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Parameter optimization of a planar BEGe detector using Monte Carlo simulations
Nuclear Instruments and Methods in Physics Research A 623 (2010) 1014–1019
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Parameter optimization of a planar BEGe detector using Monte Carlo simulations R. Luı´s , J. Bento, G. Carvalhal, P. Nogueira, L. Silva, P. Teles, P. Vaz ´gico e Nuclear - Estrada Nacional 10, 2686-953, Sacave´m, Portugal Instituto Tecnolo
a r t i c l e in f o
a b s t r a c t
Article history: Received 25 May 2010 Received in revised form 8 August 2010 Accepted 10 August 2010 Available online 25 August 2010
This work reports on the use of three state-of-the-art Monte Carlo codes (MCNPX, PENELOPE, FLUKA) in the efficiency calibration of a Broad-Energy Germanium (BEGe) detector. Initial discrepancies found between the experimental and computational efficiency values are related to the poor knowledge of some physical parameters of the detector (dead-layers, crystal dimensions, etc.). As a consequence, a sensitivity analysis was carried out. Each parameter was systematically analyzed, and an accurate model of the detector was determined. The obtained results are consistent, allowing this model to be used in computational efficiency calibrations of the equipment at stake. & 2010 Elsevier B.V. All rights reserved.
Keywords: BEGe detector Monte Carlo Efficiency calibration
1. Introduction Broad Energy Germanium (BEGe) detectors are a particular class of HPGe detectors, providing an optimized efficiency range in a broad energy interval, typically from 3 keV to 3 MeV, with a good resolution in both low and high energy regions. BEGe detectors have been used in gamma spectrometry laboratories for ordinary environmental measurements, for actinide measurements, for the detection of nuclear tests [1], in decay data evaluation [2], and in radionuclide metrology. They are also used in the study of the neutrinoless double beta decay, in the Majorana and GERDA experiments [3–6] for internal dosimetry purposes [7–9] and in XRF analyses [10]. In gamma spectrometry, the experimental calibration of BEGe detectors is performed using calibrators with the same physical characteristics of the samples to be measured and spanning the energy range of the radionuclides to be detected. This procedure has some inherent difficulties like, for instance, that certain types of samples cannot be prepared in the standard geometries for which there are calibrators available, and therefore an experimental efficiency calibration may not be performed [11–16]. Also, the radionuclides used in calibrators have decay schemes that lead to coincidence summing effects. This problem is particularly serious for BEGe detectors, since they are very efficient in the X-ray energy range, leading to g- X summing [17–19]. And finally, the preparation of calibrators is time consuming and requires a
Corresponding author.
E-mail address: raulfl[email protected] (R. Luı´s). 0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2010.08.020
high degree of expertise and adequate facilities, which may not be available in the laboratories. Monte Carlo techniques can serve as a practical tool to deal with these problems, and serve as an alternative procedure to traditional calibration. In fact, the development of computational power resulted in widespread use of Monte Carlo techniques to perform efficiency calibrations in HPGe detectors [20–26]. After appropriate validation of the computational procedure, Monte Carlo calibrations provide an easy, fast and efficient way of evaluating the detector efficiency. Overall, Monte Carlo calibration procedures can facilitate the routine measurement of different types of samples of different geometric complexity, provided that the procedure itself is well established and validated [27,28]. The main complication in setting-up a Monte Carlo calibration arises from the need to validate and appropriately define the geometry of the experimental setup [29–38]. After these are properly and clearly defined, the calibration procedure is fairly simple. The task of defining the aforementioned variables involves an accurate knowledge of the physical parameters of the detector such as the dead-layers, the crystal length and radius and the distance of the detector window to the crystal, as they can have a strong influence in the obtained results. These parameters are often poorly known from the data provided by manufacturers. Therefore, Monte Carlo codes generally give computed efficiency values that deviate significantly ð 4 10%Þ from the experimental data [39,40,21]. In this paper we report on the sensitivity analysis of these physical parameters. We have used three different state-of-theart Monte Carlo codes—PENELOPE [41], MCNPX [42] and FLUKA [43,44]. The differences between the packages and their modes of operation may lead to discrepancies between computed efficiencies, reaching 5% in some cases [45].
R. Luı´s et al. / Nuclear Instruments and Methods in Physics Research A 623 (2010) 1014–1019
Initial results demonstrate the need to fine-tune the physical parameters of the detector. This was done for each of the following parameters: dead-layers, crystal length, crystal radius and window-crystal distance. The influence of these parameters in the results was established and an appropriate set of values that better matches the experimental results was obtained.
2. Experimental setup The detection system used comprises a planar BEGe detector (Canberra, BE5030), with nominal diameter of 81 mm and nominal length of 30 mm, relative efficiency of 50%, enclosed by an aluminum endcap with a carbon epoxy window. It also includes standard analog signal processing modules (Canberra) and a 10 cm thick lead shield with 2 mm copper and 1 mm tin linings. The software Genie 2000 (Canberra, v. 3.0) was used for acquisition and analysis of spectral data and the software GESPECOR (v. 4.2) [46] was used for computing coincidence summing correction factors. A certified Eu-152 point-like source (PTB), with (30.5 7 1.5) kBq at the reference date of 2006-January-1, was used for full energy peak efficiency determination. Although Eu-152 has the advantage of having several gamma emissions, ranging from 40 to 1408 keV, it is a well known fact that this kind of measurements in large BEGe detectors may suffer, depending on the distance of the source to the detector, from coincidence summing effect. For this reason, coincidence summing correction factors were also computed for each of its gamma emissions. A source holder made of perspex with several available positions was used for measuring the sources at two distances from the detector endcap: 11.31 and 18.38 cm. The acquisition time was set so that the net peak area uncertainty was below 1%, for all peaks considered. The dead time of the detection system was less than 2.2%. Table 1 shows full energy peak efficiencies and coincidence summing correction factors for measurements at 18.38 cm.
1015
back dead layer and a 0.5 mm lateral dead layer. It has been assumed that the back dead layer extends over the diameter of the detector and that it includes the region where the rear contact is placed. The certified Eu-152 point-like source used in the experimental measurements was implemented in detail in the Monte Carlo codes and used to calculate the full energy peak efficiencies for several energies in the 40–1408 keV range. It was specified as a small volume cylindrical source (2.5 mm radius, 0.022 mm length) with uniform distribution and isotropic emission, enclosed in two mylar foils surrounded by an aluminum ring. The shielding of the experimental apparatus was also implemented in detail. No variation reduction techniques were allowed, a restriction imposed by the Monte Carlo codes for the type of tallies used in this computational problem.
