- Email: [email protected]
Parameters affecting full energy peak efficiency determination during Monte Carlo simulation
ARTICLE IN PRESS Applied Radiation and Isotopes 68 (2010) 1435–1437
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Parameters affecting full energy peak efficiency determination during Monte Carlo simulation K.L. Karfopoulos, M.J. Anagnostakis Nuclear Engineering Department, National Technical University of Athens, 15780 Athens, Greece
a r t i c l e in fo
Keywords: Monte Carlo simulation Gamma spectrometry Detector efficiency
abstract Aim of this work is to study the effect of various simulation parameters on the calculation of the full energy peak efficiency of HPGe detectors with the Monte Carlo simulation code PENELOPE. & 2009 Elsevier Ltd. All rights reserved.
1. Introduction
2. Experimental determination of detector efficiency
In the last few years several papers have been published on the efficiency calibration of HPGe detectors using Monte Carlo (MC) simulation (Helmer et al., 2003). In most cases, efficiency values calculated from simulation are compared with experimental results. Differences between experimental and simulation results are usually attributed to uncertainties in the detector dimensions and dead layer thickness, while in some cases a repetitive procedure is applied in order to reduce these differences to acceptable levels (Jurado Vargas and Guerra, 2006). This procedure is based upon new simulations with properly modified detector dimensions and characteristics (e.g. dead layer thickness). Another factor that may introduce uncertainties in the simulation results is the choice of user defined simulation parameters. This source of uncertainty is often ignored. During photon simulation, photons delivering a specific amount of energy to the detector are recorded within user defined energy windows (bins) with specific width, known as ‘‘bin width’’. Another user-defined parameter is the ‘‘cut-off’’ energy for photons and particles (electrons and positrons). When the energy of a photon or particle suffering an interaction is reduced below the corresponding cut-off energy, its energy is considered as deposited in-place. Simulations with high cut-off energy are faster but less precise than simulations with low cut-off energy. Aim of this research is to study the effect of the various simulation parameters, when using a typical MC computer code for the determination of the full energy peak efficiency and the total efficiency of HPGe detectors.
For the experimental determination of the full energy peak efficiency for photons with energy E, the net area of the full energy peak of the spectrum is considered equal to the number of photons that deliver energy E to the detector. However, there exist a small number of photons with slightly reduced energy, due to a prior Compton scattering, that may also be recorded under the full energy peak (Sima and Arnold, 2009). The percentage of these photons depends, among others, upon E. For 45 keV photons, suffering Compton scattering with deflection angle below 301 the energy loss is less than 0.5 keV. For a detector with an energy resolution of 1 keV in terms of ‘‘full width at half maximum’’ (fwhm) these photons may be recorded under the full energy peak, which extends in the region E71.5 fwhm. This results to a small peak asymmetry, which tends to be larger for low energy photons and photon sources with significant selfabsorption. This asymmetry may be so small that the photopeak is still analyzed as a singlet. Therefore, when the full energy peak efficiency is determined through simulation, all photons that may be recorded under the photopeak should be considered, including those with slightly reduced energy.
Corresponding author. Tel.: + 30 210 7722912; fax: + 30 210 7722914.
