- Email: [email protected]
A novel technique for detection efficiency determination of HPGe
Author’s Accepted Manuscript A novel technique for detection efficiency determination of HPGe Pouneh Tayyebi, Fereydoun Abbasi Davani, Mohsen Tabasi, Hossein Afarideh www.elsevier.com/locate/radphyschem
PII: DOI: Reference:
S0969-806X(16)30835-0 http://dx.doi.org/10.1016/j.radphyschem.2016.12.024 RPC7354
To appear in: Radiation Physics and Chemistry Received date: 17 August 2016 Revised date: 28 December 2016 Accepted date: 29 December 2016 Cite this article as: Pouneh Tayyebi, Fereydoun Abbasi Davani, Mohsen Tabasi and Hossein Afarideh, A novel technique for detection efficiency determination of HPGe, Radiation Physics and Chemistry, http://dx.doi.org/10.1016/j.radphyschem.2016.12.024 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A novel technique for detection efficiency determination of HPGe Pouneh Tayyebi1, 2, Fereydoun Abbasi Davani3,*, Mohsen Tabasi1, Hossein Afarideh2 1 Nuclear Science and Technology Research Institute, North Kargar, P. O. Box 113658486, Tehran, Iran 2 Department of Energy Engineering and Physics, Amirkabir University of Technology, Hafez 424, P. O. Box 15875-4413, Tehran, Iran 3 Department of Radiation Application, Shahid Beheshti University, Velenjak, P. O. Box 1983969411, Tehran, Iran * [email protected]
Abstract In this work, we present an experimental method to determine the detection efficiency of HPGe when the reference source according to the geometry of interest is not accessible. We use known activity point sources (PS) of
152
Eu,
137
Cs,
241
Am and
133
Ba to find the
detection efficiency for disc source (DS) geometry. It can be assumed that a DS consists of several PS’s. Mapping the detector surface by means of
137
Cs PS shows that there is
radial symmetry for detection efficiency vs. energy. Each radial distance on the detector surface contains some points, which can be considered as a PS. By selecting two points in two different radii and central point, the DS efficiency is obtained. To ensure that the method is correct, we measure the activity of a known activity DS considering DS efficiency obtained by PS’s. The DS comprises
137
Cs,
133
Ba and
60
Co. The relative
difference between the measured and the reported activity of DS in most energies is less than 5%.
1
Keywords Efficiency calibration, HPGe detector, Standard sources, Activity measurement.
1. Introduction High resolution gamma spectroscopy is an efficient method to determine the radionuclides in the samples. Radioactivity measurement by means of HPGe detectors necessitates known detection efficiency. Accurate calibration of the detector efficiency is performed by counting a sample and the standard sources. Source-detector configuration should be the same in the measurement of the sample and standard source as well as their properties such as size, composition, density and radionuclide contents. In many cases, there are not standard sources corresponding to the sample under investigation. Preparation of a standard source is costly and time consuming. So, one must find alternative ways to determine the detection efficiency. To overcome this difficulty, there are some methods presented in other publications such as using Monte Carlo (MC) simulations (Vidmar et al., 2010, Rodenas et al., 2000, Ewa et al., 2001) and combination of MC simulation and genetic algorithm (Ngo Quang Huy et al., 2012). In the Monte Carlo simulation, it is neccessary to have an accurate knowledge of the detector configuration and its dimensions which are usually different from those the manufacturer provides (Andreotti et al., 2014), especially via the old detector because of the dead layer (Rodenas et al., 2003, Chham et al., 2015). Moreover, the accuracy of the simulation must be evaluated (Talavera et al., 2000). The authors reported different uncertainities between MC simulation and experimental value on the order of 5-10 % (Maidana et al., 2016), superior to 20% (Gómez et al., 2015), 10% and 3% (Talavera et al., 2000). MC efficiency transfer method has overcome this problem, since it does not need to optimize manufacturer’s detector parameters with the experimental values (Gómez et al., 2015, Liye et al., 2011, Lepy et al., 2001, Piton et al., 2000). The relative deviations within 5% (Gómez et al., 2015, Liye et al., 2011) and 1-2% (Piton et al., 2000) have been reported in different publications.