4. Results and discussion In what follows, unless otherwise specified, the results will be given for the case in which the source is placed at 18.38 cm from the detector.
3. Monte Carlo modeling Three Monte Carlo codes were used to perform the simulations: MCNPX (v. 2.6.0), FLUKA (v. 2008.3c.0) and PENELOPE (v. 2008). The geometry implementation, represented in Fig. 1, was initially carried out using the nominal values provided by the manufacturer for all the detector parameters. It consisted of a cylindrical germanium crystal with 40.5 mm radius and 30 mm length supported by a copper stand and enclosed in a 1.5 mm thick aluminum casing with a 0.5 mm thick carbon epoxy window. The window is located 5 mm away from the germanium crystal. The crystal has a 0:3 mm front dead layer, a 0.7 mm
Fig. 1. Computational implementation of the BEGe detector (dimensions not to scale).
Table 1 Measured efficiencies and correction factors for coincidence summing effect for source to detector distance of 18.38 cm. Energy (keV)
Yield (%)
Efficiency
Unc. ð1sÞ
Unc. (%)
Coincidence summing correction factor
Efficiency corrected
39.82 121.78 244.70 344.28 778.91 867.38 964.08 1085.84 1112.08 1408.01
58.5 28.41 7.55 26.59 12.97 4.24 14.5 10.13 13.44 20.86
9.46E 03 9.08E 03 5.26E 03 3.65E 03 1.57E 03 1.39E 03 1.28E 03 1.15E 03 1.13E 03 8.93E 04
1.20E 04 8.35E 05 5.09E 05 3.37E 05 1.50E 05 1.63E 05 1.19E 05 1.19E 05 1.09E 05 8.15E 06
1.27 0.92 0.97 0.92 0.96 1.17 0.93 1.03 0.96 0.91
1.012 1.015 1.022 1.005 1.007 1.025 1.017 1.002 1.015 1.015
9.57E 03 9.22E 03 5.38E 03 3.67E 03 1.58E 03 1.42E 03 1.30E 03 1.15E 03 1.15E 03 9.07E 04
R. Luı´s et al. / Nuclear Instruments and Methods in Physics Research A 623 (2010) 1014–1019
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Table 2 Relative deviation between simulated and measured efficiencies—nominal parameters (18.38 cm). Energy (keV)
39.82 121.78 244.70 344.28 778.91 867.38 964.08 1085.84 1112.08 1408.01
Deviation (%) FLUKA Exp
PENELOPE Exp
MCNPX Exp
FLUKA PENELOPE
FLUKA MCNPX
PENELOPE MCNPX
5.50 2.02 5.30 6.70 9.02 8.70 9.36 10.22 9.30 10.92
6.25 2.04 5.35 6.73 8.92 10.85 8.95 10.02 8.09 10.05
8.03 2.18 6.03 7.93 10.00 9.86 10.24 10.60 8.93 11.51
0.71 0.01 0.05 0.03 0.08 1.94 0.38 0.19 1.12 0.80
2.35 0.15 0.69 1.14 0.89 1.06 0.80 0.34 0.35 0.52
1.65 0.14 0.64 1.11 0.98 0.90 1.17 0.53 0.77 1.31
4.1. Nominal parameters
8 4 FLUKA
0 (Sim - Exp) / Exp (%)
Table 2 shows the relative deviations between measured and simulated efficiencies for the configuration with the nominal parameters provided by the detector manufacturer. The efficiencies obtained with FLUKA, MCNPX and PENELOPE differ from the measured efficiencies by more than 10% for some energies, with the biggest differences in the high energy part of the efficiency spectrum. The Monte Carlo codes show good agreement with each other, with relative deviations always below 2%, except in the 39.82 keV peak, for which the relative deviation between FLUKA and MCNPX is 2.35%. The relative deviations between the computed results and the measurements are shown in Fig. 2, for the three Monte Carlo codes.
12
12 8 4 MCNPX
0
4.2. Model optimization 12
The discrepancies obtained between the computed and measured efficiencies are usual when this kind of detector is simulated, and arise mainly due to the lack of accurate knowledge of the real detector dimensions. The parameters normally chosen for optimization are
the crystal-to-window distance, the dead layer thickness and the crystal length and radius [39,40,21]. A sensitivity analysis was carried out in order to study the effects of the variation of each of the detector parameters on the full energy peak efficiency curve. In the sequence, we describe how variations from the nominal values for each of the aforementioned parameters impact on the detector efficiencies. MCNPX was the code used to perform the simulations. 4.2.1. Variation of the dead layer thickness The increase with time of the thickness of the crystal front dead layer will have an impact in the low-energy efficiency of the detector. Besides the nominal dead layer thickness value of 0:3 mm provided by the manufacturer, six different thicknesses were tested to quantify the effect of the frontal dead layer thickness in the efficiency curve: 3, 10, 15, 20, 30 and 300 mm. Fig. 3 shows the relative deviations between the computed efficiencies obtained with each of the tested dead layer thicknesses and the measured values. For the dead layer thickness to have an influence in the whole energy spectrum it needs to be increased to 0.3 mm, 1000 times its nominal value, in which case it would reduce the sensitive volume of the detector, affecting all energies. A dead layer that thick would affect too much the 39.82 keV peak efficiency, reducing it below the measured value. A thickness of
8 4 PENELOPE
0 0
200
400
600 800 1000 1200 1400 1600 Energy (keV)
Fig. 2. Relative deviations between computed and measured efficiencies.
30 mm (100 times increase) will lower the efficiency for the lowest energy, levelling it with the measured value. Increasing the nominal value by 10 times (3 mm thick dead layer) has little effect on the efficiency spectrum. The departure of the dead layer thickness from the nominal value provided by the manufacturer is expected to occur, resulting from the operation of the detector, and is well documented in the literature. A variation of the dead layer between 10 and 30 mm is likely to be needed in the final optimization.