E-mail address: [email protected] (M.J. Anagnostakis). 0969-8043/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2009.11.020
3. Detector efficiency calculation with Monte-Carlo simulation When a Monte-Carlo simulation code is used, all photons that deliver to the detector an amount of energy within a bin are used for the determination of the bin probability density pd (eV 1) by the formula: pd ¼
Np Nt dE
ARTICLE IN PRESS K.L. Karfopoulos, M.J. Anagnostakis / Applied Radiation and Isotopes 68 (2010) 1435–1437
where Np is the number of photons recorded in the bin, Nt the total number of simulated photons, dE the bin width (eV). One of the bins records the photons, which deliver all their energy (E) to the detector. Then, the full energy peak efficiency e of the detector is calculated as e =pd dE, with pd being the ‘‘photopeak’’ bin probability density. Depending on the bin width, some photons with slightly reduced energy due to prior scattering may also be recorded within this ‘‘photopeak’’ bin. It is therefore expected, that the bin width selection will have an effect on the result of the full energy peak efficiency calculation. Apart from the bin width, the ‘‘photopeak’’ bin’s specific upper and lower limits—Eu and El respectively—affect the number of photons that are recorded within the bin as well. Eu and El are dependent upon user-defined parameters. Normally, El is set just below E, so that only original photons fully absorbed in the detector are recorded. During this work the effect of: 1. energy bin width, 2. photopeak bin upper and lower limits and 3. cut-off energy for photons and particles. on the calculation of the full energy peak and total efficiency was studied. For this purpose a coaxial HPGe detector with a cylindrical source of a high-density material on top of it was simulated. Details regarding this geometry can be found elsewhere (Vidmar et al., 2008). An energy independent resolution (fwhm) of 1 keV was assumed for the detector. During this work the PENELOPE MC simulation computer code was used (Salvat et al., 2006). For this purpose, the PENMAIN user code was properly modified. Simulations were run on two computers, (a) a Pentium(R) 4 CPU 3.20 GHz, 1.0 GB RAM and, (b) an Intel(R) Dual Core CPU 2.40 GHz, 1.0 GB RAM. 3.1. The effect of bin width For the investigation of the bin width effect, two series of simulations were run with photon energies of 45 and 1500 keV, respectively. For the first series of simulations the minimum number of bins (bin size) was 30 and corresponds to a bin width of 1.5 keV (1.5 fwhm), equal to the lower half of the corresponding photopeak of the real spectrum. Several simulations were run with bin size above 30. For the second series of simulations, bin size 1000 also corresponds to a bin width of 1.5 keV. Several simulations with bin size around this value were also run. For both series of simulations, bin sizes above 30 and 1000,
peak efficiency
7.1x10-3
1 bin corrected
7.0x10-3
1500keV
-3
45keV
1.5x10
1.4x10-3
1.3x10-3 100
1000 Number of bins
10000
Fig. 1. Full energy peak efficiency for 45 and 1500 keV photons, calculated from 1 bin and from more than one bins (corrected).
respectively correspond to bin widths that were sub-multiples of 1.5 keV. The photopeak bin El and the cut-off energy for particles (10 keV) and photons (1 keV) were kept constant. All simulations were run for sufficient time to obtain statistical uncertainty of the full energy peak efficiency better than 0.2% (k=1). Fig. 1 presents full energy peak efficiency results for both photon energies, together with their standard uncertainty, as calculated:
from the content of the photopeak bin alone, and from the content of an appropriate number of bins, which cover the energy region [E 1.5 fwhmCE] (corrected efficiency). For 45 keV photons, the effect of the bin width on the full energy peak efficiency is clear. However, if a sufficient number of bins are taken into consideration, the ‘‘corrected’’ peak efficiency becomes independent of the bin width. For 1500 keV photons, it is clear that the use of energy bin width lower than 1.5 fwhm does not significantly affect the full energy peak efficiency. However, if very wide bins are used a significant increase on the peak efficiency is observed. As expected, the total efficiency is not affected by the bin size, for both energies. Therefore, it is suggested that, for the correct determination of the full energy peak efficiency for photon energy E, the photon energy region that should be taken into consideration is [E 1.5 fwhmCE]. 3.2. Effect of bin lower limit In order to investigate the effect of the photopeak lower limit El, a series of simulations were run for 45 keV photons, with 50 eV bin width, for various El values. Fig. 2 presents the results of the full energy peak efficiency calculation, using only one bin. Since the bin width remains the same and El increases, fewer photons are recorded in the photopeak bin and the photopeak efficiency is reduced. 3.3. Effect of cut-off energies The selection of cut-off energies may affect the simulation speed as well as the actual spectrum. For PENELOPE, cut-off energy of 0.001 E and 0.01 E is recommended for photons and particles, respectively. For the investigation of the cut-off energy effect two series of simulations were run:
45 keV photons, 50 eV bin width 1500 keV photons, 500 eV bin width.
peak efficiency for 45keV photons
1436
1.35E-03
1.33E-03
1.30E-03
1.28E-03 44.5
44.6
44.7
44.8
44.9
45.0
El (keV) Fig. 2. Full energy peak efficiency for 45 keV photons calculated for various El values.
