- Email: [email protected]
Estimating contamination monitor efficiency for beta radiation by means of PENELOPE-2008 Monte Carlo simulation
Applied Radiation and Isotopes 127 (2017) 87–91
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Estimating contamination monitor efficiency for beta radiation by means of PENELOPE-2008 Monte Carlo simulation
MARK
⁎
R. Merk , J. Mielcarek, J. Döring, B. Lange, Chr. Lucks BfS Federal Office for Radiation Protection, D-38201 Salzgitter, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Monte Carlo simulation Beta radiation Emergency preparedness Public exposure
Monte Carlo computer simulation of beta radiation transport within radioactively-contaminated food samples was studied and compared with experimental results. We used the Monte Carlo code PENELOPE-2008. The basic geometry of a hand-held contamination monitor and the geometry of beta-emitting food samples and surface sources were modeled, and the detection efficiency of the device was determined. Possibilities to improve the detection efficiency were tested by simulation.
1. Introduction After nuclear accidents or incidents with radioactive materials that may affect food, decision-makers depend on immediate information on activity levels in food samples. Many radionuclides with high ingestion dose coefficients are beta emitters. In interpreting measurement results, one should bear in mind that beta radiation is easily absorbed within the sample itself. An activity determination based solely on the number of detector counts could therefore considerably underestimate the true activity within the food sample (Kabai et al., 2017; Pujol and SuarezNavarro, 2004). The detector efficiency ϵ can be determined experimentally using food samples in a standard geometry. It is defined by ϵ = net counting rate measured / net emission rate. However, preparation of such samples has to be done separately for every radionuclide in question. Experience shows that such preparation procedure can be challenging experimentally, time consuming, and expensive. For example, it may be necessary to buy radionuclides that are rarely in use or supplied in a form not readily suitable for the preparation of food samples under standardized conditions. Moreover, complex preparation techniques might lead to unnecessary radiation exposure of laboratory personnel (Kabai et al., 2017; Lehto and Hou, 2011). Simulation results presented in the literature and in this article indicate that the Monte Carlo method offers promising possibilities in the theoretical investigation of detector efficiencies for the measurement of food samples based on computer modeling. Sato et al. (2013) described Monte Carlo simulations of a beta-particle detector. The authors designed a detector for measuring food samples in the aftermath of the nuclear accident in Fukushima and studied the usability of
⁎
Corresponding author. E-mail address: [email protected] (R. Merk).
http://dx.doi.org/10.1016/j.apradiso.2017.05.015 Received 11 November 2016; Received in revised form 12 May 2017; Accepted 14 May 2017 Available online 19 May 2017 0969-8043/ © 2017 Elsevier Ltd. All rights reserved.
the design by simulation. Another detector-design study based on Monte Carlo simulation is the work by Piotrowski et al. (2015). The authors simulated their LANFOS contamination monitor, a detector developed with the aim of easy and fast analysis of food samples possibly affected by the Fukushima accident. We present computational techniques that may be expanded to become a standard theoretical method to obtain information on beta detection efficiencies in case of contaminated food samples. The techniques are suited for beta radiation. Very likely, they can be adapted to other radiation types as well (Piotrowski et al., 2015). The main ingredient of this theoretical method consists of an application of the Monte Carlo method to simulate the combined radiation transport of electrons, positrons, and photons in ordinary matter. We have based our investigations on an extensive use of the Monte Carlo computer program PENELOPE-2008 (Salvat et al., 2009; Baro et al., 1995; Sempau et al., 1997), a state-of-the-art code package that serves this purpose. Excellent agreement of PENELOPE results with experimental data is shown in numerous publications and valid for many experimental situations over a broad range of energies (Baro et al., 1995; Sempau et al., 1997, 2003). In the case of gamma radiation from various gamma emitters in complex geometries, we could already demonstrate the usefulness of PENELOPE-2008 Monte Carlo simulations for radiation protection needs (Merk et al., 2013). PENELOPE modeling of beta detection efficiencies can be found in the paper by Tan and DeVol (2003). However, their simulation is for a scintillation flowcell detector. Such detectors are used for monitoring the radioactivity in aqueous streams. In the present paper, we estimate the detection efficiency of a contamination monitor by means of PENELOPE-2008 Monte Carlo
Applied Radiation and Isotopes 127 (2017) 87–91
R. Merk et al.
sophisticated, and the code is constantly updated by the developers with the most recent version being PENELOPE-2015. We therefore refer to the publications (Salvat et al., 2009; Kalos and Whitlock, 2008; Haghighat, 2015) and the review article by James (1980) for details on the physics models used and the Monte Carlo method in general. Coding the present problem in PENELOPE includes geometry and physics inputs. As for geometry, various elements of the geometric setup have to be programmed, for example, the scintillator and the sample. Also, the location of possible impact detectors has to be specified. In the PENELOPE terminology, an impact detector is an active part of the overall model geometry that is meant to count particles coming from parts of the geometry that are not active in this respect (Salvat et al., 2009). For the purpose of this work, the location of an impact detector was coded so that it would coincide with the scintillator geometry. Impact detectors can be defined within PENMAIN, which is a generic main program for PENELOPE (Salvat et al., 2009). The efficiency was read directly from one of the output files of PENMAIN (penmain-res.dat). An internal script language was used to describe the geometry of the problem in terms of mathematical quadric surfaces. For the physics part of the problem, the following basic simulation parameters were used in PENELOPE in accordance with Salvat et al. (2009). Eabs = 10 4 eV as absorption energies for electrons and positrons, and Eabs = 50 eV for photons. C1 = C2 = 0.1, Wcc = 10 3 eV , and Wcr = 10 3 eV , which are parameters for scattering and cutoff parameters for hard inelastic collisions and bremsstrahlung emission; see the work by Salvat et al. (2009) for details. In addition, the primary particles' beta spectra have to be coded. To this end, we used the DECDATA computer program (ICRP, 2008), which produces spectral raw data to generate beta spectra. In order to improve data quality, we interpolated functions between the DECDATA data points with our own computer programs. Altogether, this means that the full beta spectra were implemented. We studied radionuclides with endpoint energies between about 0.07 MeV and 1.7 MeV, and half-lives between several days and up to the order of 105 years. The radionuclides are listed in Table 1. Finally, the internal PENELOPE materials database was used to generate the properties of the materials needed in the simulation, for example, densities, by running the PENELOPE submodule MATERIAL.
