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This paper presents results of Monte Carlo modeling of the beta-radiometer device with Geiger-Mueller detector used in Belarus and Russia to measure the radioactive contamination of milk after the Chernobyl accident. This type of detector, which is not energy selective, measured the total beta-activity of the radionuclide mix. A mathematical model of the beta-radiometer device, namely DP-100, was developed, and the calibration factors for the different radionuclides that might contribute to the milk contamination were calculated. The estimated calibration factors for 131I, 137Cs, 134Cs, 90Sr, 144Ce, and 106Ru reasonably agree with calibration factors determined experimentally. The calculated calibration factors for 132Te, 132I, 133I, 136Cs, 103Ru, 140Ba, 140La, and 141Ce had not been previously determined experimentally. The obtained results allow to derive the activity of specific radionuclides, in particular 131I, from the results of the total beta-activity measurements in milk. Results of this study are important for the purposes of retrospective dosimetry that uses measurements of radioactivity in environmental samples performed with beta-radiometer devices.
The accident at the Chernobyl nuclear power plant resulted in widespread radioactive contamination, particularly of the territories of Belarus, the Russian Federation, and Ukraine. For the majority of persons living in these territories, most of the radiation exposure to the thyroid was from iodine isotopes, especially 131I. The U.S. National Cancer Institute is conducting a long-term cohort study in Belarus of thyroid cancer among the persons exposed to radiation in childhood following the Chernobyl accident. The reconstruction of the individual doses for the cohort members is based on the measurements of the 131I contents in their thyroid glands, which were performed during the few first weeks after the accident. As the consumption of locally produced milk was the main source of 131I intake by people, the determination of 131I concentration in milk can be used to confirm the validity of the thyroid doses. The measurements of total beta-activity in milk provide the opportunity to derive 131I concentration.
Sanitary and Hygiene Centers of the USSR Ministry of Health performed measurements of total beta-activity in milk in different regions of Belarus to control the level of radioactive contamination in the locally produced foodstuffs following the Chernobyl accident. The majority of the measurements of radioactivity in cow’s milk were made with a beta-radiometer device, namely DP-100, equipped with a Geiger-Mueller (GM) detector. This type of detector, which is not energy selective, recorded counts due to the activity of the radionuclide mix. In the initial processing of the results that was carried out in 1986, a so-called “official” calibration factor was used to derive the total beta-activity of the sample from the count rate recorded by the device. The “official” calibration factor corresponds to beta rays of 0.3 MeV (Lyarsky, 1965) and is independent of the time of the measurement. To estimate the activity of specific radionuclides, in particular 131I, from the results of the total beta-activity measurements in milk in a more rigorous manner, it is necessary: (1) to evaluate the time-dependent composition of the radionuclide mix in milk; and (2) to calculate the calibration factors for these radionuclides.
Drozdovitch et al. (2006) estimated the time-dependent fraction of each radionuclide in the total activity in milk by using radioecological model with parameters adapted to the local conditions. Relative contribution of each radionuclide to the count rate of the device was calculated by dividing that fraction of the activity by the calibration factor for the considered radionuclide and, then, dividing it by the total calculated count rate. Finally, to estimate the activity of a given radionuclide in milk, the actual count rate recorded by the device during the measurements in 1986 was multiplied by the relative contribution of that radionuclide to the count rate of the device and by its calibration factor.
Contamination from the Chernobyl fallout of cow’s milk with 131I, 133I, 134Cs, 136Cs, 137Cs, 89Sr, 90Sr, 103Ru, 106Ru, 140Ba, 141Ce, and 144Ce was considered in a paper by Drozdovitch et al. (2006). However, calibration factors were available only for 131I, 134Cs, 137Cs, 90Sr, 106Ru, and 144Ce. They were evaluated experimentally by Savkin et al. (1992) based on measurements of standard solutions of these radionuclides. Savkin et al. (1992) also estimated the calibration factor for 89Sr by interpolation of the calibration factors for other radionuclides with similar beta spectra and energies. However, the calibration factors for other potentially important radionuclides (132Te, 132I, 133I, 136Cs, 103Ru, 140Ba, 140La, and 141Ce) were not determined in those studies.