2
In the current work, we propose an experimental method to determine the detection efficiency for a disc source (DS) by means of point sources (PS). At first, the whole detector surface was scanned by
137
Cs PS. The results showed that there is radial
symmetry for efficiency in the low energy, 32.19 and 36.4 keV, and high energy, 661.657 keV. Due to radial symmetry, one point in each radius was selected as a reference point for measurement. By determination of the efficiency in these points, one can find the DS efficiency. To evaluate the method, the activity of known activity DS containing 133
137
Cs,
Ba and 60Co was measured considering DS efficiency, which was obtained by PS’s.
2. Materials and Methods 2.1.
Spectroscopy system
The experimental measurements were performed with a coaxial n-type HPGe detector which has a nominal 70% relative efficiency. The diameter and the thickness of Ge crystal is 73 mm and 84.1 mm, respectively. The window is carbon fiber. The detector was shielded with a cylindrical lead wall of 13 cm in thickness, and a copper foil of 2 mm in thickness. Source to detector distance is 8 mm. Gamma rays spectra were obtained by a digital multichannel analyzer and were analyzed by the GammaVision 32 V6.07 program.
2.2.
Radioactive source
A multigamma Amersham standard disc source contatining
137
Cs,
133
Ba and
60
Co was
considered as a reference source. It has diameter and active part of 9.5 cm and 7.0 cm, respectively. The planar sources with an active part of 4 mm in diameter from POLATOM were used. The active part is placed central between two plexyglass discs with 12 mm diameter and 1 mm height each one. In Table 1, the activities of the sources at the moment of the experimentation are listed.
3
Table 1 The characteristics of the sources Source
Activity (Bq) Uc (%) Ba 16711.5 2.0 137 Cs 29174 2.0 Point 152 Eu 20980 2.0 241 Am 45154 2.0 137 Cs 5852.9 Disc 133Ba 1772.3 60 Co 348.57 133
In IEEE Std 325, a point source is defined as a disc in which the diameter of the active region of radionuclide is ≤ 2 mm. By using Monte Carlo simulation with MCNPX2.7e, it can be shown that the planar source with an active part of 4 mm can be regarded as a point source. In the simulation, a typical HPGe detector and two sources with radius 0 (as a point source) and 2 mm were considered. The sources were placed 8 mm (as in the experiments) above the detector endcap on its axis. Detection efficiencies for two sources were calculated using pulse hieght tally f8. Fig. 1 shows the detector efficiency vs energy. It shows that, in spite of the different geometry, the two source have the same efficiency. So, we considered the planar source with an active part of 4 mm as a point source.
Fig. 1 Detector efficiency for two sources with radius of 0 (rectangles) and 2 mm (circles). Source to detector distance is 8 mm
4
2.3.
Source holder
To ensure that the detector has radial symmetry for efficiency, its surface was scanned with 137Cs point source. A polyethylene source holder with the diameter and thickness of 6.5 cm and 0.5 cm, respectively was used. It has 19 places to fix the point source. Fig. 2 depicts the holder with 19 circles numbered 1 to 19.
Fig. 2 Polyethylene source holder with 19 places for mapping the detector surface. The diameter of the circles is according to that of the sources, i.e. 12 mm
2.4.
Determination of the radial symmetry
The radial symmetry was determined by mapping the surface of the detector using the 137
Cs source. The response of the HPGe to 19 different source positions was measured.
Each spectrum was acquired during 600 s and repeated 3 times. There are 3 diagonal sets named set 1 to 3. Each set has 5 points characterized by the numbers shown in Fig. 2 and listed in Table 2. The results of mapping the detector in these 3 sets and 3 energies of 137
Cs are represented in Fig. 3. In this figure, the ratio of the counts in radius r,C(r), to
that of center, C(0), is shown v.s distance from the center of holder. The point number 19 (center of holder) is considered as 0 and center to center distance is 12 mm.
Table 2 Three diagonal sets and their points Set 1 -1.2 0
Set 2 -1.2 0 1.2
2.4
-2.4
19
3
5
r* -2.4 1.2 2.4 -2.4 Point 7 16 19 13 1 9 17 No. *Distance from center of the holder (cm)
5
14
Set 3 -1.2 0
1.2
2.4
15
18
11
19
6
Fig. 3 Ratio of the counts in radius r, C(r), to that of center, C(0), for a) E=32.19 keV, b) E=36.4 keV, and c) E=661.657 keV for 3 diagonal sets. The results show the radial symmetry on the detector surface It can be seen that the counts decrease moving away in radial direction. According to the uniformity observed in Fig. 3, there is a radial symmetry in each data set. It means that there is no need to measure all 5 points; just 2 points related to 2 different radii and central point are sufficient. Moreover, it shows that there is radial symmetry in low (32.19 and 36.4 keV) and high energies (661.66 keV). Fig. 4 shows that there is a uniformity between the points in each radius. So, we selected point numbers of 1, 13 and 19 as the candidate points in set 1 in distance of 2.4 cm, 1.2 cm and 0 cm from center, respectively. In Table 3, the minimum and maximum efficiencies between the points in each radius are presented.
