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A code for simulating a high-resolution gamma-ray spectrum of a fission sample
Nuclear Inst. and Methods in Physics Research, A 968 (2020) 163949
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A code for simulating a high-resolution gamma-ray spectrum of a fission sample O. Aviv ∗, A. Lipshtat, S. Vaintraub, T. Makmal Soreq Nuclear Research Center, Yavne, 81800, Israel
ARTICLE
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MSC: 00-01 99-00 Keywords: Gamma spectrometry HPGe Fission HEU GEANT4 Monte Carlo simulations
ABSTRACT A numerical model was developed that fully reconstructs a high-resolution gamma-ray spectrum of a fission sample. The code combines GEANT4 Monte Carlo simulations (used to calculate the response of a germanium detector) with the in-house Koala package (used to calculate the fission product inventory). In order to validate the model against experimental data, a highly enriched uranium sample was irradiated in a reactor and measured for up to 31 days later. A comparison between the simulated spectra and the experimental spectra exhibited a good quantitative agreement, demonstrating the high reliability of the model, especially for early times. While a simple source geometry was used for benchmarking the developed code, it can be easily extended to include complex geometries. The synthetic fission spectra can be used in several applications, e.g. assessing the capability of detector systems in identifying certain radionuclides, verification of gamma spectrometry analysis software and proficiency tests for analytical laboratories.
1. Introduction The main characteristics of interest for a High-Purity Germanium (HPGe) detector are its detection efficiency and resolution. Traditionally, the response of HPGe for gamma/X-rays is determined empirically using radioactive sources of known activities. In recent years, there is a growing trend in utilizing Monte Carlo simulations for calculating the detection efficiency of HPGe as well as other properties related to gamma/X-ray detection and quantification [1–11]. The main advantages of using numerical calculations are versatility, reduced cost and avoiding the risks associated with handling of radioactive materials. The common Monte Carlo software used for such applications include GEANT [12], PENELOPE [13], EGS [14] and MCNP [15]. A complementary aspect in using Monte Carlo for modeling the response of a high-resolution germanium detector is simulating a gammaray spectrum. Preceding knowledge of the detailed gamma-ray spectrum structure can be used to predict the capability of a HPGe in detecting certain radionuclides from a sample obtained within a radiological scenario involving multiple radionuclides (e.g. an air filter collected following a reactor accident) [16]. Depending on the scenario, the structure of the gamma-ray spectrum may vary significantly over time in accordance with the radionuclide content. A particular and highly complex study case is a high-resolution gamma-ray spectrum of a fresh fission sample. The ability to detect certain fission and activation products (e.g. 140 Ba and 134 Cs) is essential to the verification regime affiliated to the Comprehensive Test-Ban-Treaty
Organization [17]. Thus, the design of a measurement system, including crystal dimensions and shielding configuration, may be optimized using Monte Carlo simulations. Other fields where preceding knowledge of a detailed fission spectra may be beneficial include nuclear forensics [18], radio-dosimetry [19,20] and certain aspects of nuclear reactor researches [21]. This paper describes a computer code developed for generating scientifically reliable gamma-ray spectra of fission samples of varying ages. The code combines GEANT4 Monte Carlo simulations (used to calculate the response function of a HPGe detector) and the in-house Koala package (used to calculate the time-dependent inventory of fission products). The synthetic spectra were compared to experimental spectra of a Highly Enriched Uranium (HEU) sample measured at different times after irradiation. The experimental system which was used for measurements (and was considered in the model) is described in the following section. The successive section provides details about the numerical calculations used for generating the synthetic spectra, followed by results and concluding remarks. 2. Experimental methods 2.1. Measurement system All measurements were performed using a broad energy HPGe detector (Model BE5030P, Canberra), having a crystal volume of 157 cm3 , a relative detection efficiency of 50% and a resolution of 1.65 keV
∗ Corresponding author. E-mail address: [email protected] (O. Aviv).
https://doi.org/10.1016/j.nima.2020.163949 Received 10 January 2020; Received in revised form 14 February 2020; Accepted 10 April 2020 Available online 18 April 2020 0168-9002/© 2020 Elsevier B.V. All rights reserved.