The purpose of this work was to estimate the calibration factors for all radionuclides that contaminated milk after the Chernobyl accident using a mathematical model of the beta-radiometer DP-100. Accounting for all radionuclides presented in contaminated milk may greatly improve the results of estimation of 131I activity derived from total beta-activity measured in milk shortly after the Chernobyl accident.
The total beta-activity in milk was measured with the beta-radiometer DP-100 by placing the milk sample in an aluminum dish located in a plastic glass support. Both the plastic glass support with the sample and the gas end-window GM counter, namely MST-17, were placed in a lead cylindrical shield. Figure 1 shows a scheme of the DP-100 and of the geometry of measurement. Table 1 gives the size of the dish and the distance between the detector and the dish for three standard geometries that were used to measure the total beta-activity in the milk samples.
Beta particles enter the GM counter through a window in a plane metallic base that is covered with a thin layer (5 mg cm−2) of mica. Cathode of the counter is a thin layer (~ 1 μm) of metal covered the GM tube inside; anode is a metal wire placed as axis of the tube. Density of the gas inside the GM counter is around 120 g m−3. The diameter of the GM counter is 2 cm, while its length is 2.5 cm.
Any beta-particle traversing the space between the anode and the cathode is counted with a probability equal to 1. Due to the construction of the GM counter, the probability of registration of gamma-rays is three to four orders of magnitude less than that of beta-particles. However, gamma-radiation contributes to counting due to interaction of gamma-radiation with matter in the shield, milk sample, and components of the counter, which produces Compton scattering, photoelectrons and electron-positron pairs. The secondary electrons from these processes are also registered by the counter. Therefore, modeling of the process of measurement with the DP-100 device should take into account both beta and gamma chains of decay of radionuclides in the milk sample. It should be noted that emitted beta-particles (both primary and secondary) lose some energy when they interact with matter, and, therefore, only a fraction of the beta particles will reach the sensitive volume of the GM counter. This fraction needs to be calculated in order to estimate the device response. This requires modeling of the transport of the beta- and gamma-rays emitted by the source through the materials surrounding the detector.
The MCNP4 software (Briesmeister, 1994) was used to model the DP-100 device, the processes of the electron and photon transport and interaction with matter, and registration by the GM counter.
A detailed mathematical model of the DP-100 device with the GM counter was developed. All parts of the device, namely, the source of particles, the detector, and the surrounding of the detector, were considered in the Monte Carlo modeling of the process of instrumental measurements. Density and chemical composition of the constructing materials were also taken into account.
Two types of electrons were considered to be registered by the detector: (a) primary electrons emitted by the source (major contribution to the device count rate) and (b) secondary electrons resulted from the interaction of the emitted photons with the surrounding materials (minor contribution). The MCNP4 software (Briesmeister, 1994) was used to simulate the electrons and photons transport as well as generation of secondary electrons due to photoelectric effect, Compton scattering, and pair production. It was assumed that any electron was counted when it reached the sensitive volume of the detector. The source of electrons and photons was considered to be uniformly distributed in the dish with milk sample, and isotropic direction of particle’s emission from that source was also assumed. Track of electron (photon) was modeled until registration in the sensitive area of the detector or absorption by the lead shield or other parts of the device. Absorption in the milk sample was also taken into account.
The response of the DP-100 device to a mono-energetic source of electrons is defined as
η(Ei) is the response of the device to electron with energy Ei (unitless), Nc is the measured count rate (s−1), and Nh (Ei) is the total number of particles with energy Ei emitted per unit time (s−1).
The calibration factor for a monoenergetic source is defined as the activity of the sample per unit count rate and is determined as
where CF(Ei) is the calibration factor for the source of energy Ei (Bq g−1 per count min−1), M is the mass of sample (g), and k = 60 is the number of seconds in a minute (s min−1).
Response of the DP-100 device to a source with a complex energy spectrum is defined as
where η is the response of the DP-100 device for the source with a complex energy spectrum (dimensionless) and p(Ei) is the yield of particles with energy Ei (dimensionless).
The calibration factor for the DP-100 device for a source with a complex energy spectrum is defined as
where Emin is the minimal energy of electron that can pass through window of the GM counter (MeV), Emax is the maximal energy of beta-spectrum (MeV), p(E) is the beta-spectrum taken from ICRP Publication 38 (ICRP, 2003).
