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Application of PHOTON simulation software on calibration of HPGe detectors
Nuclear Instruments and Methods in Physics Research A 799 (2015) 159–165
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Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Application of PHOTON simulation software on calibration of HPGe detectors J. Nikolic a,n, J. Puzovic b, D. Todorovic a, M. Rajacic a a b
University of Belgrade Institute for Nuclear Sciences Vinča, Mike Petrovica Alasa 12-16, 11001 Belgrade, Serbia University of Belgrade Faculty of Physics, Studentski trg 6, 11000 Belgrade, Serbia
art ic l e i nf o
a b s t r a c t
Article history: Received 4 March 2015 Received in revised form 30 July 2015 Accepted 1 August 2015 Available online 12 August 2015
One of the major difficulties in gamma spectrometry of voluminous environmental samples is the efficiency calibration of the detectors used for the measurement. The direct measurement of different calibration sources, containing isolated γ-ray emitters within the energy range of interest, and subsequent fitting to a parametric function, is the most accurate and at the same time most complicated and time consuming method of efficiency calibration. Many other methods are developed in time, some of them using Monte Carlo simulation. One of such methods is a dedicated and user-friendly program PHOTON, developed to simulate the passage of photons through different media with different geometries. This program was used for efficiency calibration of three HPGe detectors, readily used in Laboratory for Environment and Radiation Protection of the Institute for Nuclear Sciences Vinca, Belgrade, Serbia. The simulation produced the spectral response of the detectors for fixed energy and for different sample geometries and matrices. Thus obtained efficiencies were compared to the values obtained by the measurement of the secondary reference materials and to the results obtained by GEANT4 simulation, in order to establish whether the simulated values agree with the experimental ones. To further analyze the results, a realistic measurement of the materials provided by the IAEA within different interlaboratory proficiency tests, was performed. The activities obtained using simulated efficiencies were compared to the reference values provided by the organizer. A good agreement in the mid energy section of the spectrum was obtained, while for low energies the lack of some parameters in the simulation libraries proved to produce unacceptable discrepancies. & 2015 Elsevier B.V. All rights reserved.
Keywords: HPGe Calibration PHOTON
1. Introduction One of the major difficulties in gamma spectrometry of voluminous environmental samples is the efficiency calibration of the detectors used for measurement. Most often the calibration by measuring standard sources is performed, a number of semi empirical methods have also been developed and, in the present time, the Monte Carlo simulations are often used to generate the spectral response of the detector [1,2]. The example of Monte Carlo simulation codes is GEANT4. It is developed to simulate the response of complex particle detectors and for variety of different high energy and nuclear interactions [3]. In case of gamma spectrometry, this code needs choosing an electromagnetic physics and corresponding database used in the development of the application for the particular detector, which may be time consuming and may require proficiency in programming language [4]. Once an application is developed, the use of GEANT4 is relatively easy.
n
Corresponding author. Tel./fax: þ 381 116308467. E-mail address: [email protected] (J. Nikolic).
http://dx.doi.org/10.1016/j.nima.2015.08.002 0168-9002/& 2015 Elsevier B.V. All rights reserved.
For users that are not proficient in programming, or for any other reason need to have a readymade application, a dedicated and user-friendly program PHOTON provides a useful tool [1]. PHOTON uses a simplified input-file structure where the system and the source are described as a series of cylindrical zones. The zones that the photons traverse can be declared as active media (sources and detectors) and others as passive media (scatterers and absorbers), each with given properties [1]. After the construction of the measurement geometry, a schematic view of the system is available. It is written in Borland Delphi and contains Borland database engine and the user interface is Windows application. It also contains its own build-in cross-section libraries. However, Rayleigh scattering, fluorescence yields, form factors, and scattering factors are not included in the cross-section libraries [5]. These simplifications have proven especially useful in environmental measurements [6], where on one hand, an ultimate precision in calibration is usually not required and on the other, a variety of different sources might be measured in the laboratory. Having talked to some other gamma spectrometry practitioners, the authors of this paper found that the using of such simplified tool would be beneficial.
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The aim of this paper is to perform an efficiency calibration of three HPGe detectors, using PHOTON simulation software and to present and validate the results. The results of the calibration will be compared to the efficiencies obtained by measuring a set of secondary reference materials produced in the Laboratory for Environment and Radiation Protection of the Institute for Nuclear Sciences Vinca, Belgrade, Serbia and to the results obtained by GEANT4 simulation. The comparison should show the agreement between the results and limitations of the application of the method. The efficiencies obtained by the PHOTON simulation will then be applied on a realistic measurement of the secondary reference materials issued within the various interlaboratory proficiency tests. The measurement uncertainties for both simulated and the experimental values will also be calculated. The efficiency obtained by PHOTON and the experimental efficiency should be within the uncertainty limits in order to be declared as acceptable.
2. Materials and methods The PHOTON simulation software defines the interaction between the γ photon and the medium through three main mechanisms: photoelectric interaction, Compton scattering and pair production. The probability of the interaction depends on the properties of the medium and on the photon energy. The crosssections and linear absorption coefficients for the interactions are interpolated and tabulated for every defined medium at the beginning of the simulation [7]. For the actual photon energy the random interaction point for a given interaction is then found according to the following expression [1]: L¼
1
μ
ln η
ð1Þ
where L represents the path length between two subsequent interactions of the photon with the medium (or the emission of the photon and the first interaction), μ is the linear absorption coefficient for a given interaction and a given medium, while η is the pseudo-random number from the (0, 1) interval [1]. For the transport of the electrons, some simplifying algorithms exist. PHOTON code uses the Bethe–Heitler formula, with the crosssections given by Seltzer and Berger in Ref. [8]. The interaction with the smallest distance to the interaction point (the smallest L) is chosen and the propagation of the photon through media is followed. The photon originates from and traverses through zones specified as consecutive cylinders with defined radius r and height h. If L is larger than the crossing point of the two zones, it is considered that the interaction did not occur in the first zone and the starting point is again selected, at the beginning of the next zone and so on until the interaction occurs. If L is larger than the dimension of last zone, it is considered that the interaction did not occur. The geometrical characteristics of the measurement system are defined in the specified module of the program. The detectors considered for the simulation were the ones commonly used in our laboratory: two p-type detectors with the relative efficiency of 20% (named Detector 1) and 50% (named Detector 3) and one n-type detector with the relative efficiency 18% (named Detector 2). The characteristics of the detectors are presented in the Table 1. The geometrical parameters needed for the simulations, were defined according to the technical features obtained from the manufacturer. In case of the central void and top dead layer, which are not given in the manufacturer's certificate, the parameters were estimated based on the known dimensions of other detectors produced by the same manufacturer [9–11]. The geometry of the measured secondary reference material was also input in the program, as well as the chemical composition of the matrix. Assuming a cylindrical symmetry, geometry includes: the dimensions of the
germanium crystal with the top dead layer, the aluminum end cap, the central void and the sample and its container. The geometrical description of the measurement system is simplified, since it does not take into account the buletization and the side dead layers. The chemical composition of the secondary reference material is defined by its chemical formula, mass fraction and density. The spectra that are a result of the simulation are defined by the zone in which the deposition of energy is considered, the number of channels into which it will be simulated, the energy calibration and the peak full width at half maximum (FWHM) which is given as an empirical equation for a given type of the detector [1]. For the purpose of efficiency calibration in this paper, the simulation of the detector response on monoenergetic gamma rays was used. Namely, the response of the detector on the single energy emitted from the secondary reference material was used to calculate the efficiency on that energy and in that specific matrix. This choice excludes the need for the coincidence summing correction. The peak shape definition was performed using FWHM and FWTM (full width at tenth maximum) parameters of the detectors. Finally, the result of the simulation was a single full energy peak at each energy emitted by the radionuclide present in the secondary reference material and for all investigated secondary reference materials. The efficiency at the investigated energy was determined as the net count in the simulated peak divided by the total number of simulated events (emitted photons). For the simulation, the equivalent of the measurement uncertainty can be estimated following the reasoning presented in Ref. [4]. For the input parameters of the simulation, the uncertainty has to be included in the uncertainty budget [4]. Since the probability of photons passing through different layers of the detector and sample is the product of individual probabilities of photon passing through an individual layer of the detector or sample, it gives the guideline for estimation of the uncertainty equivalent. Since the square of the combined relative uncertainty equals to the sum of squares of relative uncertainties, the equivalent of the relative uncertainty for the simulated efficiency, uðεÞsimulation , can be estimated according to Ref. [12] qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi X uðεÞsimulation ¼ ð2Þ ðδxi Þ2 where δxi represents the relative uncertainty of the parameter xi (values that are input in the simulation). The geometry parameters that are defined in the simulation are 6 parameters of the detector geometry (crystal diameter and length, crystal cavity diameter and length, window thickness and window to crystal gap) and 3 parameters of sample geometry (matrix density, radius and height of the sample). Since the detector model is simplified in the simulation, we have to assume that the geometry will contribute significantly to the relative uncertainty of the results. The sum of uncertainties for crystal diameter and length and crystal cavity diameter and length can be estimated to be 5.0%, in total. The sum of uncertainties for window thickness and window to crystal gap for Detector 1 and Detector 2 is estimated at 10.0%, while it was 5.0% for Detector 3. Those contributions to the uncertainty were estimated according to the previous experience in using GEANT4 and EFFTRAN [4,11,13] for detector calibration. Relative uncertainties of height of the sample were estimated to be 0.1% in case of water samples and 1.0% in case of soil, sand, charcoal and grass samples. The density of the samples was calculated by dividing the measured mass of the sample with the volume of the sample. Since all samples were cylindrical, the volume was calculated as r2Hπ where r is measured inner radius of the container and H is the sample filling height. The uncertainty of r is estimated as the uncertainty of the measuring instrument (ruler). That leads to the conclusion that the uncertainty of the sample density is 1.0–2.0%. The equivalent of relative combined uncertainty of the simulated efficiency was estimated at 7.1–11.4%
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Table 1 The characteristics of the detectors.
