficiency 90 Sr (0.46) and 137 Сs (0.44) equal to 0.45; q is the correction for backscattering of low-energy radiation.
In the fifth stage, the share of 137 Cs pulses in the counting speed of the counting sample (І Cs ) was calculated according to the formula: The observations showed that the quality of the results of calculating the share of 137 Cs pulses will largely depend on the reliability of the measured and calculated pulse fraction 90 Y, the value of which is attributed to 90 Sr.
In the sixth stage, the beta radiation activity of 90 Sr and 137 Cs (A rn , Bq) radionuclides in the preparation was calculated.
А rn , Bq=І rn •E arn (11) where rnthe radionuclide for which the calculation is performed At the seventh stage, the concentration of radionuclides in the counting samples of plant origin (A rn , Bq/kg) was calculated according to the formula: А rn , Bq/kg=А rn •m -1 •1000 (12) where mmass of the preparation, g Thus, the method of quantitative beta radiometric indication of 90 Sr and 137 Сs is based on the results of double measurement of a counting sample of plant originwithout filter and with filter. The applied system of mathematical calculations allows to calculate the concentration of 90 Y in the counting sample on the basis of the established parameters of radiation protection of the filter, and to assign it to 90 Sr which is in radiation equilibrium with 90 Y. Based on the obtained datacalculate the concentration of 137 Cs in the drug minus the fraction of the rate of counting the beta radiation pulses 90 Sr+ 90 Y.

3. Estimation of the relative total uncertainty formed during the quantitative beta-radiometric indication and comparison of the obtained results with the data of beta-spectrometric measurements of 90 Sr and 137 Cs in counting samples of plant origin
Estimation of the total relative uncertainty of the quantitative indication of beta emitting radionuclides by laboratory radiometry was made on the basis of uncertainties formed during laboratory analysis and radiometric measurement. In the laboratory analysis, uncertainties were related to the drying and weighing of the drugs, which averaged 4.0±1.0 %. In beta radiometric measurements of counting speeds of samples without filter and with filter, the average relative uncertainty was, for example, for 15 samples of plant leaves collected in 2019 -4.1 % and 11 % respectively, to which is added 25 % of measurement uncertainty attributed according to technical radiometer instructions.
The relative uncertainty of the 90 Sr and 137 Cs concentration calculated for the 2017 and 2019 counting samples did not exceed 44 % and 43 %, respectively (Table 3). Comparison of measurements of 8 counting samples of reed leaves, performed by quantitative beta radiometric indication and beta spectrometry showed that the median value of 90 Sr concentration in plant leaves obtained by beta radiometry is 440 Bq/kg, by beta spectrometry -560 Bq/kg; the same for 137 Cs -4700 Bq/kg and 4000 Bq/kg, respectively.
Comparison of two samples obtained by radiometry and spectrometry using a nonparametric Spearman correlation coefficient showed that the correlation coefficient of 90 Sr samples is 0.97, and 137 Cs samples -1. Comparison of these samples by median equality, type of statistical distribution and coefficient the samples have equal medians, the same type of statistical distribution and do not differ in coefficients of variation.
Thus, statistical analysis by the Monte Carlo method showed that the measurement results obtained by the method of quantitative beta radiometric indication, almost completely correspond to the results obtained by the method of beta spectrometry.