simulation. The detection efficiency is calculated for beta radiation emitted from standard surface sources and volume sources equivalent to standard food samples. The simulation results are compared with experimental data, where such data are available. In the following section, we introduce the methods and the PENELOPE-2008 code in view of the present application. Section 3 contains the outcome of the simulations and experimental data. Results concerning standard surface sources and volume sources equivalent to aqueous food samples are displayed and compared. Section 4 contains a brief summary. 2. Material and method 2.1. Detector The detector used was a hand-held contamination monitor with a mass of about 1 kg and a size of approximately 318×157×172 mm3. It allows to detect alpha, beta, and gamma radiation. Particles are detected with a plastic scintillator, meaning that no filling gas is necessary for this type of detector. A protective lattice-shaped entry window covers the scintillator. The detector voltage is 1.2 kV, and the device can be used within a temperature range from −10 °C to 40 °C. The background level is subtracted from the measured data automatically. Such detectors are especially useful for field work or under conditions where laboratory access is not immediately available. Contamination monitors can also be used in nuclear power plants, for decontamination procedures, in radiation laboratories, or in emergency situations (STUK, 2006). 2.2. Sample measurement Surface sources were measured in direct contact with the entry window of the detector. The setup is described in Section 2.4., Replicate devices of the same model were used as detectors in the BfS laboratory producing an averaged result for the efficiency and a random error. Food samples represent volume sources; see Section 2.4 for the setup design. Samples for determining the detector efficiency were prepared in the following way. The aqueous food sample was mixed with an active standard solution and homogenized by stirring or shaking. A certain amount of the mixture (20 mL) with a known activity was then pipetted into a planchet and measured with the detector in a defined geometry. There were various sources of random errors. For example, random errors may result from a varying thickness of the sample material in the planchet, a varying degree of homogeneity of the activity within the sample, or from activity variations in the standard. It was also observed in the BfS laboratory that, in some cases, radionuclides tended to accumulate at the bottom of the planchet.
2.4. Design of the simulated setups The first suite of the PENELOPE Monte Carlo runs to be presented here is for standard surface beta emitters. These runs are not directly linked to food samples as the latter ones are always volume sources with a thickness in the millimeter range. However, if the same radionuclides are used, simulation and comparison with experiments in the case of surface emitters can be helpful to understand the basic behavior of the efficiency as a function of the beta endpoint energy of the respective radionuclides. We expected that, in comparison with such efficiencies, volume (food) sample simulations would reveal a dimin-
2.3. Simulation code and parameters We have used the Monte Carlo computer code PENELOPE-2008 (Salvat et al., 2009) to simulate the beta radiation transport in matter and thereby estimate the beta radiation detection efficiency of a handheld contamination monitor in a geometric setup suited for food contamination measurements. For brevity, the entire code package will be termed PENELOPE in the following discussion, which will include all sub-packages delivered with the PENELOPE-2008 distribution (viewers, for example). PENELOPE is a computer program for simulating the coupled radiation transport of photons, electrons, and positrons. As possible mechanisms of interaction for electrons and positrons, the code includes elastic scattering, inelastic scattering, bremsstrahlung emission, and positron annihilation. Possible interactions of gamma radiation with matter considered in the code are the photoelectric absorption, Rayleigh scattering, Compton scattering, and electron-positron pair production. The Monte Carlo techniques used in PENELOPE are
Table 1 Radionuclides, beta endpoint energies (MeV) and half-lives (years) used in the present simulations (ICRP, 2008). Radionuclide
Beta endpoint energy (MeV)
Half-life (years)
63
0.067
1.00 × 10 2
14
0.156
5.70 × 10 3
99
0.294
2.11 × 10 5
Ni C Tc
90
Sr
131
I
36
Cl
2.88 × 101
2.19 × 10−2
0.709
3.01 × 10 5
204
0.764
3.78 × 10 0
89
1.495
1.38 × 10−1
32
1.711
3.91 × 10−2
Tl
Sr P
88
0.546 0.606
Applied Radiation and Isotopes 127 (2017) 87–91
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Fig. 2. Three-dimensional image of the geometry used in the PENELOPE simulation of volume sources, see Section 2.4 for details. The image shows two different views of the configuration. The detailed scintillator geometry is shown in Fig. 1. Opening wedges in the bottom part of the image are for visualization purposes only. Parts of the figure were produced with the PENELOPE geometry viewer (Salvat et al., 2009).
Fig. 1. Sandwich structure of the surface source and scintillator geometry as coded with PENELOPE. The zoom shows the various layers covering the scintillator. The background image shows only the parts of the geometry that are close to the interface between the surface source and scintillator, see Section 2.4 for details. A part of the figure was produced with the PENELOPE geometry viewer (Salvat et al., 2009).
ished efficiency all over the endpoint-energy range covered here. Studying standard surface sources would thus provide an upper estimate in this case. This can be an advantage in practical laboratory work since surface sources are easier to handle. Oftentimes, they are also easier to come by (BMUB, 2014). In both the surface and volume source simulations, the detector geometry was simplified by coding those parts of the geometry that have immediate relevance to calculating the efficiency. We therefore modeled the rectangular plastic scintillator and various layers on top of it, such as ZnS, aluminum and Mylar layers, and foils. We abstained from programming the complex geometry of the protective entry window; rather, the absorbing effect of the entry window was considered as a diminishing factor of 0.82 on the Monte Carlo simulation results, accounting for the total transparency according to the technical documentation of the detector. Since this value is total transparency, it was assumed to be applicable to all radionuclides studied here. The dimensions of the plastic scintillator were 24×13×0.1 cm3, the thicknesses of the layers and foils on top of the scintillator were in the micrometer range. Fig. 1 shows the sandwich structure of the layers and foils considered together with the surface source in contact with the detector. The geometry used for the quadratic standard surface source consisted of a 6-micrometer activated Eloxal (Al2O3) layer with a length of 10 cm embedded in a thin quadratic aluminum frame with a length of 12 cm and a height of 0.3 cm. For efficiency simulations in the case of aqueous food samples (volume sources), we modeled the circular geometry of an aluminum planchet containing the sample. The planchet had a diameter of 12 cm, a height of 0.8 cm, and a thickness of 0.08 cm. The sample itself was modeled as an active water layer with a thickness of 0.18 cm and therefore constituted a cylindrical volume source. We used the same plastic scintillator geometry as described above in the case of surface sources. In the experimental configuration, the contamination monitor was mounted in such a way that the distance between the sample surface and the detector was about 1.52 cm. Fig. 2 presents a threedimensional visualization of the modeled configuration. In this illustration, the details of the scintillator geometry are not visible due to their
Fig. 3. PENELOPE simulation results for the efficiency as a function of the beta endpoint energy for a surface source configuration and corresponding experimental values, see Section 3.1 for details. Also included in the plot is a fit curve to the simulation results.