7
Fig. 4 Uniformity of the efficiency between the points in each radius in E=32.19 keV Table 3 Minimum and maximum efficiency between the points at each radius and their deviations Efficiency (%) Deviation (%) Min Max 1-12 11.36 13.90 18.27 13-18 19.34 21.07 8.21 1-12 14.63 15.65 6.51 13-18 18.77 19.58 4.14 1-12 5.11 5.42 5.72 13-18 6.49 6.78 4.28
Energy (keV) r (cm) Points 32.19 36.4 661.657
2.5.
2.4 1.2 2.4 1.2 2.4 1.2
Determination of the full energy peak efficiency
Full energy peak (FEP) efficiency,ε (E), is calculated from Eq. (1). (1) where: N is the net counts under full-energy peak, f(E) is the probability of gamma emission in energy E,
8
A is the activity in Bq, and t is the live time of the measurement in s.To determine the efficiency for a DS, we assumed that a DS consists of several PS’s in each radius of the DS. So, the DS efficiency can be written as: ∑ ∑
(2)
where DSEε(E) is the DS equivalent efficiency in energy E, Ci is the number of points in radius i, n is the number of radius, and ε(E)i is the efficiency at selected point in radius i. Consequently, in our case ∑
(3)
∑
3. Results and discussion Table 4 shows the results of FEP efficiency (FEPE) measurement in 3 selected points. The results of DSEε are compared with the efficiency of DS and are given in Table 4. The relative difference is less than 4% in most energies. Fig. 5 shows the DSEε and DS efficiency vs energy. It is worth noting that in this experiment we used the same energies between the DS and PS, so no correction on true coincidence summing is necessary because all efficiency values DS and PS are affected in the same way. For other radionuclides with different true coincidence summing, it should be corrected.
Table 4 FEP efficiency for 3 selected points, DSE and DS
9
Source
241
Am
133
Ba
137
152
Cs
Eu
Energy (keV) 13.8 26.3446 59.54 80.9971 160.6109 276.3997 302.8510 356.0134 383.8481 36.4 661.657 121.7871 244.6975 344.2785 411.1163 867.37
Intensity (%) (ENDF) 42 2.4 35.9 34.06 0.645 7.164 18.33 62.05 8.94 1.3 (NuChart)
89.9 28.668 7.607 26.56 2.24 4.258
FEPE at point No. 1
13
19
2.34 6.41 19.95 13.21 9.53 6.01 6.43 6.13 5.30
3.02 8.13 28.86 15.21 11.30 6.42 6.96 6.93 6.40
3.12 8.22 30.45 15.48 11.23 6.66 7.04 7.13 6.13
Disc Source Equivalent (DSE) 2.60 7.05 23.32 13.96 10.13 6.17 6.63 6.43 5.69
------14.23 9.93 6.75 6.89 6.47 5.72
Deviation of DSE from DS (%) ------1.9 2.01 8.59 3.77 0.62 0.53
14.63
18.77
19.58
16.20
15.59
3.91
5.20 11.62 6.47 5.98 5.41 2.45
6.50 13.10 6.90 6.92 6.06 2.42
6.78 13.30 6.93 7.12 6.16 2.42
5.69 12.18 6.63 6.34 5.66 2.44
5.49 -----------
3.64 -----------
Disc Source (DS)
Fig. 5 DSEε (rectangels) and DS (circles) efficiency For validation of the presented method, the activity of the DS was measured using DSEε. The measured activity values were compared with the reported one and are presented in Table 5. As seen, the relative difference is less than 5% in most energies.