4.2.2. Variation of the crystal-to-window distance The effect of the distance from the crystal to the detector window was also studied, since this is also one of the parameters often studied when optimizing Monte Carlo detector models. Fig. 4 shows the relative deviations between the computed efficiencies for several tested distances and the measured efficiency values. The variation of this parameter does not have a big influence in the efficiency curve, when the source is placed 18.58 cm away from the detector. Its effect is to change the solid angle between the source and the crystal, but the relative change
R. Luı´s et al. / Nuclear Instruments and Methods in Physics Research A 623 (2010) 1014–1019
12 8 4 0 -4
12 8 4 0
dead layer = 0.3 µm
-4
8
dead layer = 3 µm
-4 12 8 4 0
dead layer = 10 µm
(Sim - Exp) / Exp (%)
-4 12 8 4 0
dead layer = 15 µm
-4 12 8 4
(Sim - Exp) / Exp (%)
4 0
crystal-to-window distance = 5.0 mm
12 8 4 0 -4
12
crystal-to-window distance = 5.5 mm
12 8 4 0 -4
crystal-to-window distance = 6.0 mm
12 8 4 0 -4
crystal-to-window distance = 6.5 mm
12 8 4 0 -4
crystal-to-window distance = 7.0 mm
0
0
dead layer = 20 µm
-4
1017
200
400
600
800
1000
1200
1400
1600
Energy (keV) Fig. 4. Effect of the crystal-to-window distance on the detector efficiency.
12 8 4 0
dead layer = 30 µm
-4
12 8 4 0
dead layer = 300 µm
-4 -60 0
200
400
600 800 1000 1200 1400 1600 Energy (keV)
path in germanium for the lower energy photons is shorter than the crystal length. An increase in the back dead layer was also tested, and its effect in the full energy peak efficiencies is exactly the same as when the crystal length is reduced. Varying the crystal radius affects all energies in a more similar manner, when compared with the crystal length variation. The results show that the crystal radius has a great effect on the efficiency curve. Once again, increasing the lateral dead layer of the crystal has exactly the same effect as reducing its radius in the same measure. The results for the various parameter variations show clearly that the parameters that must be optimized are, in a first stage, the crystal radius and length (or, alternatively, the lateral and back dead layers). After the optimization of these parameters, a front dead layer variation must also be considered (if needed), in order to obtain a better agreement in the low-energy part of the efficiency spectrum.
Fig. 3. Effect of the thickness of the dead layer on the detector efficiency.
of the solid angle with the crystal-to-window distance decreases with the source-to-crystal distance ðp1=d2 Þ, and hence this parameter would have a bigger impact if the source were located closer to the detector. 4.2.3. Variations of the crystal length and radius The influence of the crystal dimensions in the efficiency curve is shown in Fig. 5 (length) and Fig. 6 (radius). The length was varied from its nominal value, 30 mm to 28 mm, in 0.5 mm steps. As expected, decreasing the crystal length has a greater effect on the higher energies than on the lower ones, since the mean free
4.2.4. Global and overall optimization Several combinations of the parameters described above were tested. The combination of these parameters that yielded the best results is represented in Table 3. In order to bring the simulated efficiencies to as close to the measured efficiencies as possible for all the energies, the lateral dead layer was increased by 0.25 mm and the back dead layer was increased by 1.5 mm. The front dead layer was increased to 10 mm, to allow a better agreement in the low-energy part of the efficiency spectrum, and the crystal-towindow distance was increased by 2 mm. It is important to underline that increasing the lateral and back dead layers is equivalent, for full energy peak efficiency calculation purposes, to
R. Luı´s et al. / Nuclear Instruments and Methods in Physics Research A 623 (2010) 1014–1019
1018
12
12
8
8
4
4 0
0 crystal length = 30.0 mm
-4
crystal radius = 40.5 mm
-4
12
12
8
8
4 crystal length = 29.5 mm
(Sim - Exp) / Exp (%)
-4 12 8 4 0
crystal length = 29.0 mm
-4
(Sim - Exp) / Exp (%)
4
0
0 crystal radius = 40.0 mm
-4 12
crystal radius = 39.5 mm
8 4 0 -4
12 crystal length = 28.5 mm
8
12
4
crystal radius = 39.0 mm
8
0
4
-4
0 12 crystal length = 28.0 mm
8
-4 0
4
200
400
600
800
1000 1200 1400 1600
Energy (keV)
0
Fig. 6. Effect of the crystal radius on the detector efficiency.
-4 0
200
400
600
800
1000 1200 1400 1600
Energy (keV) Fig. 5. Effect of the crystal length on the detector efficiency.
decreasing the crystal dimensions, radius and length. We could have opted, for example, to assume that the crystal length is smaller than the value reported by the manufacturer, and assume a smaller or no increase in the back dead layer. For the detector model, we opted to change the dead layers instead of the crystal dimensions because it is generally accepted that the uncertainties in the dead layer dimensions are bigger than the uncertainties in the crystal dimensions. The simulation/measurement relative deviation after optimization is represented in Fig. 7. A good agreement between the simulated and measured efficiencies was reached. The deviations are in all cases inferior to 2.5%. The optimized model was also tested with the source placed closer to the detector, 11.31 cm instead of the previous 18.38 cm, in order to validate the model. The results are represented in Fig. 8, and clearly show that the model is also valid for this position. It is therefore possible to conclude that the optimized model can be used for calibration purposes, for point-like sources located at distances from the detector window that match those considered in the experimental setup.
5. Conclusion Broad Energy Germanium (BEGe) detectors are of paramount importance for gamma ray spectrometry in a wide range of
Table 3 Detector model optimization. Parameter
Nominal value
Optimized value
Crystal-to-window distance (mm) Crystal radius (mm) Crystal length (mm) Front dead layer thickness ðmmÞ Lateral dead layer thickness (mm) Back dead layer thickness (mm)
5 40.5 30 0.3 0.5 0.7
7 40.5 30 10 0.75 2.2
applications. An as detailed and accurate as possible description of their behavior is therefore mandatory in order to gain insight into the basic parameters characterizing the corresponding detection systems, namely the efficiencies, the correction factors and the backgrounds. Uncertainties in these parameters can be assessed using state-of-the-art Monte Carlo simulation programs, implementing the actual geometry and accurately modeling the physics of the detection processes. Deviations from the nominal parameters provided by the manufacturers can be expected, resulting from the detectors operating conditions as well as from uncertainties in the nominal parameters provided by the manufacturers, namely in the dead layer thickness, the distance from the crystal to the window and the radial and longitudinal dimensions of the crystal. In this study, three general-purpose Monte Carlo simulation programs were used, namely MCNPX, FLUKA and PENELOPE, in order to model the behavior of a BEGe detector. Using the nominal
R. Luı´s et al. / Nuclear Instruments and Methods in Physics Research A 623 (2010) 1014–1019
4 FLUKA
2 0
(Sim - Exp) / Exp (%)
-2 -4 4
Carlo codes, with relative differences between them always below 2.5%, for all energies. It was shown that relative deviations between the measured efficiencies and the efficiencies computed with the Monte Carlo codes can be brought into the 2–3% band throughout the whole energy range introducing plausible variations, documented in the literature, in the front dead layer thickness (for the low energy range), in the distance from the crystal to the detector window and in the lateral and back dead layers of the crystal.