Geometry and type of detector Relative efficiency Resolution on 122 keV on 1332 keV Peak/Compton ratio Crystal diameter Crystal lenght Crystal to window distance Central void (diameter length) Entry window
Detector 1
Detector 2
Detector 3
Closed coaxial–p type Canberra 20% (certificate) 0.850 keV (certificate) 1.8 keV (certificate) 51:1 (certificate) 49.5 mm 56.5 mm 5.5 mm 10 mm 40 mm Al
Closed reverzibile coaxial–n type Canberra 18% (certificate) 0.759 keV (experimental) 1.69 keV (experimental) 56.1:1 (experimental) 48 mm 48.5 mm 5 mm 10 mm 40 mm Be
Closed coaxial–p type Canberra 50% (certificate) 1.00 keV (experimental) 1.9 keV (experimental) 65:1 (certificate) 65 mm 67 mm 5 mm 10 mm 55 mm Al
Table 2 The geometry, composition and density of the secondary reference materials. Symbol d denotes the diameter of the container and h is the sample filling height. The thickness of all containers is 1 mm. Secondary reference material
Geometry
Composition
Density [g/cm3]
Charcoal 1 Soil 1 Sand 1 Charcoal 2 Soil 2 Sand 2 Grass 1 Grass 2 Water 1 Water 2 Aerosol
Cylinder d¼ 67 mm, h ¼ 36 mm
C 100% SiO2 90%, Ca 1%, K 4%, Fe 1%, C 4% SiO2 100% C 100% SiO2 90%, Ca 1%, K 4%, Fe 1%, C 4% SiO2 100% C 99% Other 1% C 99% Other 1% H2O 100% H2O 100% SO4 15%, NH4 15%, NO3 15%, CH 50%
0.49 1.38 1.59 0.45 1.43 1.56 0.30 0.26 1.01 1.01 0.57
Cylinder d¼ 85 mm, h ¼ 40 mm Cylinder d¼ 85 mm, h ¼ 47 mm Cylinder d¼ 85 mm, h ¼ 45 mm Cylinder d ¼67 mm, h ¼ 15 mm Cylinder d¼ 67 mm, h ¼ 28 mm Cylinder d¼ 50 mm, h ¼ 60 mm Cylinder d¼ 60 mm, h ¼ 75 mm Vial d ¼32 mm, h ¼ 12 mm
To verify the results, the efficiencies obtained in the simulation were compared to the experimentally obtained values. Experimental efficiency calibration is readily performed in the Laboratory for Environment and Radiation Protection of the Institute for Nuclear Sciences Vinca, Belgrade, Serbia. For the purpose of calibrating the detectors for environmental samples, a set of secondary reference materials was produced by spiking the chosen matrices with certified radioactive mixture solution ER X 9031-OL-426/12 issued by Czech Metrological Institute, Inspectorate for Ionizing Radiation. The radioactive solution contained following radionuclides: 241Am, 109Cd, 139 Ce, 57Co, 60Co, 137Cs, 203Hg, 113Sn, 85Sr and 88Y, with the energies that span from 59 keV to 1898 keV with total activity of 1342 Bq at reference date 31.08.2012. Matrices and geometry of secondary reference materials was aerosol placed in vial, soil, sand, charcoal and mineralized grass in cylindrical containers and water in polystyrene cylinder. The secondary reference materials were prepared by applying the procedure with activated carbon, as defined in Refs. [14,15]. The standardized solution had been diluted to the adequate specific activity by adding a carrier solution. This radioactive solution was homogeneously mixed in the bulk matrix materials previously mechanically prepared. The homogeneity was checked by measuring the aliquots of the bulk spiked matrix and was found to be below 2.0% [15]. Detailed procedures were presented in Ref. [15]. The secondary reference materials were placed in four different cylindrical polystyrene containers. The thickness of the containers was 1 mm (bottom and side walls). The geometry, composition and density of the calibration samples are listed in Table 2. After analyzing the spectra for experimental calibration, the efficiency at the given energy was calculated according to
ε¼
N U CðEÞ t UP γ UA
ð3Þ
where N represents the net count at the energy E, t is counting time, Pγ is emission probability, C(E) is coincidence correction
factor and A is source activity on the given energy, with the decay correction. Relative combined measurement uncertainty for the experimental efficiencies was calculated according to the following equation [11]: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uðεÞ ¼ ðδAÞ2 þ ðδNÞ2 þ ðδMÞ2 þ ðδPÞ2 ð4Þ where δA represents relative uncertainty of the radioactive solution activity given by the manufacturer, δN is the relative uncertainty of the number of photons in the full energy peak obtained by measuring the secondary reference material, δM is the uncertainty introduced in the process of production of the secondary reference material and δP represent other components such as sample position, “run to run” uncertainty and other unquantified contributions. Value δAþ δM is estimated to be approximately 2.0–3.0%, while δP is estimated to 2.0%. The estimation of δAþ δM was made according to Ref. [15] and the estimation of δP was based on our experience [3,10,12]. Other uncertainties are negligible. Relative measurement uncertainty uðεÞ for all energies was around 5.0% at 1σ level of confidence.
3. Results and discussion The simulation was conducted on 106 events for all three detectors and for all secondary reference materials that are used for experimental calibration. The material of the sample was defined by its chemical formula and density. Sample dimensions are also measured with care, and are constructed in the simulation code accordingly. The source to detector distance was 0 mm as it was in the measurement, meaning that the sample (with the container) was placed directly on the detector cap. The peaks were simulated at following energies: 46.5 keV (210Pb), 59.5 keV (241Am), 88 keV (109Cd), 122.1 and 136.5 keV (57Co), 165.8 keV (139Ce), 279.2 keV (203Hg), 392 keV (113Sn), 514 keV (85Sr), 661.7 keV
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Detector 1 aerosol water 1 grass 1 charcoal 1 soil 1 sand 1
1,3
1,2
water 2 grass 2 charcoal 2 soil 2 sand 2
1,2
εPHOTON/εexp
εPHOTON/εexp
1,1
1,0
Detector 2 aerosol water 1 grass 1 charcoal 1 soil 1 sand 1
1,3
1,1
1,0
0,9
0,9
0,8
0,8
0,7
water 2 grass 2 charcoal 2 soil 2 sand 2
0,7
0
200
400
600
800
1000
1200
1400
1600
1800
0
2000
200
400
600
E [keV]
1000
1200
1400
1600
1800
2000
E [keV] Detector 3 water 1 grass 1 charcoal 1 soil 1 sand 1
1,3
1,2
εPHOTON/εexp
800
aerosol grass 2 charcoal 2 soil 2 sand 2
1,1
1,0
0,9
0,8
0,7 0
200
400
600
800
1000
1200
1400
1600
1800
2000
E [keV] Fig. 1. εPHOTON/εexp ratio, where εPHOTON represents the efficiency obtained by using the PHOTON simulation аnd εexp is experimental efficiency, for all secondary reference materials.