10
Table 5 Determination of DS activity Source
133
Ba
137
Cs
Energy (keV) 80.9971 160.6109 276.3997 302.8510 356.0134 383.8481 36.4 661.657
Activity (Bq) Reported Measured 1772.3 1806.56 1772.3 1737.14 1772.3 1937.29 1772.3 1843.76 1772.3 1781.95 1772.3 1782.51 5852.9 5633.86 5852.9 5642.65
Deviation of measured activity from reported (%) 1.93 1.98 9.31 4.03 0.55 0.58 3.74 3.59
4. Conclusion We presented an experimental method to determine the efficiency of HPGe when the reference source according to the geometry of interest is not accessible. In this approach, effciencies of PS’s were used to obtain DS efficiency. The relative differences between the reported activity of disc source and that measured by presented method are less than 5%. Changing the effective parameters such as dimension of detector, the number of points and radii, are not discussed here. It is clear that increasing the number of points exhibits the better definition of DS; hence the relative difference will be decreased. In the future we shall endeavor to apply this method to determine the activity of a volume source.
References Andreotti E, Hult M, Marissens G, Lutter G, Garfagnini A, Hemmer S, von Sturm K (2014) Determination of dead-layer variation in HPGe detectors. Appl Rad Isot. 87:331-335 Chham E, Pinero Garcia F, El Bardouni T, Angeles Ferro-García M, Azahra M, Benaalilou K, Krikiz M, Elyaakoubi H, El Bakkali J, Kaddour M (2015) Technical note Monte Carlo analysis of the influence of germanium dead layer thickness on the HPGe gamma detector experimental efficiency measured by use of extended sources. Appl Rad Isot. 95:30-35 11
Ewa I.O.B, Bodizs D, Czifrus Sz, Molnar Zs (2001) Monte Carlo determination of full energy peak efficiency for a HPGe detector. Appl Rad Isot. 55:103-108 Garcia-Talavera M, Neder H, Daza M.J, Quintana B (2000) Towards a proper modeling of detector and source characteristics in Monte Carlo simulations. Appl Rad Isot. 52:777-783 Gamma Vision, Gamma-ray Spectrum Analysis and MCA Emulation for MS Windows, Software User’s Manual, version 32, V6.07
http://www.oecd-nea.org/janisweb/tree/RDD/'ENDF/B-VII.1'/RDD IEEE Std 325-1996 IEEE Standard Test Procedures for Germanium Gamma-Ray Detectors Liye L, Jizeng M, Franck D, de Carlan L, Binquan Z (2006) Monte Carlo efficiency transfer method for full energy peak efficiency calibration of three type HPGe detectors: A coaxial N-type, a coaxial P-type and four BEGe detectors. Nucl Instr Meth Phy Res A 564:608–613 Lepy M.C, et.al (2001) Intercomparison of efficiency transfer software for gamma-ray spectrometry. Appl Rad Isot. 55:493-503 Maidana N.L, Vanin V.R, García-Alvarez J.A, Hermida-López M, Brualla L (2016) Experimental HPGe coaxial detector response and efficiency compared to Monte Carlo simulations. Appl Rad Isot. 108:64-74 Morera-Gómez Y, Cartas-Aguila H.A, Alonso-Hernández C.M, Bernal-Castillo J.L, Guillén-Arruebarren A (2015) Application of the Monte Carlo efficiency transfer method to an HPGe detector with the purpose of environmental samples measurement. Appl Rad Isot. 97:59-62 Ngo Quang Huy, Do Quang Binh, Vo Xuan An (2012) A study for improving detection efficiency of an HPGe detector based gamma spectrometer using Monte Carlo simulation and genetic algorithms. Appl Rad Isot. 70:2695–2702 NuChart, Version 4.0.0, 1998 Piton F, Lepy M.C, Be M.C , Plagnard J (2000) Efficiency transfer and coincidence summing corrections for gamma-ray spectrometry. Appl Rad Isot. 52:791-795 Rodenas J, Martinavarro A, Rius V (2000) Validation of the MCNP code for the simulation of Ge-detector calibration. Nucl Instr Meth Phys Res A. 450:88-97
12
Rodenas J, Pascual A, Zarza I, Serradell V, Ortiz J, Ballesteros L (2003) Analysis of the influence of germanium dead layer on detector calibration simulation for environmental radioactive samples using the Monte Carlo method. Nucl Inst Meth Phys Res A. 496:390–399 Vidmar T, Vodenik B (2010) Extended relative method of activity determination. Appl Rad Isot. 68:2421–2424
Highlights
Exact knowledge of the detector dimension is not necessary There is no need to have standard source according to the sample It is a simple method that can be done at any laboratories
13
PII: DOI: Reference:
S0969-806X(16)30835-0 http://dx.doi.org/10.1016/j.radphyschem.2016.12.024 RPC7354