The same calculations were made for the gamma emission of the radionuclides to take into account secondary electrons produced by interaction of gamma-radiation with matter. Device response for each gamma-emitting radionuclide was calculated with the MCNP4 software taking into account the production of secondary electrons by interaction of the emitted photons with the surrounding matter and registration of the secondary electrons by the detector.
Response of the DP-100 device was calculated for electrons and photons of the energies in the range from 0.1 to 3 MeV using Monte Carlo simulations of particle transport from the source to the detector and interaction of electrons and photons with matter. Tables 2 and and33 give estimated energy-dependent device response to primary and secondary electrons, respectively.
As can be seen from Tables 2 and and3,3, the response of the DP-100 device to electron of a given energy that are products of radioactive decay is more than one order of magnitude higher than that to the secondary electrons produced by photon of the same energy. The energy-dependent device response given in Table 2 for primary electrons was fitted by the following curve:
where - A1, A2, and a are dimensionless parameters (Table 4), E is the energy of the emitted electron (MeV) and E0 is a fitted parameter value (MeV).
Figure 2 shows the estimated response of the DP-100 device for different measurement geometries and fitted function described by Equation 6. Errors in estimated response vary from (10–13)% for energies below 0.2 MeV to (3–5)% for energies above 1 MeV.
Calibration factors for the DP-100 device were calculated using Equations 5 and 6 for the following nuclides: 131I, 132Te, 132I, 133I, 134Cs, 136Cs, 137Cs, 89Sr, 90Sr, 103Ru, 106Ru, 140Ba, 140La, 141Ce, and 144Ce (Table 5). The calibration factors for 137Cs, 90Sr, 106Ru, and 144Ce include contribution from short-lived progenies 137mBa, 90Y, 106Rh, and 144Pr, respectively. It should be noted that the secondary electrons contributed significantly to the value of the calibration factor for radionuclides with low energy of electrons, but with high energy of photons, for example 136Cs.
The radionuclide-specific calibration factors calculated in this study were compared with those evaluated experimentally by Savkin et al. (1992) (Table 6). Radionuclide-specific errors in experimentally evaluated calibration factor were also taken from the paper by Savkin et al. (1992). As can be seen from Table 6, the two sets of values (calculated and experimental) are rather close, mainly within the uncertainties of the experimental calibration factor. The biggest difference between the calculated and experimental calibration factors was found for 89Sr. It is noteworthy that the calibration factor for this radionuclide given by Savkin et al. (1992) was actually estimated by interpolation on average energy of beta-spectrum and experimental calibration factors for other radionuclides. That interpolation did not take into account the fact that low-energy electrons have small contribution to the device response (Table 2). Therefore, the calibration factor for 89Sr calculated in this paper can be regarded as more accurate.
Results of the total beta-activity measurements in cow’s milk are very useful for the reconstruction of thyroid doses from 131I intake with cow’s milk in areas affected by the Chernobyl accident. These measurements were performed with radiometer DP-100 with the GM counter, which is not energy selective. As a result, the total beta-activity of the radionuclide mix was measured.
Several studies were conducted to estimate radionuclide-specific activities from the results of total beta-activity measurements (Panchenko, 1999; Savkin et al., 2004; Zvonova et al., 2004; Drozdovitch et al., 2006). However, these studies considered only the following nuclides: 131I, 137Cs, 134Cs, 90Sr, 144Ce, and 106Ru (i.e., radionuclides for which calibration factors were known at that time from experiment).
In this work, a mathematical model of the DP-100 device was used to estimate the calibration factors for a broader list of radionuclides that might contribute to the milk contamination, including 132Te, 132I, 133I, 136Cs, 103Ru, 140Ba, 140La, and 141Ce., The DP-100 calibration factors for these radionuclides had never been estimated. The calibration factors calculated for the short-lived radionuclides are especially important for the measurements performed shortly after the Chernobyl accident. Results of this study make it possible to derive the activity of 131I from the total beta-activity measurements more accuracy.
This work was supported by the National Cancer Institute (USA) within the framework of the ISTC Project B-488P; and by the Intra-Agency Agreement between the National Institute of Allergy and Infectious Diseases (USA) and the National Cancer Institute, NIAID agreement #Y2-Al-5077 and NCI agreement #Y3-CO-5117.
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