small sizes. 3. Results and discussion 3.1. Standard surface beta emitters Fig. 3 shows the results of the Monte Carlo simulations for the detector efficiency depicted as a function of the beta endpoint energy of the respective radionuclide. The results are for surface sources. Simulated values for the detector efficiency range from 0.03% to 55%. A qualitatively similar curve for a flow-cell detector is given by Tan and DeVol (2003). Fig. 3 also gives experimental values determined with the contamination monitor. When available, the absolute uncertainty of the result is indicated. Some of the measured data are from the original documentation of the detector. Measured data points with error bars were determined in our own laboratory. The coverage factor for the simulation was assumed to be 3σ as usual for the PENELOPE code package (Salvat et al., 2009). Because there were several contamination monitors of the same type available in the BfS (from different measurement teams), in order to avoid a bias, a source was measured with different devices of the same type. The uncertainty was assumed to be 1σ for each measurement in these series. With exceptions in the middle and at the higher end of the energy interval studied, the values from experiments are consistent with the Monte Carlo simulation results. The values determined in our own laboratory are all consistent with the theoretical results. Unlike the experimental data, the simulated values show a relatively smooth course with energy. The deviation of the simulated values from the experimental data ranges from 7% to more than 100% for some data 89
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2×10−3% to 21%. As expected, they are considerably smaller than the corresponding values for surface sources. The Monte Carlo simulation values can be compared with three experimental results obtained in our laboratory. Two of them (in the first third and at the higher end of the energy interval studied) are displayed in Fig. 4. They correspond to 99Tc and 32P, respectively. The third measurement was for the radionuclide with the lowest beta endpoint energy (63Ni). In this case, the efficiency was so low that we could not determine a laboratory value with the described experimental setup. This agrees with the Monte Carlo simulation result of only 2×10−3%. The other two experimental values are in good agreement with the simulated results.
points (e.g., for 32P). In the latter cases, large deviations occur for radionuclides with half-lives of the order of 10 days. Presumably, such deviations can be attributed to a missing decay correction in the experiment because the experimental values were smaller for these radionuclides than the simulated ones, indicating that the source activities assumed by the detector manufacturer were too high. In addition to simulation results and experimental values, Fig. 3 shows a fit curve to the Monte Carlo simulation results. In a very simple approach to get a relation between the efficiency and the beta endpoint energy E0 for the fit, the efficiency was related linearly to the particle intensity I (E0 ) (number of incident particles at energy E0 per second passing through a thin slice of matter). For the particle intensity as a function of distance x, a well-known exponential absorption law exists, providing a link to the mass attenuation coefficient μ / ρ (ρ and I0 representing material density and original intensity at x=0, respectively),
I (x ) = I0 exp (−μx ).
3.3. Tests to improve the detection efficiency The geometric input used for the simulations reflects the present setup in our laboratory. Measurements of radioactivity from food samples very often proceed under standard geometric conditions for better comparability or because it is demanded by standard operating procedures. Any setup changes may require modifications in the respective laboratory protocols or modifications of mechanical constructions, for example, detector or sample holders. Changing this framework haphazardly in order to improve the detection efficiency is therefore not always advisable. If the geometry is already coded, as is the case with our Monte Carlo simulations, it may be easier to simulate the effects of possible changes to the geometry. Attempts to improve the detector efficiency should consider the fact that the available amount of the food sample material is often limited, for example, due to sophisticated preparation techniques. This holds even if radiochemistry methods are not in use. For example, it may be necessary to make the sample durable for conservation of evidence. However, even if the sample is larger, the performance of the method is not necessarily better because an increase in the sample mass increases the absorption of beta particles in the larger volume of the emitting source. The question is, therefore, how the geometry itself could possibly be improved so to increase the beta detection efficiency. It will be demonstrated that the Monte Carlo method is an ideal way to test such cases without involved laboratory investigations. In our opinion, two possible methods are evident. The first method is to reduce the distance between the sample and the detector. The second one is to reduce the thickness of the sample while keeping the amount of sample material constant. Both cases can be tested by modifying the Monte Carlo input file. As for the first method, an explicit PENELOPE simulation shows no improvement of the efficiency. After bringing the top rim of the planchet in contact with the detector entry window in the model, only a negligible increase in beta efficiency was found in the simulation. It is therefore not advisable to modify the mechanical setup of the measurement device in this case. The second possibility to test is a thinner sample. For acqueous samples, this can be achieved by increasing the radius of the planchet. Increasing the radius by a factor of 21/2 halves the sample thickness (at a constant amount of the sample material). Again, modifying the existing PENELOPE geometry file is easier than changing the experimental setup and repeating all measurements. Fig. 5 shows the simulated efficiencies obtained for the larger planchet in the model geometry. The efficiencies of the original volume sources are also given for comparison. The values are depicted as a function of beta endpoint energy. It can be seen that using the larger planchet in the simulation leads to higher efficiencies over the whole energy range investigated here. The efficiency ratios can be found in Table 2. For some endpoint energies, the new efficiencies are almost twice as high.
(1)
For the mass attenuation coefficient, another well-established, but empirical relation can be stated (Nathuram et al., 1988),
μ = AE0−B , ρ
(2)
where A and B stand for empirical constants. As a first guess for B, a value of B = 1.48 was taken, consistent with the parameter range communicated by Nathuram et al. (1988). The parameters A, ρ, x, and I0 are absorbed by the respective fit parameters due to the overall approach to express the efficiency as a function of the beta endpoint energy. Nevertheless, when typical values for A from Nathuram et al. (1988) and averaged values for ρ are used, the numerically determined fit parameter in the exponent yields values for x that are compatible with the geometric dimensions of the configuration. More sophisticated approaches based, for example, on an integral ansatz, are thinkable. However, as one can see from the plot, the fit curve from the simpler procedure describes the basic course and curvature of a line directly connecting the data points from the Monte Carlo simulation. The goodness of fit is R2 = 0.974 . 3.2. Volume sources Fig. 4 shows the modeled efficiency in the case of volume sources as a function of the beta endpoint energy. The statistical uncertainty of the PENELOPE results is interpreted as 3σ (Salvat et al., 2009). When displayed on the graph, it is covered by the data point symbols for some radionuclides. For efficiency, we chose a logarithmic scale to compare the values with the surface source results, which are depicted on the same plot. In the case of volume sources, the efficiencies range from
4. Conclusion
Fig. 4. PENELOPE simulation results for the efficiency as a function of the beta endpoint energy, see Section 3.2 for details. The plot shows the results for the volume sources modeling and two experimental values for volume sources determined in our laboratory. In addition, the surface sources modeling results are displayed for comparison.