To appear in: Radiation Physics and Chemistry Received date: 17 August 2016 Revised date: 28 December 2016 Accepted date: 29 December 2016 Cite this article as: Pouneh Tayyebi, Fereydoun Abbasi Davani, Mohsen Tabasi and Hossein Afarideh, A novel technique for detection efficiency determination of HPGe, Radiation Physics and Chemistry, http://dx.doi.org/10.1016/j.radphyschem.2016.12.024 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A novel technique for detection efficiency determination of HPGe Pouneh Tayyebi1, 2, Fereydoun Abbasi Davani3,*, Mohsen Tabasi1, Hossein Afarideh2 1 Nuclear Science and Technology Research Institute, North Kargar, P. O. Box 113658486, Tehran, Iran 2 Department of Energy Engineering and Physics, Amirkabir University of Technology, Hafez 424, P. O. Box 15875-4413, Tehran, Iran 3 Department of Radiation Application, Shahid Beheshti University, Velenjak, P. O. Box 1983969411, Tehran, Iran * [email protected]
Abstract In this work, we present an experimental method to determine the detection efficiency of HPGe when the reference source according to the geometry of interest is not accessible. We use known activity point sources (PS) of
152
Eu,
137
Cs,
241
Am and
133
Ba to find the
detection efficiency for disc source (DS) geometry. It can be assumed that a DS consists of several PS’s. Mapping the detector surface by means of
137
Cs PS shows that there is
radial symmetry for detection efficiency vs. energy. Each radial distance on the detector surface contains some points, which can be considered as a PS. By selecting two points in two different radii and central point, the DS efficiency is obtained. To ensure that the method is correct, we measure the activity of a known activity DS considering DS efficiency obtained by PS’s. The DS comprises
137
Cs,
133
Ba and
60
Co. The relative
difference between the measured and the reported activity of DS in most energies is less than 5%.
1
Keywords Efficiency calibration, HPGe detector, Standard sources, Activity measurement.
1. Introduction High resolution gamma spectroscopy is an efficient method to determine the radionuclides in the samples. Radioactivity measurement by means of HPGe detectors necessitates known detection efficiency. Accurate calibration of the detector efficiency is performed by counting a sample and the standard sources. Source-detector configuration should be the same in the measurement of the sample and standard source as well as their properties such as size, composition, density and radionuclide contents. In many cases, there are not standard sources corresponding to the sample under investigation. Preparation of a standard source is costly and time consuming. So, one must find alternative ways to determine the detection efficiency. To overcome this difficulty, there are some methods presented in other publications such as using Monte Carlo (MC) simulations (Vidmar et al., 2010, Rodenas et al., 2000, Ewa et al., 2001) and combination of MC simulation and genetic algorithm (Ngo Quang Huy et al., 2012). In the Monte Carlo simulation, it is neccessary to have an accurate knowledge of the detector configuration and its dimensions which are usually different from those the manufacturer provides (Andreotti et al., 2014), especially via the old detector because of the dead layer (Rodenas et al., 2003, Chham et al., 2015). Moreover, the accuracy of the simulation must be evaluated (Talavera et al., 2000). The authors reported different uncertainities between MC simulation and experimental value on the order of 5-10 % (Maidana et al., 2016), superior to 20% (Gómez et al., 2015), 10% and 3% (Talavera et al., 2000). MC efficiency transfer method has overcome this problem, since it does not need to optimize manufacturer’s detector parameters with the experimental values (Gómez et al., 2015, Liye et al., 2011, Lepy et al., 2001, Piton et al., 2000). The relative deviations within 5% (Gómez et al., 2015, Liye et al., 2011) and 1-2% (Piton et al., 2000) have been reported in different publications.
2
In the current work, we propose an experimental method to determine the detection efficiency for a disc source (DS) by means of point sources (PS). At first, the whole detector surface was scanned by
137
Cs PS. The results showed that there is radial
symmetry for efficiency in the low energy, 32.19 and 36.4 keV, and high energy, 661.657 keV. Due to radial symmetry, one point in each radius was selected as a reference point for measurement. By determination of the efficiency in these points, one can find the DS efficiency. To evaluate the method, the activity of known activity DS containing 133
137
Cs,
Ba and 60Co was measured considering DS efficiency, which was obtained by PS’s.