MCNPX
2
References
0 -2 -4 4 PENELOPE
2 0 -2 -4
0
200
400
600 800 1000 1200 1400 1600 Energy (keV)
Fig. 7. Relative deviation between computed and measured efficiencies after optimization, with the source placed at 18.38 cm from the detector.
4 FLUKA
2 0 -2
(Sim - Exp) / Exp (%)
1019
-4 4 MCNPX
2 0 -2 -4 4 PENELOPE
2 0 -2 -4 0
200
400
600 800 1000 1200 1400 1600 Energy (keV)
Fig. 8. Relative deviation between computed and measured efficiencies after optimization, with the source placed at 11.31 cm from the detector.
parameters for the detector dimensions the simulated efficiencies deviate from the measured values from 2% to 12%, with the biggest discrepancies in the high energy part of the efficiency spectrum. A good agreement was achieved for the three Monte
[1] G. Le Petit, et al., Appl. Radiat. Isot. 64 (2006) 1307. [2] J. Gasparro, et al., Czech. J. Phys. 56 (2006) D203. ¨ [3] D. Budja´s, O. Chkvorets, S. Schonert, Background suppression using pulse shape analysis with a BEGe detector for neutrinoless double beta decay search with GERDA, in: Proceedings of the 10th Conference on the Intersections of Particle and Nuclear Physics, AIP Conference Proceedings, vol. 1182, pp. 96–99. [4] G. Giovanetti, Development of a data-acquisition system for a low-background BEGe detector, in: American Physical Society, APS April Meeting, 2010. [5] F. Avignone III, Prog. Part. Nucl. Phys. 64 (2010) 258. [6] A. Smolnikov for the GERDA collaboration, Development and installation of the GERDA experiment, Topics in astroparticle and underground physics, J. Phys. Conf. Ser. [7] J.L. Webb, et al., Radiat. Prot. Dosim. 89 (2000) 325. [8] G.H. Kramer, S.A. Allen, D. Groff, Health Phys. 85 (2003) 751. [9] L. Liye, et al., Radiat. Prot. Dosim. 127 (2007) 282. [10] F.A. Selim, et al., Nucl. Instr. and Meth. A 495 (2002) 154. [11] M. Canet, et al., Appl. Radiat. Isot. 52 (2000) 711. [12] H. Neder, G. Heusser, M. Laubenstein, Appl. Radiat. Isot. 53 (2000) 191. [13] M. Hult, et al., J. Environ. Radioact. 60 (2002) 307. [14] M. Hult, et al., Appl. Radiat. Isot. 61 (2004) 173. ¨ [15] M. Kohler, et al., Appl. Radiat. Isot. 61 (2004) 207. ˜ a, et al., Appl. Radiat. Isot. 68 (2010) 1226. [16] R.G. de Ordun [17] D. Arnold, O. Sima, Appl. Radiat. Isot. 64 (2006) 1297. [18] D. Novkovic´, et al., Nucl. Instr. and Meth. A 578 (2007) 207. [19] D. Novkovic´, et al., Nucl. Instr. and Meth. A 582 (2007) 592. [20] I.O. Ewa, et al., Appl. Radiat. Isot. 55 (2001) 103. [21] S. Hurtado, M. Garcı´a-Leo´n, R. Garcı´a-Tenorio, Nucl. Instr. and Meth. A 518 (2004) 764. [22] L. Liye, et al., Nucl. Instr. and Meth. A 564 (2006) 608. [23] C.M. Salgado, C.C. Conti, P.H. Becker, Appl. Radiat. Isot. 64 (2006) 700. [24] V. Peyres, E. Garcı´a-Torano, Nucl. Instr. and Meth. A 580 (2007) 296. [25] N.C. Dı´az, M.J. Vargas, Nucl. Instr. and Meth. A 586 (2008) 204. [26] O. Sima, D. Arnold, Appl. Radiat. Isot. 67 (2009) 701. [27] M. Garcı´a-Talavera, et al., Appl. Radiat. Isot. 52 (2000) 777. [28] J. Ro´denas, et al., Nucl. Instr. and Meth. B 263 (2007) 144. [29] S. Ashrafi, A. Likar, T. Vidmar, Nucl. Instr. and Meth. A 438 (1999) 421. [30] T. Vidmar, A. Likar, Appl. Radiat. Isot. 56 (2002) 99. [31] O. Sima, et al., Appl. Radiat. Isot. 61 (2004) 123. [32] P.N. Johnston, M. Hult, J. Gasparro, Appl. Radiat. Isot. 64 (2006) 1323. ˚ [33] J. Boson, G. Agren, L. Johansson, Nucl. Instr. and Meth. A 587 (2008) 304. [34] J. Gasparro, et al., Nucl. Instr. and Meth. A 594 (2008) 196. [35] F. Courtine, et al., Nucl. Instr. and Meth. A 596 (2008) 229. [36] D. Budja´s, et al., Appl. Radiat. Isot. 67 (2009) 706. [37] K. Karfopoulos, M. Anagnostakis, Appl. Radiat. Isot. 68 (2010) 1435. [38] O. Marzocchi, B. Breustedt, M. Urban, Appl. Radiat. Isot. 68 (2009) 1438. [39] R. Helmer, et al., Nucl. Instr. and Meth. A 511 (2003) 360. [40] M. Jurado Vargas, A.L. Guerra, Appl. Radiat. Isot. 64 (2006) 1319. [41] F. Salvat, J.M. Fernandez-Varea, J. Sempau, PENELOPE 2008: a code system for Monte Carlo simulation of electron and photon transport, OECD, 2008. [42] G.W. McKinney, et al., MCNPX overview, in: Proceedings of the 2006 HSSW, FNAL, IL, LA-UR-06-6206. [43] A. Ferrari, et al., FLUKA: A Multi-Particle Transport Code, CERN, 2008. [44] V. Vlachoudis, FLAIR: a powerful but user friendly graphical interface for FLUKA, in: Proceedings of the International Conference on Mathematics, Computational Methods & Reactor Physics (M&C 2009), Saratoga Springs, 2009. [45] T. Vidmar, et al., Appl. Radiat. Isot. 66 (2008) 764. [46] O. Sima, D. Arnold, Appl. Radiat. Isot. 53 (2000) 51.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Parameter optimization of a planar BEGe detector using Monte Carlo simulations R. Luı´s , J. Bento, G. Carvalhal, P. Nogueira, L. Silva, P. Teles, P. Vaz ´gico e Nuclear - Estrada Nacional 10, 2686-953, Sacave´m, Portugal Instituto Tecnolo
a r t i c l e in f o
a b s t r a c t
Article history: Received 25 May 2010 Received in revised form 8 August 2010 Accepted 10 August 2010 Available online 25 August 2010
This work reports on the use of three state-of-the-art Monte Carlo codes (MCNPX, PENELOPE, FLUKA) in the efficiency calibration of a Broad-Energy Germanium (BEGe) detector. Initial discrepancies found between the experimental and computational efficiency values are related to the poor knowledge of some physical parameters of the detector (dead-layers, crystal dimensions, etc.). As a consequence, a sensitivity analysis was carried out. Each parameter was systematically analyzed, and an accurate model of the detector was determined. The obtained results are consistent, allowing this model to be used in computational efficiency calibrations of the equipment at stake. & 2010 Elsevier B.V. All rights reserved.