In this article, theoretical and experimental results concerning the determination of the detection efficiency of a hand-held contamination 90
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can be the method of choice. At least, it can serve to validate the experimental results or prepare grounds for laboratory experiments with radionuclides the laboratory personnel is not yet familiar with. Acknowledgment The authors like to thank one anonymous reviewer for a very constructive review report and for providing us with valuable hints. R.M. likes to thank E. Kabai (BfS) for commenting on radiochemistry and laboratory questions. The authors thank M. Ebert and K. Behrend for their assistance in laboratory work. E. Neumann (formerly BfS-IT Neuherberg) and E. Höller (BfS-IT) provided us with Linux-powered computers used for the Monte Carlo simulations presented in this article. Fig. 5. PENELOPE simulation results for the efficiency as a function of the beta endpoint energy for two different planchet configurations, see Section 3.3 for details. The plot shows the results for the volume sources modeling in the case of standard planchets used in our laboratory and for planchets with enlarged radii (factor 21/2 ).
References Baro, J., Sempau, J., Fernandez-Varea, J.M., Salvat, F., 1995. PENELOPE: An algorithm for Monte Carlo simulation of the penetration and energy loss of electrons and positrons in matter. Nucl. Instrum. Methods Phys. Res. Sect. B 100, 31–46. BMUB (Federal Ministry for the Environment, Nature Conservation, Building and Nuclear Safety) 2014. Messanleitungen (Measurement Guide; in German), 〈www.bmub.bund. de/P1517/〉. Haghighat, A., 2015. Monte Carlo Methods for Particle Transport. CRC Press, Taylor and Francis Group, Boca Raton, FL. ICRP 2008. Nuclear decay data for dosimetric calculations. Annals of the ICRP Publication 107. Vol. 38 No. 3. The International Commission on Radiological Protection, Stockholm. James, F., 1980. Monte Carlo theory and practice. Rep. Prog. Phys. 43, 1145–1189. Kabai, E., Savkin, B., Mehlsam, I., Poppitz-Spuhler, A., 2017. Combined method for the fast determination of pure beta emitting radioisotopes in food samples. J. Radioanal. Nucl. Chem. 311, 1401–1408. Kalos, M.H., Whitlock, P.A. 2008. Monte Carlo Methods. Second Ed. Wiley-Blackwell, Weinheim. Lehto, J., Hou, X., 2011. Chemistry and Analysis of Radionuclides, Laboratory Techniques and Methodology. Wiley-VCH, Weinheim. Merk, R., Kröger, H., Edelhäuser-Hornung, L., Hoffmann, B., 2013. PENELOPE-2008 Monte Carlo simulation of gamma exposure induced by 60Co and NORMradionuclides in closed geometries. Appl. Radiat. Isot. 82, 20–27. Nathuram, R., Subrahmanian, G., Thontadarya, S.R., 1988. Mass attenuation coefficients of beta particles in 4π geometry. Phys. C 151, 547–551. Piotrowski, L.W., Casolino, M., Ebisuzaki, T., Higashide, K., 2015. The simulation of the LANFOS-H food radiation contamination detector using Geant4 package. Comput. Phys. Commun. 187, 49–54. Pujol, Ll, Suarez-Navarro, J.A., 2004. Self-absorption correction for beta radioactivity measurements in water samples. Appl. Radiat. Isot. 60, 693–702. Salvat, F., Fernandez-Varea, J.M., Sempau, J., 2009. PENELOPE-2008: A code system for Monte Carlo simulation of electron and photon transport. NEA No. 6416, OECD Nuclear Energy Agency, Issy-les-Moulineaux, France. Sato, Y., Takahashi, H., Yamada, T., Unno, Y., Yunoki, A., 2013. Monte Carlo simulation of a beta particle detector for food samples. Appl. Radiat. Isot. 81, 162–164. Sempau, J., Acosta, E., Baro, J., Fernandez-Varea, J.M., Salvat, F., 1997. An algorithm for Monte Carlo simulation of coupled electron-photon transport. Nucl. Instrum. Methods Phys. Res. Sect. B 132, 377–390. Sempau, J., Fernandez-Varea, J.M., Acosta, E., Salvat, F., 2003. Experimental benchmarks of the Monte Carlo code PENELOPE. Nucl. Instrum. Methods Phys. Res. Sect. B 207, 107–123. STUK (Radiation and Nuclear Safety Authority) 2006. Radiation monitoring systems and equipment of a nuclear power plant. STUK Guide YVL 7.11, 3rd Edition, STUK, Helsinki, Finland. Tan, H., DeVol, T.A., 2003. Monte Carlo modeling of heterogeneous scintillation flow-cell detectors. Nucl. Instrum. Methods Phys. Res. Sect. A 515, 624–633.
Table 2 Radionuclides and efficiency ratios for larger vs. standard planchets, see Section 3.3 for details. Radionuclide
Efficiency ratio (larger vs. standard planchet)
63
1.10 1.62 1.73 1.72 1.74 1.63 1.63 1.27 1.24
Ni C Tc 90 Sr 131 I 36 Cl 204 Tl 89 Sr 32 P 14 99
monitor for measuring radioactively-contaminated food samples were presented. We have studied beta emitting radionuclides with relevance to emergency preparedness and covering a broad range of beta endpoint energies and half-lives. The efficiency of a contamination monitor was calculated by means of PENELOPE Monte Carlo simulations for surface and volume sources. The modeled volume sources were equivalent to aqueous food samples used in our laboratory. Consequently, we could compare the simulation results with experimentally determined efficiency values and have observed a good agreement with the laboratory results so far. We have also presented cases in which the Monte Carlo method could serve as a means to improve the detection efficiency. Theoretical techniques have the potential to supplement classical laboratory procedures and even replace some of them in the long run. In principle, it is almost always better to have efficiencies determined in laboratory experiments. However, for reasons such as time, costs, feasibility, or radiation protection, the theoretical Monte Carlo method
91
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Estimating contamination monitor efficiency for beta radiation by means of PENELOPE-2008 Monte Carlo simulation
MARK
⁎
R. Merk , J. Mielcarek, J. Döring, B. Lange, Chr. Lucks BfS Federal Office for Radiation Protection, D-38201 Salzgitter, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Monte Carlo simulation Beta radiation Emergency preparedness Public exposure
Monte Carlo computer simulation of beta radiation transport within radioactively-contaminated food samples was studied and compared with experimental results. We used the Monte Carlo code PENELOPE-2008. The basic geometry of a hand-held contamination monitor and the geometry of beta-emitting food samples and surface sources were modeled, and the detection efficiency of the device was determined. Possibilities to improve the detection efficiency were tested by simulation.