2. Materials and Methods 2.1.
Spectroscopy system
The experimental measurements were performed with a coaxial n-type HPGe detector which has a nominal 70% relative efficiency. The diameter and the thickness of Ge crystal is 73 mm and 84.1 mm, respectively. The window is carbon fiber. The detector was shielded with a cylindrical lead wall of 13 cm in thickness, and a copper foil of 2 mm in thickness. Source to detector distance is 8 mm. Gamma rays spectra were obtained by a digital multichannel analyzer and were analyzed by the GammaVision 32 V6.07 program.
2.2.
Radioactive source
A multigamma Amersham standard disc source contatining
137
Cs,
133
Ba and
60
Co was
considered as a reference source. It has diameter and active part of 9.5 cm and 7.0 cm, respectively. The planar sources with an active part of 4 mm in diameter from POLATOM were used. The active part is placed central between two plexyglass discs with 12 mm diameter and 1 mm height each one. In Table 1, the activities of the sources at the moment of the experimentation are listed.
3
Table 1 The characteristics of the sources Source
Activity (Bq) Uc (%) Ba 16711.5 2.0 137 Cs 29174 2.0 Point 152 Eu 20980 2.0 241 Am 45154 2.0 137 Cs 5852.9 Disc 133Ba 1772.3 60 Co 348.57 133
In IEEE Std 325, a point source is defined as a disc in which the diameter of the active region of radionuclide is ≤ 2 mm. By using Monte Carlo simulation with MCNPX2.7e, it can be shown that the planar source with an active part of 4 mm can be regarded as a point source. In the simulation, a typical HPGe detector and two sources with radius 0 (as a point source) and 2 mm were considered. The sources were placed 8 mm (as in the experiments) above the detector endcap on its axis. Detection efficiencies for two sources were calculated using pulse hieght tally f8. Fig. 1 shows the detector efficiency vs energy. It shows that, in spite of the different geometry, the two source have the same efficiency. So, we considered the planar source with an active part of 4 mm as a point source.
Fig. 1 Detector efficiency for two sources with radius of 0 (rectangles) and 2 mm (circles). Source to detector distance is 8 mm
4
2.3.
Source holder
To ensure that the detector has radial symmetry for efficiency, its surface was scanned with 137Cs point source. A polyethylene source holder with the diameter and thickness of 6.5 cm and 0.5 cm, respectively was used. It has 19 places to fix the point source. Fig. 2 depicts the holder with 19 circles numbered 1 to 19.
Fig. 2 Polyethylene source holder with 19 places for mapping the detector surface. The diameter of the circles is according to that of the sources, i.e. 12 mm
2.4.
Determination of the radial symmetry
The radial symmetry was determined by mapping the surface of the detector using the 137
Cs source. The response of the HPGe to 19 different source positions was measured.
Each spectrum was acquired during 600 s and repeated 3 times. There are 3 diagonal sets named set 1 to 3. Each set has 5 points characterized by the numbers shown in Fig. 2 and listed in Table 2. The results of mapping the detector in these 3 sets and 3 energies of 137
Cs are represented in Fig. 3. In this figure, the ratio of the counts in radius r,C(r), to
that of center, C(0), is shown v.s distance from the center of holder. The point number 19 (center of holder) is considered as 0 and center to center distance is 12 mm.
Table 2 Three diagonal sets and their points Set 1 -1.2 0
Set 2 -1.2 0 1.2
2.4
-2.4
19
3
5
r* -2.4 1.2 2.4 -2.4 Point 7 16 19 13 1 9 17 No. *Distance from center of the holder (cm)
5
14
Set 3 -1.2 0
1.2
2.4
15
18
11
19
6
Fig. 3 Ratio of the counts in radius r, C(r), to that of center, C(0), for a) E=32.19 keV, b) E=36.4 keV, and c) E=661.657 keV for 3 diagonal sets. The results show the radial symmetry on the detector surface It can be seen that the counts decrease moving away in radial direction. According to the uniformity observed in Fig. 3, there is a radial symmetry in each data set. It means that there is no need to measure all 5 points; just 2 points related to 2 different radii and central point are sufficient. Moreover, it shows that there is radial symmetry in low (32.19 and 36.4 keV) and high energies (661.66 keV). Fig. 4 shows that there is a uniformity between the points in each radius. So, we selected point numbers of 1, 13 and 19 as the candidate points in set 1 in distance of 2.4 cm, 1.2 cm and 0 cm from center, respectively. In Table 3, the minimum and maximum efficiencies between the points in each radius are presented.