(137Cs), 898 and 1836 keV (88Y) and 1173.2 and 1332.5 keV (60Co). The net count at each full energy peak was calculated as a sum of counts in certain number of channels. The number of channels that will be used is determined according to the FWHM and FWTM for each detector. FWHM is required parameter in the simulation and is defined as [16] pffiffiffi FWHM ¼ a þb U E
ð5Þ
where a and b represent the coefficients characteristic for each detector. Values for a and b were defined by GENIE2000 gamma spectrometry analysis software in the realistic spectrum of the secondary reference material for which the simulation is performed. FWTM was also defined by the GENIE2000. In the Laboratory, as a part of quality control and quality assurance procedure, FWHM and FWTM are readily checked for stability on a weekly basis, so it is confirmed that these characteristics of the detector are not changing with time. The typical FWTM in measured spectra was from 2.5 keV for low, to 4.7 keV for energies above 1200 keV in all three detectors. It is assumed that the simulated peak should have the same width at the base as the one in the measured spectrum. The efficiency at a given energy is then derived by dividing the net
count in the simulated full energy peak by number of events simulated (106). The measurement of the secondary reference materials was conducted on all three detectors for the duration of 60,000 s. The samples were placed coaxially on the end cap of the detector. Background radiation was measured by placing a blank sample of the same geometry and composition as the secondary reference material. Background spectrum was subtracted from the spectrum of the calibration sample using GENIE2000 software. After analysis of the spectrum, experimental efficiencies were calculated using Eq. (3). Coincidence correction factors were calculated using EFFTRAN software [17]. The corrections ranged from 0.1% for low, to as much as 9.2% for high energies. Coincidence was more prominent for Detector 2 due to its beryllium window and the fact that it is an n-type detector. For Detector 1 and Detector 3, corrections were needed only for energies of 88Y and 60Co. Both calculated and measured efficiencies were then fitted using following fitting function [18]
ln ε ¼
5 X i¼1
ai ðln EÞi 1
ð6Þ
J. Nikolic et al. / Nuclear Instruments and Methods in Physics Research A 799 (2015) 159–165
Detector 1 aerosol water 1 grass 1 charcoal 1 soil 1 sand 1
1,4 1,3
water 2 grass 2 charcoal 2 soil 2 sand 2
1,3 1,2
ePHOTON / eGEANT4
εPHOTON/εGEANT4
Detector 2 aerosol water 1 grass 1 charcoal 1 soil 1 sand 1
1,4
1,2 1,1 1,0 0,9
water 2 grass 2 charcoal 2 soil 2 sand 2
1,1 1,0 0,9
0,8
0,8
0,7
0,7
0,6
163
0,6 0
200
400
600
800
1000
1200
1400
1600
1800
2000
0
200
400
600
E [keV]
800
1000
1200
1400
1600
1800
2000
E [keV] Detector 3 water 1 grass 1 charcoal 1 soil 1 sand 1
1,4 1,3
aerosol grass 2 charcoal 2 soil 2 sand 2
εPHOTON/εGEANT4
1,2 1,1 1,0 0,9 0,8 0,7 0,6 0
200
400
600
800
1000
1200
1400
1600
1800
2000
E [keV] Fig. 2. εPHOTON/εGEANT4 ratio, where εPHOTON represents the efficiency obtained by using the PHOTON simulation аnd εGEANT4 is the efficiency obtained by using GEANT4 simulation, for all secondary reference materials.
where ε is efficiency, E is energy given in keV and ai are fitting coefficients. It is established that for our detectors, the best calibration curve is achieved by using the function with i¼5 (the 4th order polynomial). The obtained calibration curve is used in any realistic measurement. During simulation it has been noted that for energies below 80 keV, the full energy peaks were significantly higher than in the measured spectrum of the secondary reference materials. This problem is noted, in some degree, in all codes based on Monte Carlo simulation, since the simulation is sensitive to all imperfections of the detector geometry, especially the dead layer thickness and homogeneity and other defects [19]. Efficiency calibration for low energies is proved to be a significant drawback and the corrections have to be made in PHOTON code libraries as well. Due to that, the peaks on 46 keV and 59 keV are omitted from further calculations. Experimental efficiencies and efficiencies obtained by PHOTON were compared and the ratio between the simulated and measured efficiencies, for all investigated secondary reference materials, are presented in Fig. 1. As it can be seen from the Fig. 1, the discrepancies between simulated and experimental efficiencies do not show any specific trends. As expected, the greatest discrepancies are for low energies and are larger for heavier matrices (soil and sand). The relative
discrepancies ranged from 0.2% to 16.9% for Detector 1, from 0.1% to 22.2% for Detector 2 and from o0.1% to 19.1% for Detector 3. Although the ranges of the relative discrepancies are large, most of the individual discrepancies are around 5–10%. Larger discrepancies (10–15%) can be attributed to an imperfect knowledge and simplified construction of the complex geometry of the detector and/or to an inappropriate account for the imperfections of the process of charge collection [18] The unacceptably high discrepancies (discrepancies that are more than twofold higher than the measurement uncertainty of the experimental results) that were up to 30% were noticed for sand 1 and sand 2 secondary reference materials for Detectors 2 and 3 and soil 1 and soil 2 for Detector 1. The reason for the large discrepancies in the part of the spectrum with energies above 1200 keV, in case of Detector 1 and Detector 2, is in the simplifications in the cross-section libraries. It has been shown in [5] that the PHOTON spectral shape and the yields of the peaks with the results of the MCNP 4B code without bremsstrahlung, show good agreement. That leads to the conclusion that the adding of proper bremsstrahlung production processes in the PHOTON code would greatly improve results for the energies 4 1200 keV. It can be noted that all the results in the mid energy section of the spectrum (100–1200 keV roughly) show good agreement, thus indicating the limitations of the applicability of the PHOTON simulation.