1. Introduction After nuclear accidents or incidents with radioactive materials that may affect food, decision-makers depend on immediate information on activity levels in food samples. Many radionuclides with high ingestion dose coefficients are beta emitters. In interpreting measurement results, one should bear in mind that beta radiation is easily absorbed within the sample itself. An activity determination based solely on the number of detector counts could therefore considerably underestimate the true activity within the food sample (Kabai et al., 2017; Pujol and SuarezNavarro, 2004). The detector efficiency ϵ can be determined experimentally using food samples in a standard geometry. It is defined by ϵ = net counting rate measured / net emission rate. However, preparation of such samples has to be done separately for every radionuclide in question. Experience shows that such preparation procedure can be challenging experimentally, time consuming, and expensive. For example, it may be necessary to buy radionuclides that are rarely in use or supplied in a form not readily suitable for the preparation of food samples under standardized conditions. Moreover, complex preparation techniques might lead to unnecessary radiation exposure of laboratory personnel (Kabai et al., 2017; Lehto and Hou, 2011). Simulation results presented in the literature and in this article indicate that the Monte Carlo method offers promising possibilities in the theoretical investigation of detector efficiencies for the measurement of food samples based on computer modeling. Sato et al. (2013) described Monte Carlo simulations of a beta-particle detector. The authors designed a detector for measuring food samples in the aftermath of the nuclear accident in Fukushima and studied the usability of
⁎
Corresponding author. E-mail address: [email protected] (R. Merk).
http://dx.doi.org/10.1016/j.apradiso.2017.05.015 Received 11 November 2016; Received in revised form 12 May 2017; Accepted 14 May 2017 Available online 19 May 2017 0969-8043/ © 2017 Elsevier Ltd. All rights reserved.
the design by simulation. Another detector-design study based on Monte Carlo simulation is the work by Piotrowski et al. (2015). The authors simulated their LANFOS contamination monitor, a detector developed with the aim of easy and fast analysis of food samples possibly affected by the Fukushima accident. We present computational techniques that may be expanded to become a standard theoretical method to obtain information on beta detection efficiencies in case of contaminated food samples. The techniques are suited for beta radiation. Very likely, they can be adapted to other radiation types as well (Piotrowski et al., 2015). The main ingredient of this theoretical method consists of an application of the Monte Carlo method to simulate the combined radiation transport of electrons, positrons, and photons in ordinary matter. We have based our investigations on an extensive use of the Monte Carlo computer program PENELOPE-2008 (Salvat et al., 2009; Baro et al., 1995; Sempau et al., 1997), a state-of-the-art code package that serves this purpose. Excellent agreement of PENELOPE results with experimental data is shown in numerous publications and valid for many experimental situations over a broad range of energies (Baro et al., 1995; Sempau et al., 1997, 2003). In the case of gamma radiation from various gamma emitters in complex geometries, we could already demonstrate the usefulness of PENELOPE-2008 Monte Carlo simulations for radiation protection needs (Merk et al., 2013). PENELOPE modeling of beta detection efficiencies can be found in the paper by Tan and DeVol (2003). However, their simulation is for a scintillation flowcell detector. Such detectors are used for monitoring the radioactivity in aqueous streams. In the present paper, we estimate the detection efficiency of a contamination monitor by means of PENELOPE-2008 Monte Carlo
Applied Radiation and Isotopes 127 (2017) 87–91
R. Merk et al.
sophisticated, and the code is constantly updated by the developers with the most recent version being PENELOPE-2015. We therefore refer to the publications (Salvat et al., 2009; Kalos and Whitlock, 2008; Haghighat, 2015) and the review article by James (1980) for details on the physics models used and the Monte Carlo method in general. Coding the present problem in PENELOPE includes geometry and physics inputs. As for geometry, various elements of the geometric setup have to be programmed, for example, the scintillator and the sample. Also, the location of possible impact detectors has to be specified. In the PENELOPE terminology, an impact detector is an active part of the overall model geometry that is meant to count particles coming from parts of the geometry that are not active in this respect (Salvat et al., 2009). For the purpose of this work, the location of an impact detector was coded so that it would coincide with the scintillator geometry. Impact detectors can be defined within PENMAIN, which is a generic main program for PENELOPE (Salvat et al., 2009). The efficiency was read directly from one of the output files of PENMAIN (penmain-res.dat). An internal script language was used to describe the geometry of the problem in terms of mathematical quadric surfaces. For the physics part of the problem, the following basic simulation parameters were used in PENELOPE in accordance with Salvat et al. (2009). Eabs = 10 4 eV as absorption energies for electrons and positrons, and Eabs = 50 eV for photons. C1 = C2 = 0.1, Wcc = 10 3 eV , and Wcr = 10 3 eV , which are parameters for scattering and cutoff parameters for hard inelastic collisions and bremsstrahlung emission; see the work by Salvat et al. (2009) for details. In addition, the primary particles' beta spectra have to be coded. To this end, we used the DECDATA computer program (ICRP, 2008), which produces spectral raw data to generate beta spectra. In order to improve data quality, we interpolated functions between the DECDATA data points with our own computer programs. Altogether, this means that the full beta spectra were implemented. We studied radionuclides with endpoint energies between about 0.07 MeV and 1.7 MeV, and half-lives between several days and up to the order of 105 years. The radionuclides are listed in Table 1. Finally, the internal PENELOPE materials database was used to generate the properties of the materials needed in the simulation, for example, densities, by running the PENELOPE submodule MATERIAL.