7
Fig. 4 Uniformity of the efficiency between the points in each radius in E=32.19 keV Table 3 Minimum and maximum efficiency between the points at each radius and their deviations Efficiency (%) Deviation (%) Min Max 1-12 11.36 13.90 18.27 13-18 19.34 21.07 8.21 1-12 14.63 15.65 6.51 13-18 18.77 19.58 4.14 1-12 5.11 5.42 5.72 13-18 6.49 6.78 4.28
Energy (keV) r (cm) Points 32.19 36.4 661.657
2.5.
2.4 1.2 2.4 1.2 2.4 1.2
Determination of the full energy peak efficiency
Full energy peak (FEP) efficiency,ε (E), is calculated from Eq. (1). (1) where: N is the net counts under full-energy peak, f(E) is the probability of gamma emission in energy E,
8
A is the activity in Bq, and t is the live time of the measurement in s.To determine the efficiency for a DS, we assumed that a DS consists of several PS’s in each radius of the DS. So, the DS efficiency can be written as: ∑ ∑
(2)
where DSEε(E) is the DS equivalent efficiency in energy E, Ci is the number of points in radius i, n is the number of radius, and ε(E)i is the efficiency at selected point in radius i. Consequently, in our case ∑
(3)
∑
3. Results and discussion Table 4 shows the results of FEP efficiency (FEPE) measurement in 3 selected points. The results of DSEε are compared with the efficiency of DS and are given in Table 4. The relative difference is less than 4% in most energies. Fig. 5 shows the DSEε and DS efficiency vs energy. It is worth noting that in this experiment we used the same energies between the DS and PS, so no correction on true coincidence summing is necessary because all efficiency values DS and PS are affected in the same way. For other radionuclides with different true coincidence summing, it should be corrected.
Table 4 FEP efficiency for 3 selected points, DSE and DS
9
Source
241
Am
133
Ba
137
152
Cs
Eu
Energy (keV) 13.8 26.3446 59.54 80.9971 160.6109 276.3997 302.8510 356.0134 383.8481 36.4 661.657 121.7871 244.6975 344.2785 411.1163 867.37
Intensity (%) (ENDF) 42 2.4 35.9 34.06 0.645 7.164 18.33 62.05 8.94 1.3 (NuChart)
89.9 28.668 7.607 26.56 2.24 4.258
FEPE at point No. 1
13
19
2.34 6.41 19.95 13.21 9.53 6.01 6.43 6.13 5.30
3.02 8.13 28.86 15.21 11.30 6.42 6.96 6.93 6.40
3.12 8.22 30.45 15.48 11.23 6.66 7.04 7.13 6.13
Disc Source Equivalent (DSE) 2.60 7.05 23.32 13.96 10.13 6.17 6.63 6.43 5.69
------14.23 9.93 6.75 6.89 6.47 5.72
Deviation of DSE from DS (%) ------1.9 2.01 8.59 3.77 0.62 0.53
14.63
18.77
19.58
16.20
15.59
3.91
5.20 11.62 6.47 5.98 5.41 2.45
6.50 13.10 6.90 6.92 6.06 2.42
6.78 13.30 6.93 7.12 6.16 2.42
5.69 12.18 6.63 6.34 5.66 2.44
5.49 -----------
3.64 -----------
Disc Source (DS)
Fig. 5 DSEε (rectangels) and DS (circles) efficiency For validation of the presented method, the activity of the DS was measured using DSEε. The measured activity values were compared with the reported one and are presented in Table 5. As seen, the relative difference is less than 5% in most energies.