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Table 3 Activity concentration of the analytes calculated with efficiencies obtained using PHOTON simulation, GEANT4 simulation and target values. Values denoted with the asterisk n were obtained as a mean value of the results reported by the participants. Letter N denotes an unacceptable result. Detector 1 [Bq/kg] PHOTON
Detector 2 [Bq/kg] GEANT4
PHOTON
IAEA-TEL-2012-03, hay, measured in geometry grass 2 Cs 840 7 80 8007 80 820 7 60 Cs 320 7 30 3007 30 310 7 30 IAEA-TEL-2014-03, sediment, measured in geometry sand 2 238 U / 207 2 226 Ra / 237 2 137 Cs / 13 72 228 Ac / 13 72 40 K / 310 7 30 IAEA-TEL-2014-03, water, measured in geometry water 2 137 Cs 13.5 7 0.5 12.0 7 0.5 / 134 Cs 22.2 7 0.7 20.4 7 0.7 / 210 Pb 277 3 N 327 4 N / IAEA-TEL-2011-03, water, measured in geometry water 2 60 Co / 8.17 0.8 133 Ba / 2.4 70.4 137 Cs / 3.3 70.3 134 Cs / 4.2 70.4 152 Eu / 7.8 7 0.5 241 Am / 2.2 70.2 IAEA-TEL-2012-03, water, measured in geometry water 1 241 Am / / 137 Cs / / 137
134
Detector 3 [Bq/kg] GEANT4
PHOTON
Target value [Bq/kg] [17] GEANT4
860 7 30 N 3307 20
7307 50 290 7 20
8107 30 3107 20
785 724 306 720
227 2 17.6 70.7 11.0 7 0.4 11.6 7 0.4 2787 9
157 3 227 2 14.57 0.7 N 137 2 3107 20
21 74 19.8 7 0.9 13.3 7 0.4 11.8 7 0.6 2787 9
16.0 7 3.8n 19.0 7 4.8n 12.0 7 0.4 12.17 1.5n 2707 27n
7.0 7 0.4 2.2 7 0.2 2.9 7 0.3 3.8 7 0.2 7.3 7 0.4 2.2 7 0.2
Since the efficiency calibration was performed for the same three detectors and same secondary reference materials, using GEANT4 simulation, the comparison between efficiencies obtained using PHOTON and GEANT4 was performed. The GEANT4 simulation produced results that are of the similar accuracy as PHOTON simulation in comparison to the experimental values [4,11]. The discrepancies between PHOTON and GEANT4 results (Fig. 2) ranged from 0.1% to 17.1% for Detector 1, from 0.3% to 35.0% for Detector 2 and from 0.4% to 26.0% for Detector 3. The largest discrepancies were, as expected, for heavy matrices (sand 2 and soil 2) and for low energies. To test the validity of the results, a measurement was conducted using reference materials issued by IAEA in the framework of several proficiency tests. The measured reference materials are IAEA-TEL-2012-03, hay, measured in geometry grass 2, IAEA-TEL2014-03, sediment, measured in geometry sand 2, IAEA-TEL-201103, water, measured in geometry water 2 on Detector 1, IAEA-TEL2014-03, water, measured in geometry water 2 on Detector 2 and IAEA-TEL-2012-03, water, measured in geometry water 1 on Detector 3. To evaluate the trueness of the results, using of the utest criterion is recommended in Ref. [20] AIAEA APHOTON ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi q utest ¼ ð7Þ u2IAEA þ u2PHOTON where APHOTON and uPHOTON are activity concentration of the radionuclide in the sample and relative combined uncertainty calculated for results using PHOTON simulated efficiencies and AIAEA and uIAEA is activity and uncertainty published by IAEA. The relative combined uncertainty uPHOTON was calculated according to the following equation: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uPHOTON ¼ uðεÞsimulation 2 þðδNÞ2 þ ðδf it Þ2 ð8Þ where uðεÞsimulation is defined in Eq. (2), δN is relative uncertainty of the sample net count. Measured samples contained radionuclides other than those present in the secondary reference materials investigated in the simulation. That is why efficiencies for energies that are of interest had to be determined. That was done by fitting
/ / /
12.06 70.1 21.4 70.2 49.87 71.23
/ / / / / /
7.6 70.1 2.5 7 0.1 3.17 0.1 3.8 7 0.1 7.7 70.1 2.4 7 0.1
1367 12 110 710
1407 10 1037 7
120.9 7 0.74 102.5 7 0.75
the simulated efficiencies with the function given in Eq. (6). The uncertainty introduced by fitting the simulated efficiencies is represented by δf it and is estimated to be 1.0%. Other sources of the uncertainty were negligible. The same criterion was applied for results obtained using GEANT4 simulated efficiencies. The activity concentrations obtained using PHOTON simulated efficiency and GEANT 4 simulated efficiency, along with the target values provided by the IAEA are presented in Table 3. For this case, the limiting value for the utest parameter was set to 2.58 for a level of probability at 99% to determine if a result passes the test (u o2.58) [21]. As it can be seen from the Table 3, only two results calculated using PHOTON were determined to be unacceptable. One is the result for 137Cs in sediment, measured on Detector 3. In this case, the efficiency was underestimated, thus producing a result that is significantly higher than the target value. Since the matrix of the sample is lighter and has smaller density than the matrix of the secondary reference material, the efficiency applied on this measurement is not adequate. A new simulation using the characteristics of the sample in question, rather than the sand secondary reference material should produce better agreement with the target value. The second unacceptable result is the activity of the 210Pb in the water measured on Detector 2. As it was said, the simulation produced unrealistic values of count for low energy part of the spectrum so the efficiency for 210Pb was extrapolated. In case of Detector 2, which is n-type, the extrapolation did not produce satisfactory result. In general it is not recommended to perform extrapolation, but in cases of Detectors 1 and 3 (p-type) it produced acceptable results for 241Am in water. This can be attributed to the different calibration curve shape for the n-type and p-type detectors. The n-type detector should have a mild slope with relatively high efficiency in low energy part of the spectrum and maximum at about 60 keV, whereas the extrapolation produced to high efficiency without the maximum. By comparing the results obtained using PHOTON and GEANT4 simulated efficiencies, it is noticeable that PHOTON produces higher efficiency for geometries sand 2 and grass 2. The difference
J. Nikolic et al. / Nuclear Instruments and Methods in Physics Research A 799 (2015) 159–165
in the results obtained by these two simulations was significant, but the results were acceptable. For the water samples the PHOTON efficiencies were slightly lower, but the difference in the results between PHOTON and GEANT4 is not significant. This can be taken as the confirmation that the detector model in the PHOTON simulation was treated properly. All the other results, obtained for the radionuclides that emit photons of energy higher than 100 keV are acceptable, proving that PHOTON simulation produced accurate values for efficiency for measured samples. 4. Conclusion In this paper an efficiency calibration was performed using PHOTON, user friendly Monte Carlo simulation code. The calibration was performed for three HPGe detectors, readily used in the Laboratory for Environment and Radiation Protection of the Institute for Nuclear Sciences, Vinca, Belgrade, Serbia. The results of the simulation were compared to the experimental values, obtained by measuring different secondary reference materials. The discrepancies between experimental and simulated spectra were significant for energies o80 keV, so it was decided not to take into account the efficiencies at energies of 46 keV and 59 keV. For energies above 80 keV, the results showed reasonably good agreement with the experimental values. The relative discrepancies ranged from 0.2% to 16.9% for Detector 1, from 0.1% to 22.2% for Detector 2 and from o0.1% to 19.1% for Detector 3. Although the ranges of the relative discrepancies are large, most of the individual discrepancies are around 5–10%, proving that the PHOTON simulation software is viable for calibration for environmental samples. The efficiencies obtained using PHOTON, were also compared to the ones obtained using GEANT4 simulation and the comparison showed a relatively good agreement between the results. To further validate the results, a measurement was conducted using reference materials issued by IAEA in the framework of several proficiency tests. The results using both PHOTON and GEANT4 simulated efficiencies were compared to the target value. All except two results calculated using efficiency obtained by PHOTON were acceptable according to the utest criterion recommended by IAEA. This showed that PHOTON simulation can be used for efficiency calibration for the environmental samples, for radionuclides emitting photons with energy higher than 80 keV.
165
Since it is fast and the user does not require the knowledge of a programming language, it proved practical in routine measurements.
5. Acknoledgement This paper was realized as a part of the project III 43009 financed by the Ministry of Education, Science and Technological Development of the Republic of Serbia.