simulation. The detection efficiency is calculated for beta radiation emitted from standard surface sources and volume sources equivalent to standard food samples. The simulation results are compared with experimental data, where such data are available. In the following section, we introduce the methods and the PENELOPE-2008 code in view of the present application. Section 3 contains the outcome of the simulations and experimental data. Results concerning standard surface sources and volume sources equivalent to aqueous food samples are displayed and compared. Section 4 contains a brief summary. 2. Material and method 2.1. Detector The detector used was a hand-held contamination monitor with a mass of about 1 kg and a size of approximately 318×157×172 mm3. It allows to detect alpha, beta, and gamma radiation. Particles are detected with a plastic scintillator, meaning that no filling gas is necessary for this type of detector. A protective lattice-shaped entry window covers the scintillator. The detector voltage is 1.2 kV, and the device can be used within a temperature range from −10 °C to 40 °C. The background level is subtracted from the measured data automatically. Such detectors are especially useful for field work or under conditions where laboratory access is not immediately available. Contamination monitors can also be used in nuclear power plants, for decontamination procedures, in radiation laboratories, or in emergency situations (STUK, 2006). 2.2. Sample measurement Surface sources were measured in direct contact with the entry window of the detector. The setup is described in Section 2.4., Replicate devices of the same model were used as detectors in the BfS laboratory producing an averaged result for the efficiency and a random error. Food samples represent volume sources; see Section 2.4 for the setup design. Samples for determining the detector efficiency were prepared in the following way. The aqueous food sample was mixed with an active standard solution and homogenized by stirring or shaking. A certain amount of the mixture (20 mL) with a known activity was then pipetted into a planchet and measured with the detector in a defined geometry. There were various sources of random errors. For example, random errors may result from a varying thickness of the sample material in the planchet, a varying degree of homogeneity of the activity within the sample, or from activity variations in the standard. It was also observed in the BfS laboratory that, in some cases, radionuclides tended to accumulate at the bottom of the planchet.
2.4. Design of the simulated setups The first suite of the PENELOPE Monte Carlo runs to be presented here is for standard surface beta emitters. These runs are not directly linked to food samples as the latter ones are always volume sources with a thickness in the millimeter range. However, if the same radionuclides are used, simulation and comparison with experiments in the case of surface emitters can be helpful to understand the basic behavior of the efficiency as a function of the beta endpoint energy of the respective radionuclides. We expected that, in comparison with such efficiencies, volume (food) sample simulations would reveal a dimin-
2.3. Simulation code and parameters We have used the Monte Carlo computer code PENELOPE-2008 (Salvat et al., 2009) to simulate the beta radiation transport in matter and thereby estimate the beta radiation detection efficiency of a handheld contamination monitor in a geometric setup suited for food contamination measurements. For brevity, the entire code package will be termed PENELOPE in the following discussion, which will include all sub-packages delivered with the PENELOPE-2008 distribution (viewers, for example). PENELOPE is a computer program for simulating the coupled radiation transport of photons, electrons, and positrons. As possible mechanisms of interaction for electrons and positrons, the code includes elastic scattering, inelastic scattering, bremsstrahlung emission, and positron annihilation. Possible interactions of gamma radiation with matter considered in the code are the photoelectric absorption, Rayleigh scattering, Compton scattering, and electron-positron pair production. The Monte Carlo techniques used in PENELOPE are
Table 1 Radionuclides, beta endpoint energies (MeV) and half-lives (years) used in the present simulations (ICRP, 2008). Radionuclide
Beta endpoint energy (MeV)
Half-life (years)
63
0.067
1.00 × 10 2
14
0.156
5.70 × 10 3
99
0.294
2.11 × 10 5
Ni C Tc
90
Sr
131
I
36
Cl
2.88 × 101
2.19 × 10−2
0.709
3.01 × 10 5
204
0.764
3.78 × 10 0
89
1.495
1.38 × 10−1
32
1.711
3.91 × 10−2
Tl
Sr P
88
0.546 0.606
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Fig. 2. Three-dimensional image of the geometry used in the PENELOPE simulation of volume sources, see Section 2.4 for details. The image shows two different views of the configuration. The detailed scintillator geometry is shown in Fig. 1. Opening wedges in the bottom part of the image are for visualization purposes only. Parts of the figure were produced with the PENELOPE geometry viewer (Salvat et al., 2009).
Fig. 1. Sandwich structure of the surface source and scintillator geometry as coded with PENELOPE. The zoom shows the various layers covering the scintillator. The background image shows only the parts of the geometry that are close to the interface between the surface source and scintillator, see Section 2.4 for details. A part of the figure was produced with the PENELOPE geometry viewer (Salvat et al., 2009).
ished efficiency all over the endpoint-energy range covered here. Studying standard surface sources would thus provide an upper estimate in this case. This can be an advantage in practical laboratory work since surface sources are easier to handle. Oftentimes, they are also easier to come by (BMUB, 2014). In both the surface and volume source simulations, the detector geometry was simplified by coding those parts of the geometry that have immediate relevance to calculating the efficiency. We therefore modeled the rectangular plastic scintillator and various layers on top of it, such as ZnS, aluminum and Mylar layers, and foils. We abstained from programming the complex geometry of the protective entry window; rather, the absorbing effect of the entry window was considered as a diminishing factor of 0.82 on the Monte Carlo simulation results, accounting for the total transparency according to the technical documentation of the detector. Since this value is total transparency, it was assumed to be applicable to all radionuclides studied here. The dimensions of the plastic scintillator were 24×13×0.1 cm3, the thicknesses of the layers and foils on top of the scintillator were in the micrometer range. Fig. 1 shows the sandwich structure of the layers and foils considered together with the surface source in contact with the detector. The geometry used for the quadratic standard surface source consisted of a 6-micrometer activated Eloxal (Al2O3) layer with a length of 10 cm embedded in a thin quadratic aluminum frame with a length of 12 cm and a height of 0.3 cm. For efficiency simulations in the case of aqueous food samples (volume sources), we modeled the circular geometry of an aluminum planchet containing the sample. The planchet had a diameter of 12 cm, a height of 0.8 cm, and a thickness of 0.08 cm. The sample itself was modeled as an active water layer with a thickness of 0.18 cm and therefore constituted a cylindrical volume source. We used the same plastic scintillator geometry as described above in the case of surface sources. In the experimental configuration, the contamination monitor was mounted in such a way that the distance between the sample surface and the detector was about 1.52 cm. Fig. 2 presents a threedimensional visualization of the modeled configuration. In this illustration, the details of the scintillator geometry are not visible due to their
Fig. 3. PENELOPE simulation results for the efficiency as a function of the beta endpoint energy for a surface source configuration and corresponding experimental values, see Section 3.1 for details. Also included in the plot is a fit curve to the simulation results.