Keywords: BEGe detector Monte Carlo Efficiency calibration
1. Introduction Broad Energy Germanium (BEGe) detectors are a particular class of HPGe detectors, providing an optimized efficiency range in a broad energy interval, typically from 3 keV to 3 MeV, with a good resolution in both low and high energy regions. BEGe detectors have been used in gamma spectrometry laboratories for ordinary environmental measurements, for actinide measurements, for the detection of nuclear tests [1], in decay data evaluation [2], and in radionuclide metrology. They are also used in the study of the neutrinoless double beta decay, in the Majorana and GERDA experiments [3–6] for internal dosimetry purposes [7–9] and in XRF analyses [10]. In gamma spectrometry, the experimental calibration of BEGe detectors is performed using calibrators with the same physical characteristics of the samples to be measured and spanning the energy range of the radionuclides to be detected. This procedure has some inherent difficulties like, for instance, that certain types of samples cannot be prepared in the standard geometries for which there are calibrators available, and therefore an experimental efficiency calibration may not be performed [11–16]. Also, the radionuclides used in calibrators have decay schemes that lead to coincidence summing effects. This problem is particularly serious for BEGe detectors, since they are very efficient in the X-ray energy range, leading to g- X summing [17–19]. And finally, the preparation of calibrators is time consuming and requires a
Corresponding author.
E-mail address: raulfl[email protected] (R. Luı´s). 0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2010.08.020
high degree of expertise and adequate facilities, which may not be available in the laboratories. Monte Carlo techniques can serve as a practical tool to deal with these problems, and serve as an alternative procedure to traditional calibration. In fact, the development of computational power resulted in widespread use of Monte Carlo techniques to perform efficiency calibrations in HPGe detectors [20–26]. After appropriate validation of the computational procedure, Monte Carlo calibrations provide an easy, fast and efficient way of evaluating the detector efficiency. Overall, Monte Carlo calibration procedures can facilitate the routine measurement of different types of samples of different geometric complexity, provided that the procedure itself is well established and validated [27,28]. The main complication in setting-up a Monte Carlo calibration arises from the need to validate and appropriately define the geometry of the experimental setup [29–38]. After these are properly and clearly defined, the calibration procedure is fairly simple. The task of defining the aforementioned variables involves an accurate knowledge of the physical parameters of the detector such as the dead-layers, the crystal length and radius and the distance of the detector window to the crystal, as they can have a strong influence in the obtained results. These parameters are often poorly known from the data provided by manufacturers. Therefore, Monte Carlo codes generally give computed efficiency values that deviate significantly ð 4 10%Þ from the experimental data [39,40,21]. In this paper we report on the sensitivity analysis of these physical parameters. We have used three different state-of-theart Monte Carlo codes—PENELOPE [41], MCNPX [42] and FLUKA [43,44]. The differences between the packages and their modes of operation may lead to discrepancies between computed efficiencies, reaching 5% in some cases [45].
R. Luı´s et al. / Nuclear Instruments and Methods in Physics Research A 623 (2010) 1014–1019
Initial results demonstrate the need to fine-tune the physical parameters of the detector. This was done for each of the following parameters: dead-layers, crystal length, crystal radius and window-crystal distance. The influence of these parameters in the results was established and an appropriate set of values that better matches the experimental results was obtained.
2. Experimental setup The detection system used comprises a planar BEGe detector (Canberra, BE5030), with nominal diameter of 81 mm and nominal length of 30 mm, relative efficiency of 50%, enclosed by an aluminum endcap with a carbon epoxy window. It also includes standard analog signal processing modules (Canberra) and a 10 cm thick lead shield with 2 mm copper and 1 mm tin linings. The software Genie 2000 (Canberra, v. 3.0) was used for acquisition and analysis of spectral data and the software GESPECOR (v. 4.2) [46] was used for computing coincidence summing correction factors. A certified Eu-152 point-like source (PTB), with (30.5 7 1.5) kBq at the reference date of 2006-January-1, was used for full energy peak efficiency determination. Although Eu-152 has the advantage of having several gamma emissions, ranging from 40 to 1408 keV, it is a well known fact that this kind of measurements in large BEGe detectors may suffer, depending on the distance of the source to the detector, from coincidence summing effect. For this reason, coincidence summing correction factors were also computed for each of its gamma emissions. A source holder made of perspex with several available positions was used for measuring the sources at two distances from the detector endcap: 11.31 and 18.38 cm. The acquisition time was set so that the net peak area uncertainty was below 1%, for all peaks considered. The dead time of the detection system was less than 2.2%. Table 1 shows full energy peak efficiencies and coincidence summing correction factors for measurements at 18.38 cm.
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back dead layer and a 0.5 mm lateral dead layer. It has been assumed that the back dead layer extends over the diameter of the detector and that it includes the region where the rear contact is placed. The certified Eu-152 point-like source used in the experimental measurements was implemented in detail in the Monte Carlo codes and used to calculate the full energy peak efficiencies for several energies in the 40–1408 keV range. It was specified as a small volume cylindrical source (2.5 mm radius, 0.022 mm length) with uniform distribution and isotropic emission, enclosed in two mylar foils surrounded by an aluminum ring. The shielding of the experimental apparatus was also implemented in detail. No variation reduction techniques were allowed, a restriction imposed by the Monte Carlo codes for the type of tallies used in this computational problem.