References [1] J. Puzovic, I. Anicin, Nuclear Instruments and Methods in Physics Research A 414 (1998) 279. [2] R.L. Heath, INEL summary of activities related to nuclear data on the internet, Workshop on DOE Nuclear Data Program Services via the Internet, August, 1996. [3] S. Agostinelli, et al., Nuclear Instruments and Methods in Physics Research A 506 (2003) 250. [4] J.D. Nikolic, D. Jokovic, D. Todorovic, M. Rajacic, Journal of Radiological Protection 34 (2014) N47. [5] I. Oriona, L. Wielopolski, Nuclear Instruments and Methods in Physics Research A 480 (2002) 729. [6] G. Gilmore, Practical Gamma-ray Spectrometry, 2nd ed., Wiley, New York, 2008. [7] M.J. Berger, J.H. Hubbell, XCOM: photon cross sections on a personal computer, NBSIR 87-3597. [8] S.M. Seltzer, M.J. Berger, Nuclear Instruments and Methods B 12 (1985) 95. [9] P. Dryak, P. Kovar, Applied Radiation and Isotopes 64 (2006) 1346. [10] T. Vidmar, A. Likar, Applied Radiation and Isotopes 56 (2002) 99. [11] J. Nikolić, T. Vidmar, D. Joković, M. Rajačić, D. Todorović, Nuclear Instruments and Methods A 763 (2014) 347. [12] C. Dovlete, P.P. Povinec, Quantification of uncertainty in gamma-spectrometric analysis of environmental samples in IAEA-TECDOC-1401. [13] T.i.m. Vidmar, Nuclear Instruments and Methods in Physics Research A 550 (2005) 603. [14] M. Taskaeva, E. Taskaev, I. Penev, Applied Radiation and Isotopes 47 (9) (1996) 981. [15] I. Vukanac, M. Djurasevic, A. Kandic, D. Novkovic, L. Nadjerdj, Z. Milosevic, Applied Radiation and Isotopes 66 (2008) 792. [16] GENIE 2000 Operation manual, Canberra Industries, Meriden CT 06450 2002. [17] T. Vidmar, G. Kanisch, G. Vidmar, Applied Radiation and Isotopes 69 (2011) 908. [18] E.K. Osae, B.J.B. Nyarko, Y. Serfor-Armah, E.O. Darko, Journal of Radioanalytical and Nuclear Chemistry 242 (1999) 617. [19] J.-M. Laborie, G. Le Petit, D. Abt, M. Girard Monte, Applied Radiation and Isotopes 53 (2000) 57. [20] IAEA Analytical Quality in Nuclear Applications Series No. 18 Vienna, 2010. [21] IAEA Interlaboratory studies, online at 〈http://nucleus.iaea.org/rpst/Reference Products/Proficiency_Tests/〉.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Application of PHOTON simulation software on calibration of HPGe detectors J. Nikolic a,n, J. Puzovic b, D. Todorovic a, M. Rajacic a a b
University of Belgrade Institute for Nuclear Sciences Vinča, Mike Petrovica Alasa 12-16, 11001 Belgrade, Serbia University of Belgrade Faculty of Physics, Studentski trg 6, 11000 Belgrade, Serbia
art ic l e i nf o
a b s t r a c t
Article history: Received 4 March 2015 Received in revised form 30 July 2015 Accepted 1 August 2015 Available online 12 August 2015
One of the major difficulties in gamma spectrometry of voluminous environmental samples is the efficiency calibration of the detectors used for the measurement. The direct measurement of different calibration sources, containing isolated γ-ray emitters within the energy range of interest, and subsequent fitting to a parametric function, is the most accurate and at the same time most complicated and time consuming method of efficiency calibration. Many other methods are developed in time, some of them using Monte Carlo simulation. One of such methods is a dedicated and user-friendly program PHOTON, developed to simulate the passage of photons through different media with different geometries. This program was used for efficiency calibration of three HPGe detectors, readily used in Laboratory for Environment and Radiation Protection of the Institute for Nuclear Sciences Vinca, Belgrade, Serbia. The simulation produced the spectral response of the detectors for fixed energy and for different sample geometries and matrices. Thus obtained efficiencies were compared to the values obtained by the measurement of the secondary reference materials and to the results obtained by GEANT4 simulation, in order to establish whether the simulated values agree with the experimental ones. To further analyze the results, a realistic measurement of the materials provided by the IAEA within different interlaboratory proficiency tests, was performed. The activities obtained using simulated efficiencies were compared to the reference values provided by the organizer. A good agreement in the mid energy section of the spectrum was obtained, while for low energies the lack of some parameters in the simulation libraries proved to produce unacceptable discrepancies. & 2015 Elsevier B.V. All rights reserved.
Keywords: HPGe Calibration PHOTON
1. Introduction One of the major difficulties in gamma spectrometry of voluminous environmental samples is the efficiency calibration of the detectors used for measurement. Most often the calibration by measuring standard sources is performed, a number of semi empirical methods have also been developed and, in the present time, the Monte Carlo simulations are often used to generate the spectral response of the detector [1,2]. The example of Monte Carlo simulation codes is GEANT4. It is developed to simulate the response of complex particle detectors and for variety of different high energy and nuclear interactions [3]. In case of gamma spectrometry, this code needs choosing an electromagnetic physics and corresponding database used in the development of the application for the particular detector, which may be time consuming and may require proficiency in programming language [4]. Once an application is developed, the use of GEANT4 is relatively easy.
n
Corresponding author. Tel./fax: þ 381 116308467. E-mail address: [email protected] (J. Nikolic).
http://dx.doi.org/10.1016/j.nima.2015.08.002 0168-9002/& 2015 Elsevier B.V. All rights reserved.
For users that are not proficient in programming, or for any other reason need to have a readymade application, a dedicated and user-friendly program PHOTON provides a useful tool [1]. PHOTON uses a simplified input-file structure where the system and the source are described as a series of cylindrical zones. The zones that the photons traverse can be declared as active media (sources and detectors) and others as passive media (scatterers and absorbers), each with given properties [1]. After the construction of the measurement geometry, a schematic view of the system is available. It is written in Borland Delphi and contains Borland database engine and the user interface is Windows application. It also contains its own build-in cross-section libraries. However, Rayleigh scattering, fluorescence yields, form factors, and scattering factors are not included in the cross-section libraries [5]. These simplifications have proven especially useful in environmental measurements [6], where on one hand, an ultimate precision in calibration is usually not required and on the other, a variety of different sources might be measured in the laboratory. Having talked to some other gamma spectrometry practitioners, the authors of this paper found that the using of such simplified tool would be beneficial.
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The aim of this paper is to perform an efficiency calibration of three HPGe detectors, using PHOTON simulation software and to present and validate the results. The results of the calibration will be compared to the efficiencies obtained by measuring a set of secondary reference materials produced in the Laboratory for Environment and Radiation Protection of the Institute for Nuclear Sciences Vinca, Belgrade, Serbia and to the results obtained by GEANT4 simulation. The comparison should show the agreement between the results and limitations of the application of the method. The efficiencies obtained by the PHOTON simulation will then be applied on a realistic measurement of the secondary reference materials issued within the various interlaboratory proficiency tests. The measurement uncertainties for both simulated and the experimental values will also be calculated. The efficiency obtained by PHOTON and the experimental efficiency should be within the uncertainty limits in order to be declared as acceptable.