small sizes. 3. Results and discussion 3.1. Standard surface beta emitters Fig. 3 shows the results of the Monte Carlo simulations for the detector efficiency depicted as a function of the beta endpoint energy of the respective radionuclide. The results are for surface sources. Simulated values for the detector efficiency range from 0.03% to 55%. A qualitatively similar curve for a flow-cell detector is given by Tan and DeVol (2003). Fig. 3 also gives experimental values determined with the contamination monitor. When available, the absolute uncertainty of the result is indicated. Some of the measured data are from the original documentation of the detector. Measured data points with error bars were determined in our own laboratory. The coverage factor for the simulation was assumed to be 3σ as usual for the PENELOPE code package (Salvat et al., 2009). Because there were several contamination monitors of the same type available in the BfS (from different measurement teams), in order to avoid a bias, a source was measured with different devices of the same type. The uncertainty was assumed to be 1σ for each measurement in these series. With exceptions in the middle and at the higher end of the energy interval studied, the values from experiments are consistent with the Monte Carlo simulation results. The values determined in our own laboratory are all consistent with the theoretical results. Unlike the experimental data, the simulated values show a relatively smooth course with energy. The deviation of the simulated values from the experimental data ranges from 7% to more than 100% for some data 89
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2×10−3% to 21%. As expected, they are considerably smaller than the corresponding values for surface sources. The Monte Carlo simulation values can be compared with three experimental results obtained in our laboratory. Two of them (in the first third and at the higher end of the energy interval studied) are displayed in Fig. 4. They correspond to 99Tc and 32P, respectively. The third measurement was for the radionuclide with the lowest beta endpoint energy (63Ni). In this case, the efficiency was so low that we could not determine a laboratory value with the described experimental setup. This agrees with the Monte Carlo simulation result of only 2×10−3%. The other two experimental values are in good agreement with the simulated results.
points (e.g., for 32P). In the latter cases, large deviations occur for radionuclides with half-lives of the order of 10 days. Presumably, such deviations can be attributed to a missing decay correction in the experiment because the experimental values were smaller for these radionuclides than the simulated ones, indicating that the source activities assumed by the detector manufacturer were too high. In addition to simulation results and experimental values, Fig. 3 shows a fit curve to the Monte Carlo simulation results. In a very simple approach to get a relation between the efficiency and the beta endpoint energy E0 for the fit, the efficiency was related linearly to the particle intensity I (E0 ) (number of incident particles at energy E0 per second passing through a thin slice of matter). For the particle intensity as a function of distance x, a well-known exponential absorption law exists, providing a link to the mass attenuation coefficient μ / ρ (ρ and I0 representing material density and original intensity at x=0, respectively),
I (x ) = I0 exp (−μx ).
3.3. Tests to improve the detection efficiency The geometric input used for the simulations reflects the present setup in our laboratory. Measurements of radioactivity from food samples very often proceed under standard geometric conditions for better comparability or because it is demanded by standard operating procedures. Any setup changes may require modifications in the respective laboratory protocols or modifications of mechanical constructions, for example, detector or sample holders. Changing this framework haphazardly in order to improve the detection efficiency is therefore not always advisable. If the geometry is already coded, as is the case with our Monte Carlo simulations, it may be easier to simulate the effects of possible changes to the geometry. Attempts to improve the detector efficiency should consider the fact that the available amount of the food sample material is often limited, for example, due to sophisticated preparation techniques. This holds even if radiochemistry methods are not in use. For example, it may be necessary to make the sample durable for conservation of evidence. However, even if the sample is larger, the performance of the method is not necessarily better because an increase in the sample mass increases the absorption of beta particles in the larger volume of the emitting source. The question is, therefore, how the geometry itself could possibly be improved so to increase the beta detection efficiency. It will be demonstrated that the Monte Carlo method is an ideal way to test such cases without involved laboratory investigations. In our opinion, two possible methods are evident. The first method is to reduce the distance between the sample and the detector. The second one is to reduce the thickness of the sample while keeping the amount of sample material constant. Both cases can be tested by modifying the Monte Carlo input file. As for the first method, an explicit PENELOPE simulation shows no improvement of the efficiency. After bringing the top rim of the planchet in contact with the detector entry window in the model, only a negligible increase in beta efficiency was found in the simulation. It is therefore not advisable to modify the mechanical setup of the measurement device in this case. The second possibility to test is a thinner sample. For acqueous samples, this can be achieved by increasing the radius of the planchet. Increasing the radius by a factor of 21/2 halves the sample thickness (at a constant amount of the sample material). Again, modifying the existing PENELOPE geometry file is easier than changing the experimental setup and repeating all measurements. Fig. 5 shows the simulated efficiencies obtained for the larger planchet in the model geometry. The efficiencies of the original volume sources are also given for comparison. The values are depicted as a function of beta endpoint energy. It can be seen that using the larger planchet in the simulation leads to higher efficiencies over the whole energy range investigated here. The efficiency ratios can be found in Table 2. For some endpoint energies, the new efficiencies are almost twice as high.
(1)
For the mass attenuation coefficient, another well-established, but empirical relation can be stated (Nathuram et al., 1988),
μ = AE0−B , ρ
(2)
where A and B stand for empirical constants. As a first guess for B, a value of B = 1.48 was taken, consistent with the parameter range communicated by Nathuram et al. (1988). The parameters A, ρ, x, and I0 are absorbed by the respective fit parameters due to the overall approach to express the efficiency as a function of the beta endpoint energy. Nevertheless, when typical values for A from Nathuram et al. (1988) and averaged values for ρ are used, the numerically determined fit parameter in the exponent yields values for x that are compatible with the geometric dimensions of the configuration. More sophisticated approaches based, for example, on an integral ansatz, are thinkable. However, as one can see from the plot, the fit curve from the simpler procedure describes the basic course and curvature of a line directly connecting the data points from the Monte Carlo simulation. The goodness of fit is R2 = 0.974 . 3.2. Volume sources Fig. 4 shows the modeled efficiency in the case of volume sources as a function of the beta endpoint energy. The statistical uncertainty of the PENELOPE results is interpreted as 3σ (Salvat et al., 2009). When displayed on the graph, it is covered by the data point symbols for some radionuclides. For efficiency, we chose a logarithmic scale to compare the values with the surface source results, which are depicted on the same plot. In the case of volume sources, the efficiencies range from
4. Conclusion
Fig. 4. PENELOPE simulation results for the efficiency as a function of the beta endpoint energy, see Section 3.2 for details. The plot shows the results for the volume sources modeling and two experimental values for volume sources determined in our laboratory. In addition, the surface sources modeling results are displayed for comparison.