ARTICLE IN PRESS K.L. Karfopoulos, M.J. Anagnostakis / Applied Radiation and Isotopes 68 (2010) 1435–1437
1437
Table 1. Simulation speed (simulated photons per second) for different photon and particle cut-off energies. Particles cut-off energy (eV)
Photon energy E = 45 keV 450 1000 3000 10 000 Particles cut-off energy (eV)
Photon energy E = 1500 keV 500 1000 5000 10 000 15 000
Photons cut-off energy (eV) 50
200
500
1000
5000
10 000
761 1093 2222 5397
762 1114 2264 5555
759 1100 2198 5492
758 1077 2220 5557
760 1088 2235 5514
791 1132 2325 5440
Photons cut-off energy (eV) 50
200
500
1000
5000
144 234 793 1224 1354
147 237 850 1360 1354
151 237 847 1355 1508
151 238 929 1569 1768
150 235 925 1588 1789
Each series includes simulations with several combinations of photon and particle cut-offs. For the combinations tested, no effect was observed on the full energy peak and total efficiency determination. Table 1 presents the number of photons simulated per second for each simulation. It may be concluded that the particle cut-off energy has a significant effect on the simulation time. It should be stressed that for photon cut-off energies above 10 keV there is also an observable distortion of the simulated spectrum of photons absorbed by the detector (Sima and Arnold, 2009). In this case the 35.1 keV Ge Ka escape peak and 9.9 keV Ge Ka X-rays that are produced in the detector dead layer are removed from the spectrum.
4. Conclusions During this work the effect of various PENELOPE simulation parameters on the full energy peak determination of a Ge detector were investigated. It was concluded that the good understanding of the simulation computer code that is being used and the careful
selection of its various parameters, is of great importance for the accuracy of the results and the simulation speed obtained. Furthermore, the detector resolution should always be taken into consideration. The conclusions drawn from this work are applicable and may be extended to other Monte Carlo simulation computer codes. References Helmer, R.G., Hardy, J.C., Jacob, V.E., Sanchez-Vega, M., Neilson, R.G., Nelson, J., 2003. The use of Monte Carlo calculations in the determination of a Ge detector efficiency curve. Nuclear Instruments and Methods A 511, 360–381. Jurado Vargas, M., Guerra, A.L., 2006. Application of Penelope code to the efficiency calibration of coaxial germanium detectors. Applied Radiation and Isotopes 64, 1319–1322. Salvat, F., Fernandez-Varea, J.M., Sempau, J., 2006. PENELOPE-2006. A Code System for Monte Carlo Simulation of Electron and Photon Transport. OECD Nuclear Energy Agency, Issy-les-Moulineaux. Sima, O., Arnold, D., 2009. On the Monte Carlo simulation of HPGe gammaspectrometry systems. Applied Radiation and Isotopes 67 (5), 701–705. Vidmar, T. An intercomparison of Monte Carlo codes used in gamma-ray spectrometry. Applied Radiation and Isotopes 66, 764–768.
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Parameters affecting full energy peak efficiency determination during Monte Carlo simulation K.L. Karfopoulos, M.J. Anagnostakis Nuclear Engineering Department, National Technical University of Athens, 15780 Athens, Greece
a r t i c l e in fo
Keywords: Monte Carlo simulation Gamma spectrometry Detector efficiency
abstract Aim of this work is to study the effect of various simulation parameters on the calculation of the full energy peak efficiency of HPGe detectors with the Monte Carlo simulation code PENELOPE. & 2009 Elsevier Ltd. All rights reserved.
1. Introduction
2. Experimental determination of detector efficiency
In the last few years several papers have been published on the efficiency calibration of HPGe detectors using Monte Carlo (MC) simulation (Helmer et al., 2003). In most cases, efficiency values calculated from simulation are compared with experimental results. Differences between experimental and simulation results are usually attributed to uncertainties in the detector dimensions and dead layer thickness, while in some cases a repetitive procedure is applied in order to reduce these differences to acceptable levels (Jurado Vargas and Guerra, 2006). This procedure is based upon new simulations with properly modified detector dimensions and characteristics (e.g. dead layer thickness). Another factor that may introduce uncertainties in the simulation results is the choice of user defined simulation parameters. This source of uncertainty is often ignored. During photon simulation, photons delivering a specific amount of energy to the detector are recorded within user defined energy windows (bins) with specific width, known as ‘‘bin width’’. Another user-defined parameter is the ‘‘cut-off’’ energy for photons and particles (electrons and positrons). When the energy of a photon or particle suffering an interaction is reduced below the corresponding cut-off energy, its energy is considered as deposited in-place. Simulations with high cut-off energy are faster but less precise than simulations with low cut-off energy. Aim of this research is to study the effect of the various simulation parameters, when using a typical MC computer code for the determination of the full energy peak efficiency and the total efficiency of HPGe detectors.