4. Results and discussion In what follows, unless otherwise specified, the results will be given for the case in which the source is placed at 18.38 cm from the detector.
3. Monte Carlo modeling Three Monte Carlo codes were used to perform the simulations: MCNPX (v. 2.6.0), FLUKA (v. 2008.3c.0) and PENELOPE (v. 2008). The geometry implementation, represented in Fig. 1, was initially carried out using the nominal values provided by the manufacturer for all the detector parameters. It consisted of a cylindrical germanium crystal with 40.5 mm radius and 30 mm length supported by a copper stand and enclosed in a 1.5 mm thick aluminum casing with a 0.5 mm thick carbon epoxy window. The window is located 5 mm away from the germanium crystal. The crystal has a 0:3 mm front dead layer, a 0.7 mm
Fig. 1. Computational implementation of the BEGe detector (dimensions not to scale).
Table 1 Measured efficiencies and correction factors for coincidence summing effect for source to detector distance of 18.38 cm. Energy (keV)
Yield (%)
Efficiency
Unc. ð1sÞ
Unc. (%)
Coincidence summing correction factor
Efficiency corrected
39.82 121.78 244.70 344.28 778.91 867.38 964.08 1085.84 1112.08 1408.01
58.5 28.41 7.55 26.59 12.97 4.24 14.5 10.13 13.44 20.86
9.46E 03 9.08E 03 5.26E 03 3.65E 03 1.57E 03 1.39E 03 1.28E 03 1.15E 03 1.13E 03 8.93E 04
1.20E 04 8.35E 05 5.09E 05 3.37E 05 1.50E 05 1.63E 05 1.19E 05 1.19E 05 1.09E 05 8.15E 06
1.27 0.92 0.97 0.92 0.96 1.17 0.93 1.03 0.96 0.91
1.012 1.015 1.022 1.005 1.007 1.025 1.017 1.002 1.015 1.015
9.57E 03 9.22E 03 5.38E 03 3.67E 03 1.58E 03 1.42E 03 1.30E 03 1.15E 03 1.15E 03 9.07E 04
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Table 2 Relative deviation between simulated and measured efficiencies—nominal parameters (18.38 cm). Energy (keV)
39.82 121.78 244.70 344.28 778.91 867.38 964.08 1085.84 1112.08 1408.01
Deviation (%) FLUKA Exp
PENELOPE Exp
MCNPX Exp
FLUKA PENELOPE
FLUKA MCNPX
PENELOPE MCNPX
5.50 2.02 5.30 6.70 9.02 8.70 9.36 10.22 9.30 10.92
6.25 2.04 5.35 6.73 8.92 10.85 8.95 10.02 8.09 10.05
8.03 2.18 6.03 7.93 10.00 9.86 10.24 10.60 8.93 11.51
0.71 0.01 0.05 0.03 0.08 1.94 0.38 0.19 1.12 0.80
2.35 0.15 0.69 1.14 0.89 1.06 0.80 0.34 0.35 0.52
1.65 0.14 0.64 1.11 0.98 0.90 1.17 0.53 0.77 1.31
4.1. Nominal parameters
8 4 FLUKA
0 (Sim - Exp) / Exp (%)
Table 2 shows the relative deviations between measured and simulated efficiencies for the configuration with the nominal parameters provided by the detector manufacturer. The efficiencies obtained with FLUKA, MCNPX and PENELOPE differ from the measured efficiencies by more than 10% for some energies, with the biggest differences in the high energy part of the efficiency spectrum. The Monte Carlo codes show good agreement with each other, with relative deviations always below 2%, except in the 39.82 keV peak, for which the relative deviation between FLUKA and MCNPX is 2.35%. The relative deviations between the computed results and the measurements are shown in Fig. 2, for the three Monte Carlo codes.
12
12 8 4 MCNPX
0
4.2. Model optimization 12
The discrepancies obtained between the computed and measured efficiencies are usual when this kind of detector is simulated, and arise mainly due to the lack of accurate knowledge of the real detector dimensions. The parameters normally chosen for optimization are
the crystal-to-window distance, the dead layer thickness and the crystal length and radius [39,40,21]. A sensitivity analysis was carried out in order to study the effects of the variation of each of the detector parameters on the full energy peak efficiency curve. In the sequence, we describe how variations from the nominal values for each of the aforementioned parameters impact on the detector efficiencies. MCNPX was the code used to perform the simulations. 4.2.1. Variation of the dead layer thickness The increase with time of the thickness of the crystal front dead layer will have an impact in the low-energy efficiency of the detector. Besides the nominal dead layer thickness value of 0:3 mm provided by the manufacturer, six different thicknesses were tested to quantify the effect of the frontal dead layer thickness in the efficiency curve: 3, 10, 15, 20, 30 and 300 mm. Fig. 3 shows the relative deviations between the computed efficiencies obtained with each of the tested dead layer thicknesses and the measured values. For the dead layer thickness to have an influence in the whole energy spectrum it needs to be increased to 0.3 mm, 1000 times its nominal value, in which case it would reduce the sensitive volume of the detector, affecting all energies. A dead layer that thick would affect too much the 39.82 keV peak efficiency, reducing it below the measured value. A thickness of
8 4 PENELOPE
0 0
200
400
600 800 1000 1200 1400 1600 Energy (keV)
Fig. 2. Relative deviations between computed and measured efficiencies.
30 mm (100 times increase) will lower the efficiency for the lowest energy, levelling it with the measured value. Increasing the nominal value by 10 times (3 mm thick dead layer) has little effect on the efficiency spectrum. The departure of the dead layer thickness from the nominal value provided by the manufacturer is expected to occur, resulting from the operation of the detector, and is well documented in the literature. A variation of the dead layer between 10 and 30 mm is likely to be needed in the final optimization.