2. Materials and methods The PHOTON simulation software defines the interaction between the γ photon and the medium through three main mechanisms: photoelectric interaction, Compton scattering and pair production. The probability of the interaction depends on the properties of the medium and on the photon energy. The crosssections and linear absorption coefficients for the interactions are interpolated and tabulated for every defined medium at the beginning of the simulation [7]. For the actual photon energy the random interaction point for a given interaction is then found according to the following expression [1]: L¼
1
μ
ln η
ð1Þ
where L represents the path length between two subsequent interactions of the photon with the medium (or the emission of the photon and the first interaction), μ is the linear absorption coefficient for a given interaction and a given medium, while η is the pseudo-random number from the (0, 1) interval [1]. For the transport of the electrons, some simplifying algorithms exist. PHOTON code uses the Bethe–Heitler formula, with the crosssections given by Seltzer and Berger in Ref. [8]. The interaction with the smallest distance to the interaction point (the smallest L) is chosen and the propagation of the photon through media is followed. The photon originates from and traverses through zones specified as consecutive cylinders with defined radius r and height h. If L is larger than the crossing point of the two zones, it is considered that the interaction did not occur in the first zone and the starting point is again selected, at the beginning of the next zone and so on until the interaction occurs. If L is larger than the dimension of last zone, it is considered that the interaction did not occur. The geometrical characteristics of the measurement system are defined in the specified module of the program. The detectors considered for the simulation were the ones commonly used in our laboratory: two p-type detectors with the relative efficiency of 20% (named Detector 1) and 50% (named Detector 3) and one n-type detector with the relative efficiency 18% (named Detector 2). The characteristics of the detectors are presented in the Table 1. The geometrical parameters needed for the simulations, were defined according to the technical features obtained from the manufacturer. In case of the central void and top dead layer, which are not given in the manufacturer's certificate, the parameters were estimated based on the known dimensions of other detectors produced by the same manufacturer [9–11]. The geometry of the measured secondary reference material was also input in the program, as well as the chemical composition of the matrix. Assuming a cylindrical symmetry, geometry includes: the dimensions of the
germanium crystal with the top dead layer, the aluminum end cap, the central void and the sample and its container. The geometrical description of the measurement system is simplified, since it does not take into account the buletization and the side dead layers. The chemical composition of the secondary reference material is defined by its chemical formula, mass fraction and density. The spectra that are a result of the simulation are defined by the zone in which the deposition of energy is considered, the number of channels into which it will be simulated, the energy calibration and the peak full width at half maximum (FWHM) which is given as an empirical equation for a given type of the detector [1]. For the purpose of efficiency calibration in this paper, the simulation of the detector response on monoenergetic gamma rays was used. Namely, the response of the detector on the single energy emitted from the secondary reference material was used to calculate the efficiency on that energy and in that specific matrix. This choice excludes the need for the coincidence summing correction. The peak shape definition was performed using FWHM and FWTM (full width at tenth maximum) parameters of the detectors. Finally, the result of the simulation was a single full energy peak at each energy emitted by the radionuclide present in the secondary reference material and for all investigated secondary reference materials. The efficiency at the investigated energy was determined as the net count in the simulated peak divided by the total number of simulated events (emitted photons). For the simulation, the equivalent of the measurement uncertainty can be estimated following the reasoning presented in Ref. [4]. For the input parameters of the simulation, the uncertainty has to be included in the uncertainty budget [4]. Since the probability of photons passing through different layers of the detector and sample is the product of individual probabilities of photon passing through an individual layer of the detector or sample, it gives the guideline for estimation of the uncertainty equivalent. Since the square of the combined relative uncertainty equals to the sum of squares of relative uncertainties, the equivalent of the relative uncertainty for the simulated efficiency, uðεÞsimulation , can be estimated according to Ref. [12] qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi X uðεÞsimulation ¼ ð2Þ ðδxi Þ2 where δxi represents the relative uncertainty of the parameter xi (values that are input in the simulation). The geometry parameters that are defined in the simulation are 6 parameters of the detector geometry (crystal diameter and length, crystal cavity diameter and length, window thickness and window to crystal gap) and 3 parameters of sample geometry (matrix density, radius and height of the sample). Since the detector model is simplified in the simulation, we have to assume that the geometry will contribute significantly to the relative uncertainty of the results. The sum of uncertainties for crystal diameter and length and crystal cavity diameter and length can be estimated to be 5.0%, in total. The sum of uncertainties for window thickness and window to crystal gap for Detector 1 and Detector 2 is estimated at 10.0%, while it was 5.0% for Detector 3. Those contributions to the uncertainty were estimated according to the previous experience in using GEANT4 and EFFTRAN [4,11,13] for detector calibration. Relative uncertainties of height of the sample were estimated to be 0.1% in case of water samples and 1.0% in case of soil, sand, charcoal and grass samples. The density of the samples was calculated by dividing the measured mass of the sample with the volume of the sample. Since all samples were cylindrical, the volume was calculated as r2Hπ where r is measured inner radius of the container and H is the sample filling height. The uncertainty of r is estimated as the uncertainty of the measuring instrument (ruler). That leads to the conclusion that the uncertainty of the sample density is 1.0–2.0%. The equivalent of relative combined uncertainty of the simulated efficiency was estimated at 7.1–11.4%
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Table 1 The characteristics of the detectors.
Geometry and type of detector Relative efficiency Resolution on 122 keV on 1332 keV Peak/Compton ratio Crystal diameter Crystal lenght Crystal to window distance Central void (diameter length) Entry window
Detector 1
Detector 2
Detector 3
Closed coaxial–p type Canberra 20% (certificate) 0.850 keV (certificate) 1.8 keV (certificate) 51:1 (certificate) 49.5 mm 56.5 mm 5.5 mm 10 mm 40 mm Al
Closed reverzibile coaxial–n type Canberra 18% (certificate) 0.759 keV (experimental) 1.69 keV (experimental) 56.1:1 (experimental) 48 mm 48.5 mm 5 mm 10 mm 40 mm Be
Closed coaxial–p type Canberra 50% (certificate) 1.00 keV (experimental) 1.9 keV (experimental) 65:1 (certificate) 65 mm 67 mm 5 mm 10 mm 55 mm Al
Table 2 The geometry, composition and density of the secondary reference materials. Symbol d denotes the diameter of the container and h is the sample filling height. The thickness of all containers is 1 mm. Secondary reference material
Geometry
Composition
Density [g/cm3]
Charcoal 1 Soil 1 Sand 1 Charcoal 2 Soil 2 Sand 2 Grass 1 Grass 2 Water 1 Water 2 Aerosol
Cylinder d¼ 67 mm, h ¼ 36 mm
C 100% SiO2 90%, Ca 1%, K 4%, Fe 1%, C 4% SiO2 100% C 100% SiO2 90%, Ca 1%, K 4%, Fe 1%, C 4% SiO2 100% C 99% Other 1% C 99% Other 1% H2O 100% H2O 100% SO4 15%, NH4 15%, NO3 15%, CH 50%
0.49 1.38 1.59 0.45 1.43 1.56 0.30 0.26 1.01 1.01 0.57
Cylinder d¼ 85 mm, h ¼ 40 mm Cylinder d¼ 85 mm, h ¼ 47 mm Cylinder d¼ 85 mm, h ¼ 45 mm Cylinder d ¼67 mm, h ¼ 15 mm Cylinder d¼ 67 mm, h ¼ 28 mm Cylinder d¼ 50 mm, h ¼ 60 mm Cylinder d¼ 60 mm, h ¼ 75 mm Vial d ¼32 mm, h ¼ 12 mm
To verify the results, the efficiencies obtained in the simulation were compared to the experimentally obtained values. Experimental efficiency calibration is readily performed in the Laboratory for Environment and Radiation Protection of the Institute for Nuclear Sciences Vinca, Belgrade, Serbia. For the purpose of calibrating the detectors for environmental samples, a set of secondary reference materials was produced by spiking the chosen matrices with certified radioactive mixture solution ER X 9031-OL-426/12 issued by Czech Metrological Institute, Inspectorate for Ionizing Radiation. The radioactive solution contained following radionuclides: 241Am, 109Cd, 139 Ce, 57Co, 60Co, 137Cs, 203Hg, 113Sn, 85Sr and 88Y, with the energies that span from 59 keV to 1898 keV with total activity of 1342 Bq at reference date 31.08.2012. Matrices and geometry of secondary reference materials was aerosol placed in vial, soil, sand, charcoal and mineralized grass in cylindrical containers and water in polystyrene cylinder. The secondary reference materials were prepared by applying the procedure with activated carbon, as defined in Refs. [14,15]. The standardized solution had been diluted to the adequate specific activity by adding a carrier solution. This radioactive solution was homogeneously mixed in the bulk matrix materials previously mechanically prepared. The homogeneity was checked by measuring the aliquots of the bulk spiked matrix and was found to be below 2.0% [15]. Detailed procedures were presented in Ref. [15]. The secondary reference materials were placed in four different cylindrical polystyrene containers. The thickness of the containers was 1 mm (bottom and side walls). The geometry, composition and density of the calibration samples are listed in Table 2. After analyzing the spectra for experimental calibration, the efficiency at the given energy was calculated according to
ε¼
N U CðEÞ t UP γ UA
ð3Þ
where N represents the net count at the energy E, t is counting time, Pγ is emission probability, C(E) is coincidence correction
factor and A is source activity on the given energy, with the decay correction. Relative combined measurement uncertainty for the experimental efficiencies was calculated according to the following equation [11]: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uðεÞ ¼ ðδAÞ2 þ ðδNÞ2 þ ðδMÞ2 þ ðδPÞ2 ð4Þ where δA represents relative uncertainty of the radioactive solution activity given by the manufacturer, δN is the relative uncertainty of the number of photons in the full energy peak obtained by measuring the secondary reference material, δM is the uncertainty introduced in the process of production of the secondary reference material and δP represent other components such as sample position, “run to run” uncertainty and other unquantified contributions. Value δAþ δM is estimated to be approximately 2.0–3.0%, while δP is estimated to 2.0%. The estimation of δAþ δM was made according to Ref. [15] and the estimation of δP was based on our experience [3,10,12]. Other uncertainties are negligible. Relative measurement uncertainty uðεÞ for all energies was around 5.0% at 1σ level of confidence.