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Table 5 Determination of DS activity Source
133
Ba
137
Cs
Energy (keV) 80.9971 160.6109 276.3997 302.8510 356.0134 383.8481 36.4 661.657
Activity (Bq) Reported Measured 1772.3 1806.56 1772.3 1737.14 1772.3 1937.29 1772.3 1843.76 1772.3 1781.95 1772.3 1782.51 5852.9 5633.86 5852.9 5642.65
Deviation of measured activity from reported (%) 1.93 1.98 9.31 4.03 0.55 0.58 3.74 3.59
4. Conclusion We presented an experimental method to determine the efficiency of HPGe when the reference source according to the geometry of interest is not accessible. In this approach, effciencies of PS’s were used to obtain DS efficiency. The relative differences between the reported activity of disc source and that measured by presented method are less than 5%. Changing the effective parameters such as dimension of detector, the number of points and radii, are not discussed here. It is clear that increasing the number of points exhibits the better definition of DS; hence the relative difference will be decreased. In the future we shall endeavor to apply this method to determine the activity of a volume source.
References Andreotti E, Hult M, Marissens G, Lutter G, Garfagnini A, Hemmer S, von Sturm K (2014) Determination of dead-layer variation in HPGe detectors. Appl Rad Isot. 87:331-335 Chham E, Pinero Garcia F, El Bardouni T, Angeles Ferro-García M, Azahra M, Benaalilou K, Krikiz M, Elyaakoubi H, El Bakkali J, Kaddour M (2015) Technical note Monte Carlo analysis of the influence of germanium dead layer thickness on the HPGe gamma detector experimental efficiency measured by use of extended sources. Appl Rad Isot. 95:30-35 11
Ewa I.O.B, Bodizs D, Czifrus Sz, Molnar Zs (2001) Monte Carlo determination of full energy peak efficiency for a HPGe detector. Appl Rad Isot. 55:103-108 Garcia-Talavera M, Neder H, Daza M.J, Quintana B (2000) Towards a proper modeling of detector and source characteristics in Monte Carlo simulations. Appl Rad Isot. 52:777-783 Gamma Vision, Gamma-ray Spectrum Analysis and MCA Emulation for MS Windows, Software User’s Manual, version 32, V6.07
http://www.oecd-nea.org/janisweb/tree/RDD/'ENDF/B-VII.1'/RDD IEEE Std 325-1996 IEEE Standard Test Procedures for Germanium Gamma-Ray Detectors Liye L, Jizeng M, Franck D, de Carlan L, Binquan Z (2006) Monte Carlo efficiency transfer method for full energy peak efficiency calibration of three type HPGe detectors: A coaxial N-type, a coaxial P-type and four BEGe detectors. Nucl Instr Meth Phy Res A 564:608–613 Lepy M.C, et.al (2001) Intercomparison of efficiency transfer software for gamma-ray spectrometry. Appl Rad Isot. 55:493-503 Maidana N.L, Vanin V.R, García-Alvarez J.A, Hermida-López M, Brualla L (2016) Experimental HPGe coaxial detector response and efficiency compared to Monte Carlo simulations. Appl Rad Isot. 108:64-74 Morera-Gómez Y, Cartas-Aguila H.A, Alonso-Hernández C.M, Bernal-Castillo J.L, Guillén-Arruebarren A (2015) Application of the Monte Carlo efficiency transfer method to an HPGe detector with the purpose of environmental samples measurement. Appl Rad Isot. 97:59-62 Ngo Quang Huy, Do Quang Binh, Vo Xuan An (2012) A study for improving detection efficiency of an HPGe detector based gamma spectrometer using Monte Carlo simulation and genetic algorithms. Appl Rad Isot. 70:2695–2702 NuChart, Version 4.0.0, 1998 Piton F, Lepy M.C, Be M.C , Plagnard J (2000) Efficiency transfer and coincidence summing corrections for gamma-ray spectrometry. Appl Rad Isot. 52:791-795 Rodenas J, Martinavarro A, Rius V (2000) Validation of the MCNP code for the simulation of Ge-detector calibration. Nucl Instr Meth Phys Res A. 450:88-97
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Rodenas J, Pascual A, Zarza I, Serradell V, Ortiz J, Ballesteros L (2003) Analysis of the influence of germanium dead layer on detector calibration simulation for environmental radioactive samples using the Monte Carlo method. Nucl Inst Meth Phys Res A. 496:390–399 Vidmar T, Vodenik B (2010) Extended relative method of activity determination. Appl Rad Isot. 68:2421–2424
Highlights
Exact knowledge of the detector dimension is not necessary There is no need to have standard source according to the sample It is a simple method that can be done at any laboratories
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