4.2.2. Variation of the crystal-to-window distance The effect of the distance from the crystal to the detector window was also studied, since this is also one of the parameters often studied when optimizing Monte Carlo detector models. Fig. 4 shows the relative deviations between the computed efficiencies for several tested distances and the measured efficiency values. The variation of this parameter does not have a big influence in the efficiency curve, when the source is placed 18.58 cm away from the detector. Its effect is to change the solid angle between the source and the crystal, but the relative change
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12 8 4 0 -4
12 8 4 0
dead layer = 0.3 µm
-4
8
dead layer = 3 µm
-4 12 8 4 0
dead layer = 10 µm
(Sim - Exp) / Exp (%)
-4 12 8 4 0
dead layer = 15 µm
-4 12 8 4
(Sim - Exp) / Exp (%)
4 0
crystal-to-window distance = 5.0 mm
12 8 4 0 -4
12
crystal-to-window distance = 5.5 mm
12 8 4 0 -4
crystal-to-window distance = 6.0 mm
12 8 4 0 -4
crystal-to-window distance = 6.5 mm
12 8 4 0 -4
crystal-to-window distance = 7.0 mm
0
0
dead layer = 20 µm
-4
1017
200
400
600
800
1000
1200
1400
1600
Energy (keV) Fig. 4. Effect of the crystal-to-window distance on the detector efficiency.
12 8 4 0
dead layer = 30 µm
-4
12 8 4 0
dead layer = 300 µm
-4 -60 0
200
400
600 800 1000 1200 1400 1600 Energy (keV)
path in germanium for the lower energy photons is shorter than the crystal length. An increase in the back dead layer was also tested, and its effect in the full energy peak efficiencies is exactly the same as when the crystal length is reduced. Varying the crystal radius affects all energies in a more similar manner, when compared with the crystal length variation. The results show that the crystal radius has a great effect on the efficiency curve. Once again, increasing the lateral dead layer of the crystal has exactly the same effect as reducing its radius in the same measure. The results for the various parameter variations show clearly that the parameters that must be optimized are, in a first stage, the crystal radius and length (or, alternatively, the lateral and back dead layers). After the optimization of these parameters, a front dead layer variation must also be considered (if needed), in order to obtain a better agreement in the low-energy part of the efficiency spectrum.
Fig. 3. Effect of the thickness of the dead layer on the detector efficiency.
of the solid angle with the crystal-to-window distance decreases with the source-to-crystal distance ðp1=d2 Þ, and hence this parameter would have a bigger impact if the source were located closer to the detector. 4.2.3. Variations of the crystal length and radius The influence of the crystal dimensions in the efficiency curve is shown in Fig. 5 (length) and Fig. 6 (radius). The length was varied from its nominal value, 30 mm to 28 mm, in 0.5 mm steps. As expected, decreasing the crystal length has a greater effect on the higher energies than on the lower ones, since the mean free
4.2.4. Global and overall optimization Several combinations of the parameters described above were tested. The combination of these parameters that yielded the best results is represented in Table 3. In order to bring the simulated efficiencies to as close to the measured efficiencies as possible for all the energies, the lateral dead layer was increased by 0.25 mm and the back dead layer was increased by 1.5 mm. The front dead layer was increased to 10 mm, to allow a better agreement in the low-energy part of the efficiency spectrum, and the crystal-towindow distance was increased by 2 mm. It is important to underline that increasing the lateral and back dead layers is equivalent, for full energy peak efficiency calculation purposes, to
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12
12
8
8
4
4 0
0 crystal length = 30.0 mm
-4
crystal radius = 40.5 mm
-4
12
12
8
8
4 crystal length = 29.5 mm
(Sim - Exp) / Exp (%)
-4 12 8 4 0
crystal length = 29.0 mm
-4
(Sim - Exp) / Exp (%)
4
0
0 crystal radius = 40.0 mm
-4 12
crystal radius = 39.5 mm
8 4 0 -4
12 crystal length = 28.5 mm
8
12
4
crystal radius = 39.0 mm
8
0
4
-4
0 12 crystal length = 28.0 mm
8
-4 0
4
200
400
600
800
1000 1200 1400 1600
Energy (keV)
0
Fig. 6. Effect of the crystal radius on the detector efficiency.
-4 0
200
400
600
800
1000 1200 1400 1600
Energy (keV) Fig. 5. Effect of the crystal length on the detector efficiency.
decreasing the crystal dimensions, radius and length. We could have opted, for example, to assume that the crystal length is smaller than the value reported by the manufacturer, and assume a smaller or no increase in the back dead layer. For the detector model, we opted to change the dead layers instead of the crystal dimensions because it is generally accepted that the uncertainties in the dead layer dimensions are bigger than the uncertainties in the crystal dimensions. The simulation/measurement relative deviation after optimization is represented in Fig. 7. A good agreement between the simulated and measured efficiencies was reached. The deviations are in all cases inferior to 2.5%. The optimized model was also tested with the source placed closer to the detector, 11.31 cm instead of the previous 18.38 cm, in order to validate the model. The results are represented in Fig. 8, and clearly show that the model is also valid for this position. It is therefore possible to conclude that the optimized model can be used for calibration purposes, for point-like sources located at distances from the detector window that match those considered in the experimental setup.
5. Conclusion Broad Energy Germanium (BEGe) detectors are of paramount importance for gamma ray spectrometry in a wide range of
Table 3 Detector model optimization. Parameter
Nominal value
Optimized value
Crystal-to-window distance (mm) Crystal radius (mm) Crystal length (mm) Front dead layer thickness ðmmÞ Lateral dead layer thickness (mm) Back dead layer thickness (mm)
5 40.5 30 0.3 0.5 0.7
7 40.5 30 10 0.75 2.2
applications. An as detailed and accurate as possible description of their behavior is therefore mandatory in order to gain insight into the basic parameters characterizing the corresponding detection systems, namely the efficiencies, the correction factors and the backgrounds. Uncertainties in these parameters can be assessed using state-of-the-art Monte Carlo simulation programs, implementing the actual geometry and accurately modeling the physics of the detection processes. Deviations from the nominal parameters provided by the manufacturers can be expected, resulting from the detectors operating conditions as well as from uncertainties in the nominal parameters provided by the manufacturers, namely in the dead layer thickness, the distance from the crystal to the window and the radial and longitudinal dimensions of the crystal. In this study, three general-purpose Monte Carlo simulation programs were used, namely MCNPX, FLUKA and PENELOPE, in order to model the behavior of a BEGe detector. Using the nominal
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4 FLUKA
2 0
(Sim - Exp) / Exp (%)
-2 -4 4
Carlo codes, with relative differences between them always below 2.5%, for all energies. It was shown that relative deviations between the measured efficiencies and the efficiencies computed with the Monte Carlo codes can be brought into the 2–3% band throughout the whole energy range introducing plausible variations, documented in the literature, in the front dead layer thickness (for the low energy range), in the distance from the crystal to the detector window and in the lateral and back dead layers of the crystal.