3. Results and discussion The simulation was conducted on 106 events for all three detectors and for all secondary reference materials that are used for experimental calibration. The material of the sample was defined by its chemical formula and density. Sample dimensions are also measured with care, and are constructed in the simulation code accordingly. The source to detector distance was 0 mm as it was in the measurement, meaning that the sample (with the container) was placed directly on the detector cap. The peaks were simulated at following energies: 46.5 keV (210Pb), 59.5 keV (241Am), 88 keV (109Cd), 122.1 and 136.5 keV (57Co), 165.8 keV (139Ce), 279.2 keV (203Hg), 392 keV (113Sn), 514 keV (85Sr), 661.7 keV
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Detector 1 aerosol water 1 grass 1 charcoal 1 soil 1 sand 1
1,3
1,2
water 2 grass 2 charcoal 2 soil 2 sand 2
1,2
εPHOTON/εexp
εPHOTON/εexp
1,1
1,0
Detector 2 aerosol water 1 grass 1 charcoal 1 soil 1 sand 1
1,3
1,1
1,0
0,9
0,9
0,8
0,8
0,7
water 2 grass 2 charcoal 2 soil 2 sand 2
0,7
0
200
400
600
800
1000
1200
1400
1600
1800
0
2000
200
400
600
E [keV]
1000
1200
1400
1600
1800
2000
E [keV] Detector 3 water 1 grass 1 charcoal 1 soil 1 sand 1
1,3
1,2
εPHOTON/εexp
800
aerosol grass 2 charcoal 2 soil 2 sand 2
1,1
1,0
0,9
0,8
0,7 0
200
400
600
800
1000
1200
1400
1600
1800
2000
E [keV] Fig. 1. εPHOTON/εexp ratio, where εPHOTON represents the efficiency obtained by using the PHOTON simulation аnd εexp is experimental efficiency, for all secondary reference materials.
(137Cs), 898 and 1836 keV (88Y) and 1173.2 and 1332.5 keV (60Co). The net count at each full energy peak was calculated as a sum of counts in certain number of channels. The number of channels that will be used is determined according to the FWHM and FWTM for each detector. FWHM is required parameter in the simulation and is defined as [16] pffiffiffi FWHM ¼ a þb U E
ð5Þ
where a and b represent the coefficients characteristic for each detector. Values for a and b were defined by GENIE2000 gamma spectrometry analysis software in the realistic spectrum of the secondary reference material for which the simulation is performed. FWTM was also defined by the GENIE2000. In the Laboratory, as a part of quality control and quality assurance procedure, FWHM and FWTM are readily checked for stability on a weekly basis, so it is confirmed that these characteristics of the detector are not changing with time. The typical FWTM in measured spectra was from 2.5 keV for low, to 4.7 keV for energies above 1200 keV in all three detectors. It is assumed that the simulated peak should have the same width at the base as the one in the measured spectrum. The efficiency at a given energy is then derived by dividing the net
count in the simulated full energy peak by number of events simulated (106). The measurement of the secondary reference materials was conducted on all three detectors for the duration of 60,000 s. The samples were placed coaxially on the end cap of the detector. Background radiation was measured by placing a blank sample of the same geometry and composition as the secondary reference material. Background spectrum was subtracted from the spectrum of the calibration sample using GENIE2000 software. After analysis of the spectrum, experimental efficiencies were calculated using Eq. (3). Coincidence correction factors were calculated using EFFTRAN software [17]. The corrections ranged from 0.1% for low, to as much as 9.2% for high energies. Coincidence was more prominent for Detector 2 due to its beryllium window and the fact that it is an n-type detector. For Detector 1 and Detector 3, corrections were needed only for energies of 88Y and 60Co. Both calculated and measured efficiencies were then fitted using following fitting function [18]
ln ε ¼
5 X i¼1
ai ðln EÞi 1
ð6Þ
J. Nikolic et al. / Nuclear Instruments and Methods in Physics Research A 799 (2015) 159–165
Detector 1 aerosol water 1 grass 1 charcoal 1 soil 1 sand 1
1,4 1,3
water 2 grass 2 charcoal 2 soil 2 sand 2
1,3 1,2
ePHOTON / eGEANT4
εPHOTON/εGEANT4
Detector 2 aerosol water 1 grass 1 charcoal 1 soil 1 sand 1
1,4
1,2 1,1 1,0 0,9
water 2 grass 2 charcoal 2 soil 2 sand 2
1,1 1,0 0,9
0,8
0,8
0,7
0,7
0,6
163
0,6 0
200
400
600
800
1000
1200
1400
1600
1800
2000
0
200
400
600
E [keV]
800
1000
1200
1400
1600
1800
2000
E [keV] Detector 3 water 1 grass 1 charcoal 1 soil 1 sand 1
1,4 1,3
aerosol grass 2 charcoal 2 soil 2 sand 2
εPHOTON/εGEANT4
1,2 1,1 1,0 0,9 0,8 0,7 0,6 0
200
400
600
800
1000
1200
1400
1600
1800
2000
E [keV] Fig. 2. εPHOTON/εGEANT4 ratio, where εPHOTON represents the efficiency obtained by using the PHOTON simulation аnd εGEANT4 is the efficiency obtained by using GEANT4 simulation, for all secondary reference materials.
where ε is efficiency, E is energy given in keV and ai are fitting coefficients. It is established that for our detectors, the best calibration curve is achieved by using the function with i¼5 (the 4th order polynomial). The obtained calibration curve is used in any realistic measurement. During simulation it has been noted that for energies below 80 keV, the full energy peaks were significantly higher than in the measured spectrum of the secondary reference materials. This problem is noted, in some degree, in all codes based on Monte Carlo simulation, since the simulation is sensitive to all imperfections of the detector geometry, especially the dead layer thickness and homogeneity and other defects [19]. Efficiency calibration for low energies is proved to be a significant drawback and the corrections have to be made in PHOTON code libraries as well. Due to that, the peaks on 46 keV and 59 keV are omitted from further calculations. Experimental efficiencies and efficiencies obtained by PHOTON were compared and the ratio between the simulated and measured efficiencies, for all investigated secondary reference materials, are presented in Fig. 1. As it can be seen from the Fig. 1, the discrepancies between simulated and experimental efficiencies do not show any specific trends. As expected, the greatest discrepancies are for low energies and are larger for heavier matrices (soil and sand). The relative
discrepancies ranged from 0.2% to 16.9% for Detector 1, from 0.1% to 22.2% for Detector 2 and from o0.1% to 19.1% for Detector 3. Although the ranges of the relative discrepancies are large, most of the individual discrepancies are around 5–10%. Larger discrepancies (10–15%) can be attributed to an imperfect knowledge and simplified construction of the complex geometry of the detector and/or to an inappropriate account for the imperfections of the process of charge collection [18] The unacceptably high discrepancies (discrepancies that are more than twofold higher than the measurement uncertainty of the experimental results) that were up to 30% were noticed for sand 1 and sand 2 secondary reference materials for Detectors 2 and 3 and soil 1 and soil 2 for Detector 1. The reason for the large discrepancies in the part of the spectrum with energies above 1200 keV, in case of Detector 1 and Detector 2, is in the simplifications in the cross-section libraries. It has been shown in [5] that the PHOTON spectral shape and the yields of the peaks with the results of the MCNP 4B code without bremsstrahlung, show good agreement. That leads to the conclusion that the adding of proper bremsstrahlung production processes in the PHOTON code would greatly improve results for the energies 4 1200 keV. It can be noted that all the results in the mid energy section of the spectrum (100–1200 keV roughly) show good agreement, thus indicating the limitations of the applicability of the PHOTON simulation.