For the experimental determination of the full energy peak efficiency for photons with energy E, the net area of the full energy peak of the spectrum is considered equal to the number of photons that deliver energy E to the detector. However, there exist a small number of photons with slightly reduced energy, due to a prior Compton scattering, that may also be recorded under the full energy peak (Sima and Arnold, 2009). The percentage of these photons depends, among others, upon E. For 45 keV photons, suffering Compton scattering with deflection angle below 301 the energy loss is less than 0.5 keV. For a detector with an energy resolution of 1 keV in terms of ‘‘full width at half maximum’’ (fwhm) these photons may be recorded under the full energy peak, which extends in the region E71.5 fwhm. This results to a small peak asymmetry, which tends to be larger for low energy photons and photon sources with significant selfabsorption. This asymmetry may be so small that the photopeak is still analyzed as a singlet. Therefore, when the full energy peak efficiency is determined through simulation, all photons that may be recorded under the photopeak should be considered, including those with slightly reduced energy.
Corresponding author. Tel.: + 30 210 7722912; fax: + 30 210 7722914.
E-mail address: [email protected] (M.J. Anagnostakis). 0969-8043/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2009.11.020
3. Detector efficiency calculation with Monte-Carlo simulation When a Monte-Carlo simulation code is used, all photons that deliver to the detector an amount of energy within a bin are used for the determination of the bin probability density pd (eV 1) by the formula: pd ¼
Np Nt dE
ARTICLE IN PRESS K.L. Karfopoulos, M.J. Anagnostakis / Applied Radiation and Isotopes 68 (2010) 1435–1437
where Np is the number of photons recorded in the bin, Nt the total number of simulated photons, dE the bin width (eV). One of the bins records the photons, which deliver all their energy (E) to the detector. Then, the full energy peak efficiency e of the detector is calculated as e =pd dE, with pd being the ‘‘photopeak’’ bin probability density. Depending on the bin width, some photons with slightly reduced energy due to prior scattering may also be recorded within this ‘‘photopeak’’ bin. It is therefore expected, that the bin width selection will have an effect on the result of the full energy peak efficiency calculation. Apart from the bin width, the ‘‘photopeak’’ bin’s specific upper and lower limits—Eu and El respectively—affect the number of photons that are recorded within the bin as well. Eu and El are dependent upon user-defined parameters. Normally, El is set just below E, so that only original photons fully absorbed in the detector are recorded. During this work the effect of: 1. energy bin width, 2. photopeak bin upper and lower limits and 3. cut-off energy for photons and particles. on the calculation of the full energy peak and total efficiency was studied. For this purpose a coaxial HPGe detector with a cylindrical source of a high-density material on top of it was simulated. Details regarding this geometry can be found elsewhere (Vidmar et al., 2008). An energy independent resolution (fwhm) of 1 keV was assumed for the detector. During this work the PENELOPE MC simulation computer code was used (Salvat et al., 2006). For this purpose, the PENMAIN user code was properly modified. Simulations were run on two computers, (a) a Pentium(R) 4 CPU 3.20 GHz, 1.0 GB RAM and, (b) an Intel(R) Dual Core CPU 2.40 GHz, 1.0 GB RAM. 3.1. The effect of bin width For the investigation of the bin width effect, two series of simulations were run with photon energies of 45 and 1500 keV, respectively. For the first series of simulations the minimum number of bins (bin size) was 30 and corresponds to a bin width of 1.5 keV (1.5 fwhm), equal to the lower half of the corresponding photopeak of the real spectrum. Several simulations were run with bin size above 30. For the second series of simulations, bin size 1000 also corresponds to a bin width of 1.5 keV. Several simulations with bin size around this value were also run. For both series of simulations, bin sizes above 30 and 1000,
peak efficiency
7.1x10-3
1 bin corrected
7.0x10-3
1500keV
-3
45keV
1.5x10
1.4x10-3
1.3x10-3 100
1000 Number of bins
10000
Fig. 1. Full energy peak efficiency for 45 and 1500 keV photons, calculated from 1 bin and from more than one bins (corrected).