MCNPX
2
References
0 -2 -4 4 PENELOPE
2 0 -2 -4
0
200
400
600 800 1000 1200 1400 1600 Energy (keV)
Fig. 7. Relative deviation between computed and measured efficiencies after optimization, with the source placed at 18.38 cm from the detector.
4 FLUKA
2 0 -2
(Sim - Exp) / Exp (%)
1019
-4 4 MCNPX
2 0 -2 -4 4 PENELOPE
2 0 -2 -4 0
200
400
600 800 1000 1200 1400 1600 Energy (keV)
Fig. 8. Relative deviation between computed and measured efficiencies after optimization, with the source placed at 11.31 cm from the detector.
parameters for the detector dimensions the simulated efficiencies deviate from the measured values from 2% to 12%, with the biggest discrepancies in the high energy part of the efficiency spectrum. A good agreement was achieved for the three Monte
[1] G. Le Petit, et al., Appl. Radiat. Isot. 64 (2006) 1307. [2] J. Gasparro, et al., Czech. J. Phys. 56 (2006) D203. ¨ [3] D. Budja´s, O. Chkvorets, S. Schonert, Background suppression using pulse shape analysis with a BEGe detector for neutrinoless double beta decay search with GERDA, in: Proceedings of the 10th Conference on the Intersections of Particle and Nuclear Physics, AIP Conference Proceedings, vol. 1182, pp. 96–99. [4] G. Giovanetti, Development of a data-acquisition system for a low-background BEGe detector, in: American Physical Society, APS April Meeting, 2010. [5] F. Avignone III, Prog. Part. Nucl. Phys. 64 (2010) 258. [6] A. Smolnikov for the GERDA collaboration, Development and installation of the GERDA experiment, Topics in astroparticle and underground physics, J. Phys. Conf. Ser. [7] J.L. Webb, et al., Radiat. Prot. Dosim. 89 (2000) 325. [8] G.H. Kramer, S.A. Allen, D. Groff, Health Phys. 85 (2003) 751. [9] L. Liye, et al., Radiat. Prot. Dosim. 127 (2007) 282. [10] F.A. Selim, et al., Nucl. Instr. and Meth. A 495 (2002) 154. [11] M. Canet, et al., Appl. Radiat. Isot. 52 (2000) 711. [12] H. Neder, G. Heusser, M. Laubenstein, Appl. Radiat. Isot. 53 (2000) 191. [13] M. Hult, et al., J. Environ. Radioact. 60 (2002) 307. [14] M. Hult, et al., Appl. Radiat. Isot. 61 (2004) 173. ¨ [15] M. Kohler, et al., Appl. Radiat. Isot. 61 (2004) 207. ˜ a, et al., Appl. Radiat. Isot. 68 (2010) 1226. [16] R.G. de Ordun [17] D. Arnold, O. Sima, Appl. Radiat. Isot. 64 (2006) 1297. [18] D. Novkovic´, et al., Nucl. Instr. and Meth. A 578 (2007) 207. [19] D. Novkovic´, et al., Nucl. Instr. and Meth. A 582 (2007) 592. [20] I.O. Ewa, et al., Appl. Radiat. Isot. 55 (2001) 103. [21] S. Hurtado, M. Garcı´a-Leo´n, R. Garcı´a-Tenorio, Nucl. Instr. and Meth. A 518 (2004) 764. [22] L. Liye, et al., Nucl. Instr. and Meth. A 564 (2006) 608. [23] C.M. Salgado, C.C. Conti, P.H. Becker, Appl. Radiat. Isot. 64 (2006) 700. [24] V. Peyres, E. Garcı´a-Torano, Nucl. Instr. and Meth. A 580 (2007) 296. [25] N.C. Dı´az, M.J. Vargas, Nucl. Instr. and Meth. A 586 (2008) 204. [26] O. Sima, D. Arnold, Appl. Radiat. Isot. 67 (2009) 701. [27] M. Garcı´a-Talavera, et al., Appl. Radiat. Isot. 52 (2000) 777. [28] J. Ro´denas, et al., Nucl. Instr. and Meth. B 263 (2007) 144. [29] S. Ashrafi, A. Likar, T. Vidmar, Nucl. Instr. and Meth. A 438 (1999) 421. [30] T. Vidmar, A. Likar, Appl. Radiat. Isot. 56 (2002) 99. [31] O. Sima, et al., Appl. Radiat. Isot. 61 (2004) 123. [32] P.N. Johnston, M. Hult, J. Gasparro, Appl. Radiat. Isot. 64 (2006) 1323. ˚ [33] J. Boson, G. Agren, L. Johansson, Nucl. Instr. and Meth. A 587 (2008) 304. [34] J. Gasparro, et al., Nucl. Instr. and Meth. A 594 (2008) 196. [35] F. Courtine, et al., Nucl. Instr. and Meth. A 596 (2008) 229. [36] D. Budja´s, et al., Appl. Radiat. Isot. 67 (2009) 706. [37] K. Karfopoulos, M. Anagnostakis, Appl. Radiat. Isot. 68 (2010) 1435. [38] O. Marzocchi, B. Breustedt, M. Urban, Appl. Radiat. Isot. 68 (2009) 1438. [39] R. Helmer, et al., Nucl. Instr. and Meth. A 511 (2003) 360. [40] M. Jurado Vargas, A.L. Guerra, Appl. Radiat. Isot. 64 (2006) 1319. [41] F. Salvat, J.M. Fernandez-Varea, J. Sempau, PENELOPE 2008: a code system for Monte Carlo simulation of electron and photon transport, OECD, 2008. [42] G.W. McKinney, et al., MCNPX overview, in: Proceedings of the 2006 HSSW, FNAL, IL, LA-UR-06-6206. [43] A. Ferrari, et al., FLUKA: A Multi-Particle Transport Code, CERN, 2008. [44] V. Vlachoudis, FLAIR: a powerful but user friendly graphical interface for FLUKA, in: Proceedings of the International Conference on Mathematics, Computational Methods & Reactor Physics (M&C 2009), Saratoga Springs, 2009. [45] T. Vidmar, et al., Appl. Radiat. Isot. 66 (2008) 764. [46] O. Sima, D. Arnold, Appl. Radiat. Isot. 53 (2000) 51.