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Table 3 Activity concentration of the analytes calculated with efficiencies obtained using PHOTON simulation, GEANT4 simulation and target values. Values denoted with the asterisk n were obtained as a mean value of the results reported by the participants. Letter N denotes an unacceptable result. Detector 1 [Bq/kg] PHOTON
Detector 2 [Bq/kg] GEANT4
PHOTON
IAEA-TEL-2012-03, hay, measured in geometry grass 2 Cs 840 7 80 8007 80 820 7 60 Cs 320 7 30 3007 30 310 7 30 IAEA-TEL-2014-03, sediment, measured in geometry sand 2 238 U / 207 2 226 Ra / 237 2 137 Cs / 13 72 228 Ac / 13 72 40 K / 310 7 30 IAEA-TEL-2014-03, water, measured in geometry water 2 137 Cs 13.5 7 0.5 12.0 7 0.5 / 134 Cs 22.2 7 0.7 20.4 7 0.7 / 210 Pb 277 3 N 327 4 N / IAEA-TEL-2011-03, water, measured in geometry water 2 60 Co / 8.17 0.8 133 Ba / 2.4 70.4 137 Cs / 3.3 70.3 134 Cs / 4.2 70.4 152 Eu / 7.8 7 0.5 241 Am / 2.2 70.2 IAEA-TEL-2012-03, water, measured in geometry water 1 241 Am / / 137 Cs / / 137
134
Detector 3 [Bq/kg] GEANT4
PHOTON
Target value [Bq/kg] [17] GEANT4
860 7 30 N 3307 20
7307 50 290 7 20
8107 30 3107 20
785 724 306 720
227 2 17.6 70.7 11.0 7 0.4 11.6 7 0.4 2787 9
157 3 227 2 14.57 0.7 N 137 2 3107 20
21 74 19.8 7 0.9 13.3 7 0.4 11.8 7 0.6 2787 9
16.0 7 3.8n 19.0 7 4.8n 12.0 7 0.4 12.17 1.5n 2707 27n
7.0 7 0.4 2.2 7 0.2 2.9 7 0.3 3.8 7 0.2 7.3 7 0.4 2.2 7 0.2
Since the efficiency calibration was performed for the same three detectors and same secondary reference materials, using GEANT4 simulation, the comparison between efficiencies obtained using PHOTON and GEANT4 was performed. The GEANT4 simulation produced results that are of the similar accuracy as PHOTON simulation in comparison to the experimental values [4,11]. The discrepancies between PHOTON and GEANT4 results (Fig. 2) ranged from 0.1% to 17.1% for Detector 1, from 0.3% to 35.0% for Detector 2 and from 0.4% to 26.0% for Detector 3. The largest discrepancies were, as expected, for heavy matrices (sand 2 and soil 2) and for low energies. To test the validity of the results, a measurement was conducted using reference materials issued by IAEA in the framework of several proficiency tests. The measured reference materials are IAEA-TEL-2012-03, hay, measured in geometry grass 2, IAEA-TEL2014-03, sediment, measured in geometry sand 2, IAEA-TEL-201103, water, measured in geometry water 2 on Detector 1, IAEA-TEL2014-03, water, measured in geometry water 2 on Detector 2 and IAEA-TEL-2012-03, water, measured in geometry water 1 on Detector 3. To evaluate the trueness of the results, using of the utest criterion is recommended in Ref. [20] AIAEA APHOTON ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi q utest ¼ ð7Þ u2IAEA þ u2PHOTON where APHOTON and uPHOTON are activity concentration of the radionuclide in the sample and relative combined uncertainty calculated for results using PHOTON simulated efficiencies and AIAEA and uIAEA is activity and uncertainty published by IAEA. The relative combined uncertainty uPHOTON was calculated according to the following equation: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uPHOTON ¼ uðεÞsimulation 2 þðδNÞ2 þ ðδf it Þ2 ð8Þ where uðεÞsimulation is defined in Eq. (2), δN is relative uncertainty of the sample net count. Measured samples contained radionuclides other than those present in the secondary reference materials investigated in the simulation. That is why efficiencies for energies that are of interest had to be determined. That was done by fitting
/ / /
12.06 70.1 21.4 70.2 49.87 71.23
/ / / / / /
7.6 70.1 2.5 7 0.1 3.17 0.1 3.8 7 0.1 7.7 70.1 2.4 7 0.1
1367 12 110 710
1407 10 1037 7
120.9 7 0.74 102.5 7 0.75
the simulated efficiencies with the function given in Eq. (6). The uncertainty introduced by fitting the simulated efficiencies is represented by δf it and is estimated to be 1.0%. Other sources of the uncertainty were negligible. The same criterion was applied for results obtained using GEANT4 simulated efficiencies. The activity concentrations obtained using PHOTON simulated efficiency and GEANT 4 simulated efficiency, along with the target values provided by the IAEA are presented in Table 3. For this case, the limiting value for the utest parameter was set to 2.58 for a level of probability at 99% to determine if a result passes the test (u o2.58) [21]. As it can be seen from the Table 3, only two results calculated using PHOTON were determined to be unacceptable. One is the result for 137Cs in sediment, measured on Detector 3. In this case, the efficiency was underestimated, thus producing a result that is significantly higher than the target value. Since the matrix of the sample is lighter and has smaller density than the matrix of the secondary reference material, the efficiency applied on this measurement is not adequate. A new simulation using the characteristics of the sample in question, rather than the sand secondary reference material should produce better agreement with the target value. The second unacceptable result is the activity of the 210Pb in the water measured on Detector 2. As it was said, the simulation produced unrealistic values of count for low energy part of the spectrum so the efficiency for 210Pb was extrapolated. In case of Detector 2, which is n-type, the extrapolation did not produce satisfactory result. In general it is not recommended to perform extrapolation, but in cases of Detectors 1 and 3 (p-type) it produced acceptable results for 241Am in water. This can be attributed to the different calibration curve shape for the n-type and p-type detectors. The n-type detector should have a mild slope with relatively high efficiency in low energy part of the spectrum and maximum at about 60 keV, whereas the extrapolation produced to high efficiency without the maximum. By comparing the results obtained using PHOTON and GEANT4 simulated efficiencies, it is noticeable that PHOTON produces higher efficiency for geometries sand 2 and grass 2. The difference
J. Nikolic et al. / Nuclear Instruments and Methods in Physics Research A 799 (2015) 159–165
in the results obtained by these two simulations was significant, but the results were acceptable. For the water samples the PHOTON efficiencies were slightly lower, but the difference in the results between PHOTON and GEANT4 is not significant. This can be taken as the confirmation that the detector model in the PHOTON simulation was treated properly. All the other results, obtained for the radionuclides that emit photons of energy higher than 100 keV are acceptable, proving that PHOTON simulation produced accurate values for efficiency for measured samples. 4. Conclusion In this paper an efficiency calibration was performed using PHOTON, user friendly Monte Carlo simulation code. The calibration was performed for three HPGe detectors, readily used in the Laboratory for Environment and Radiation Protection of the Institute for Nuclear Sciences, Vinca, Belgrade, Serbia. The results of the simulation were compared to the experimental values, obtained by measuring different secondary reference materials. The discrepancies between experimental and simulated spectra were significant for energies o80 keV, so it was decided not to take into account the efficiencies at energies of 46 keV and 59 keV. For energies above 80 keV, the results showed reasonably good agreement with the experimental values. The relative discrepancies ranged from 0.2% to 16.9% for Detector 1, from 0.1% to 22.2% for Detector 2 and from o0.1% to 19.1% for Detector 3. Although the ranges of the relative discrepancies are large, most of the individual discrepancies are around 5–10%, proving that the PHOTON simulation software is viable for calibration for environmental samples. The efficiencies obtained using PHOTON, were also compared to the ones obtained using GEANT4 simulation and the comparison showed a relatively good agreement between the results. To further validate the results, a measurement was conducted using reference materials issued by IAEA in the framework of several proficiency tests. The results using both PHOTON and GEANT4 simulated efficiencies were compared to the target value. All except two results calculated using efficiency obtained by PHOTON were acceptable according to the utest criterion recommended by IAEA. This showed that PHOTON simulation can be used for efficiency calibration for the environmental samples, for radionuclides emitting photons with energy higher than 80 keV.
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Since it is fast and the user does not require the knowledge of a programming language, it proved practical in routine measurements.
5. Acknoledgement This paper was realized as a part of the project III 43009 financed by the Ministry of Education, Science and Technological Development of the Republic of Serbia.
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