respectively correspond to bin widths that were sub-multiples of 1.5 keV. The photopeak bin El and the cut-off energy for particles (10 keV) and photons (1 keV) were kept constant. All simulations were run for sufficient time to obtain statistical uncertainty of the full energy peak efficiency better than 0.2% (k=1). Fig. 1 presents full energy peak efficiency results for both photon energies, together with their standard uncertainty, as calculated:
from the content of the photopeak bin alone, and from the content of an appropriate number of bins, which cover the energy region [E 1.5 fwhmCE] (corrected efficiency). For 45 keV photons, the effect of the bin width on the full energy peak efficiency is clear. However, if a sufficient number of bins are taken into consideration, the ‘‘corrected’’ peak efficiency becomes independent of the bin width. For 1500 keV photons, it is clear that the use of energy bin width lower than 1.5 fwhm does not significantly affect the full energy peak efficiency. However, if very wide bins are used a significant increase on the peak efficiency is observed. As expected, the total efficiency is not affected by the bin size, for both energies. Therefore, it is suggested that, for the correct determination of the full energy peak efficiency for photon energy E, the photon energy region that should be taken into consideration is [E 1.5 fwhmCE]. 3.2. Effect of bin lower limit In order to investigate the effect of the photopeak lower limit El, a series of simulations were run for 45 keV photons, with 50 eV bin width, for various El values. Fig. 2 presents the results of the full energy peak efficiency calculation, using only one bin. Since the bin width remains the same and El increases, fewer photons are recorded in the photopeak bin and the photopeak efficiency is reduced. 3.3. Effect of cut-off energies The selection of cut-off energies may affect the simulation speed as well as the actual spectrum. For PENELOPE, cut-off energy of 0.001 E and 0.01 E is recommended for photons and particles, respectively. For the investigation of the cut-off energy effect two series of simulations were run:
45 keV photons, 50 eV bin width 1500 keV photons, 500 eV bin width.
peak efficiency for 45keV photons
1436
1.35E-03
1.33E-03
1.30E-03
1.28E-03 44.5
44.6
44.7
44.8
44.9
45.0
El (keV) Fig. 2. Full energy peak efficiency for 45 keV photons calculated for various El values.
ARTICLE IN PRESS K.L. Karfopoulos, M.J. Anagnostakis / Applied Radiation and Isotopes 68 (2010) 1435–1437
1437
Table 1. Simulation speed (simulated photons per second) for different photon and particle cut-off energies. Particles cut-off energy (eV)
Photon energy E = 45 keV 450 1000 3000 10 000 Particles cut-off energy (eV)
Photon energy E = 1500 keV 500 1000 5000 10 000 15 000
Photons cut-off energy (eV) 50
200
500
1000
5000
10 000
761 1093 2222 5397
762 1114 2264 5555
759 1100 2198 5492
758 1077 2220 5557
760 1088 2235 5514
791 1132 2325 5440
Photons cut-off energy (eV) 50
200
500
1000
5000
144 234 793 1224 1354
147 237 850 1360 1354
151 237 847 1355 1508
151 238 929 1569 1768
150 235 925 1588 1789
Each series includes simulations with several combinations of photon and particle cut-offs. For the combinations tested, no effect was observed on the full energy peak and total efficiency determination. Table 1 presents the number of photons simulated per second for each simulation. It may be concluded that the particle cut-off energy has a significant effect on the simulation time. It should be stressed that for photon cut-off energies above 10 keV there is also an observable distortion of the simulated spectrum of photons absorbed by the detector (Sima and Arnold, 2009). In this case the 35.1 keV Ge Ka escape peak and 9.9 keV Ge Ka X-rays that are produced in the detector dead layer are removed from the spectrum.
4. Conclusions During this work the effect of various PENELOPE simulation parameters on the full energy peak determination of a Ge detector were investigated. It was concluded that the good understanding of the simulation computer code that is being used and the careful
selection of its various parameters, is of great importance for the accuracy of the results and the simulation speed obtained. Furthermore, the detector resolution should always be taken into consideration. The conclusions drawn from this work are applicable and may be extended to other Monte Carlo simulation computer codes. References Helmer, R.G., Hardy, J.C., Jacob, V.E., Sanchez-Vega, M., Neilson, R.G., Nelson, J., 2003. The use of Monte Carlo calculations in the determination of a Ge detector efficiency curve. Nuclear Instruments and Methods A 511, 360–381. Jurado Vargas, M., Guerra, A.L., 2006. Application of Penelope code to the efficiency calibration of coaxial germanium detectors. Applied Radiation and Isotopes 64, 1319–1322. Salvat, F., Fernandez-Varea, J.M., Sempau, J., 2006. PENELOPE-2006. A Code System for Monte Carlo Simulation of Electron and Photon Transport. OECD Nuclear Energy Agency, Issy-les-Moulineaux. Sima, O., Arnold, D., 2009. On the Monte Carlo simulation of HPGe gammaspectrometry systems. Applied Radiation and Isotopes 67 (5), 701–705. Vidmar, T. An intercomparison of Monte Carlo codes used in gamma-ray spectrometry. Applied Radiation and Isotopes 66, 764–768.