In this article, theoretical and experimental results concerning the determination of the detection efficiency of a hand-held contamination 90
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can be the method of choice. At least, it can serve to validate the experimental results or prepare grounds for laboratory experiments with radionuclides the laboratory personnel is not yet familiar with. Acknowledgment The authors like to thank one anonymous reviewer for a very constructive review report and for providing us with valuable hints. R.M. likes to thank E. Kabai (BfS) for commenting on radiochemistry and laboratory questions. The authors thank M. Ebert and K. Behrend for their assistance in laboratory work. E. Neumann (formerly BfS-IT Neuherberg) and E. Höller (BfS-IT) provided us with Linux-powered computers used for the Monte Carlo simulations presented in this article. Fig. 5. PENELOPE simulation results for the efficiency as a function of the beta endpoint energy for two different planchet configurations, see Section 3.3 for details. The plot shows the results for the volume sources modeling in the case of standard planchets used in our laboratory and for planchets with enlarged radii (factor 21/2 ).
References Baro, J., Sempau, J., Fernandez-Varea, J.M., Salvat, F., 1995. PENELOPE: An algorithm for Monte Carlo simulation of the penetration and energy loss of electrons and positrons in matter. Nucl. Instrum. Methods Phys. Res. Sect. B 100, 31–46. BMUB (Federal Ministry for the Environment, Nature Conservation, Building and Nuclear Safety) 2014. Messanleitungen (Measurement Guide; in German), 〈www.bmub.bund. de/P1517/〉. Haghighat, A., 2015. Monte Carlo Methods for Particle Transport. CRC Press, Taylor and Francis Group, Boca Raton, FL. ICRP 2008. Nuclear decay data for dosimetric calculations. Annals of the ICRP Publication 107. Vol. 38 No. 3. The International Commission on Radiological Protection, Stockholm. James, F., 1980. Monte Carlo theory and practice. Rep. Prog. Phys. 43, 1145–1189. Kabai, E., Savkin, B., Mehlsam, I., Poppitz-Spuhler, A., 2017. Combined method for the fast determination of pure beta emitting radioisotopes in food samples. J. Radioanal. Nucl. Chem. 311, 1401–1408. Kalos, M.H., Whitlock, P.A. 2008. Monte Carlo Methods. Second Ed. Wiley-Blackwell, Weinheim. Lehto, J., Hou, X., 2011. Chemistry and Analysis of Radionuclides, Laboratory Techniques and Methodology. Wiley-VCH, Weinheim. Merk, R., Kröger, H., Edelhäuser-Hornung, L., Hoffmann, B., 2013. PENELOPE-2008 Monte Carlo simulation of gamma exposure induced by 60Co and NORMradionuclides in closed geometries. Appl. Radiat. Isot. 82, 20–27. Nathuram, R., Subrahmanian, G., Thontadarya, S.R., 1988. Mass attenuation coefficients of beta particles in 4π geometry. Phys. C 151, 547–551. Piotrowski, L.W., Casolino, M., Ebisuzaki, T., Higashide, K., 2015. The simulation of the LANFOS-H food radiation contamination detector using Geant4 package. Comput. Phys. Commun. 187, 49–54. Pujol, Ll, Suarez-Navarro, J.A., 2004. Self-absorption correction for beta radioactivity measurements in water samples. Appl. Radiat. Isot. 60, 693–702. Salvat, F., Fernandez-Varea, J.M., Sempau, J., 2009. PENELOPE-2008: A code system for Monte Carlo simulation of electron and photon transport. NEA No. 6416, OECD Nuclear Energy Agency, Issy-les-Moulineaux, France. Sato, Y., Takahashi, H., Yamada, T., Unno, Y., Yunoki, A., 2013. Monte Carlo simulation of a beta particle detector for food samples. Appl. Radiat. Isot. 81, 162–164. Sempau, J., Acosta, E., Baro, J., Fernandez-Varea, J.M., Salvat, F., 1997. An algorithm for Monte Carlo simulation of coupled electron-photon transport. Nucl. Instrum. Methods Phys. Res. Sect. B 132, 377–390. Sempau, J., Fernandez-Varea, J.M., Acosta, E., Salvat, F., 2003. Experimental benchmarks of the Monte Carlo code PENELOPE. Nucl. Instrum. Methods Phys. Res. Sect. B 207, 107–123. STUK (Radiation and Nuclear Safety Authority) 2006. Radiation monitoring systems and equipment of a nuclear power plant. STUK Guide YVL 7.11, 3rd Edition, STUK, Helsinki, Finland. Tan, H., DeVol, T.A., 2003. Monte Carlo modeling of heterogeneous scintillation flow-cell detectors. Nucl. Instrum. Methods Phys. Res. Sect. A 515, 624–633.
Table 2 Radionuclides and efficiency ratios for larger vs. standard planchets, see Section 3.3 for details. Radionuclide
Efficiency ratio (larger vs. standard planchet)
63
1.10 1.62 1.73 1.72 1.74 1.63 1.63 1.27 1.24
Ni C Tc 90 Sr 131 I 36 Cl 204 Tl 89 Sr 32 P 14 99
monitor for measuring radioactively-contaminated food samples were presented. We have studied beta emitting radionuclides with relevance to emergency preparedness and covering a broad range of beta endpoint energies and half-lives. The efficiency of a contamination monitor was calculated by means of PENELOPE Monte Carlo simulations for surface and volume sources. The modeled volume sources were equivalent to aqueous food samples used in our laboratory. Consequently, we could compare the simulation results with experimentally determined efficiency values and have observed a good agreement with the laboratory results so far. We have also presented cases in which the Monte Carlo method could serve as a means to improve the detection efficiency. Theoretical techniques have the potential to supplement classical laboratory procedures and even replace some of them in the long run. In principle, it is almost always better to have efficiencies determined in laboratory experiments. However, for reasons such as time, costs, feasibility, or radiation protection, the theoretical Monte Carlo method
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