Discussion of research results
Modern methods of radiometry of beta-emitting radionuclides are based on more sensitive scintillation detectors and involve radiochemical isolation of certain radionuclides from the sample, followed by measurement of the activity of thin counting samples [11]. Beta spectrometry, which also uses highly sensitive scintillation detectors, is based on the registration of continuous beta spectra, which differ from each other in shape and posi-tion on the energy scale. The method of energy intervals or windows is used to process the spectra of betaemitting radionuclides [12]. Unlike beta radiometry with chemical release of radionuclides and analysis of a thin counting sample, beta energy spectrometry makes it possible to measure thick counting preparations without prior chemical isolation. Our proposed method is based on the use of a less sensitive gas discharge detector and does not involve the chemical release of radionuclides. The counting rate of beta particles emitted by a thick counting sample is measured. The disadvantage of our proposed method is its lower sensitivity and indirect registration of 90 Sr 137 Cs by measuring 90 Y. Compared with highsensitivity beta-radiometry, our proposed method does not require complex laboratory equipment procedures and significant costs. To create a counting sample, it is enough to dry the sample, grind it, take a sample and fill the radiometer cuvette with it. The lower sensitivity of the method is compensated by its expressiveness and reduction of the components of the total uncertainty, which is achieved due to the reduction of the number of analytical procedures in the manufacture of the calculation sample. Similar to beta spectrometry, the method of quantitative indication of radionuclides is also based on the use of an energy interval, but only one for 90 Y, which is provided by the use of a radiation filter.
Study limitations. Despite the fact that the proposed method is qualitatively significantly inferior to the spectrometry of beta radiation energy, at the same time it is significantly less expensive in terms of the cost of hardware. The method of quantitative indication of beta-emitting radionuclides can be used as an auxiliary in the control of radionuclide contamination and radioecological studies, if necessary, increase the number of measured samples and for special methodological developments.
Prospects for further research. The proposed method of quantitative indication of 90 Sr and 137 Cs, performed by laboratory beta radiometry using a beta radiation energy filter is promising for use in conditions of man-made pollution, when the activity of 90 Sr and 137 Cs in counting samples is not less than three times higher than the concentration of natural beta. Due to the costeffectiveness, lack of complex preparation of drugs for analysis, expressiveness and high sensitivity of the method, it is also promising in conducting radioecological surveys of areas contaminated with man-made radionuclides, and for developing and improving methods of radioecological indication of the environment.

Conclusions
1. In plant samples with ChEZ there are 4 beta emitting radionuclides -natural 40 K, man-made 90 Sr + 90 Y and 137 Cs. In this case, the concentration of 40 K is usually less than 1 % compared to the concentration of man-made radionuclides, so when measuring 90 Sr and 137 Cs in counting samples of beta radiation 40 K can be neglected. The proposed method of quantitative radiometric indication of beta-emitting radionuclides involves measuring the speed of counting the radiation of counting samples without a filter and using a filter made of fine molybdenum. When measuring the beta particle flux without a filter, the total number of pulses from betaemitting radionuclides in the sample, both low-energy 90 Sr and 137 Cs and high-energy 90 Y, is recorded. When using a molybdenum filter, in samples with ChEZ, more than 95 % of 90 Y radiation is detected. This makes it possible to determine the activity of 90 Y in the counting sample by taking into account the difference in the efficiency of recording pulses from high and low energy radiation.
2. Based on the results of research, a procedure for mathematical calculation of the concentration of 90 Sr and 137 Cs in counting samples of plant leaves was developed. The applied calculation system allows to calculate the concentration of 90 Y in the counting sample on the basis of the established parameters of radiation protection, and to assign it to 90 Sr, with which 90 Y is in a state of radiation equilibrium. Based on the obtained data, the concentration of 137 Cs in the drug is calculated minus the fraction of the rate of counting the beta radiation pulses 90 Sr + 90 Y.
3. The total relative uncertainty of the quantitative indication of beta emitting radionuclides by laboratory radiometry consists of uncertainties formed during drying and weighing of drugs, radiometric measurement and due to the radiometer prescribed by the technical documentation. The total relative uncertainty of the measured 90 Sr and 137 Cs concentrations calculated for the 2017 and 2019 calculation samples did not exceed 44 % and 43 %, respectively. Statistical analysis by the Monte Carlo method showed that the measurement results obtained by the method of quantitative beta radiometric indication correspond to the results obtained by the method of beta spectrometry. The proposed measurement method can be used as an aid in the control of radionuclide contamination and radioecological research.