O. Aviv, A. Lipshtat, S. Vaintraub et al.
Nuclear Inst. and Methods in Physics Research, A 968 (2020) 163949
Fig. 1. Left: Calculated atomic abundance (inventory) of fission products 24 h after fission of different times after fission.
for a gamma-ray energy of 1332.5 keV. The detector is housed in a low background shielding cell (Model ULB777, Canberra), consisting of low activity lead (100 mm) and an inner layer of high-purity copper (1.6 mm). In addition, a plastic scintillator (CosmicGuard™, Canberra) operated in anti-coincidence with the germanium detector was used to further reduce background events caused by cosmic radiation. The detector signal was fed into a digital processing unit (Lynx™, Canberra), which includes a multi-channel analyzer with 16,384 channels. Data acquisition and spectral analysis were performed using the software Genie2k™ [22]. The measurement system was calibrated for energy, resolution and detection efficiency in a wide range of photon energies using a set of certified point-like sources (54 Mn, 57 Co, 60 Co, 88 Y, 133 Ba, 137 Cs and 241 Am), measured separately at 10 cm from the center of the detector endcap.
The Koala code was used to calculate the inventory at various times after fission. The Koala package is a set of Python scripts [27], aimed at calculating and visualizing time-dependent inventory of fission products [19]. It consists of a branching matrix of 561 isotopes and is based on an efficient solver for the Bateman equation: ∑ 𝑑𝑁𝑖 = −𝜆𝑖 𝑁𝑖 + 𝛼𝑗𝑖 𝜆𝑗 𝑁𝑗 (1) 𝑑𝑡 𝑗 Where 𝑁𝑖 (𝑡) is the number of atoms of isotope i at time t with respect to the time of fission, 𝜆𝑖 is the respective decay constant and 𝛼𝑗𝑖 is the branching fraction from the parent isotope j to the considered daughter. The solver is based on writing the Bateman equation in a vector form: 𝑑 | ⟩ | ⟩ (2) | = C| | 𝑑𝑡 | ⎛ 𝑁1 (𝑡) ⎞ ⎟ ⎜ 𝑁2 (𝑡) ⎟ is the inventory state vector and C𝑖𝑗 ≡ where | (𝑡)⟩ = ⎜ ⎟ ⎜ ⋮ ⎜ 𝑁 (𝑡) ⎟ 𝑛 ⎝ ⎠ 𝜆𝑖 (𝛼𝑖𝑗 − 1). The major challenge is to diagonalize the matrix C. However, this step needs to be done only once. The diagonalized matrix enables practically immediate solution of the equation for any initial condition (0) and for any time t. Thus, the typical duration of the calculation for the inventory of all 561 fission products and for 10 different times is only few minutes. The advantage of this approach is that both the duration of calculation and its accumulated error do not increase with t. The Koala package includes sets of standard initial conditions for uranium and plutonium isotopes irradiated by either fast or slow neutrons. Other sets of initial conditions can be easily defined. In this work, the option of a pure 235 U isotope that was irradiated by slow neutrons was selected. This option represents the experimental procedure rather well as the HEU (U900) sample used in this work was irradiated in a ‘‘Rabbit’’ system, which is characterized mainly by thermal neutrons [24]. As an example, Fig. 1 (left) shows the atomic abundance (inventory) of fission products (both stable and radioactive isotopes) calculated to 24 h after irradiation of 235 U by slow neutrons. The time dependent inventory for selected fission products is shown Fig. 1 (right).
A sample of 0.2 mg of the Certified Reference Material U900 (highly purified U3 O8 fine powder, with 235 U enriched to 90%) was inserted into a quartz ampule. The sample was irradiated at the Israeli Research Reactor#1 (IRR1) during 20 s using a pneumatic transfer device (‘‘Rabbit’’) [23,24]. The sample was positioned at a distance of 10 cm from the HPGe endcap in a rigid plastic holder to ensure identical measurement geometry throughout the experimental campaign. Sample measurements were performed prior to irradiation and up to 31 days later, where each measurement lasted 24 h. The entire experimental procedure balanced between the requirement for sufficient statistics for both the short-lived and long-lived fission products on the one hand, and the requirements for low system dead time, low cascade summing effects and low random summing effects, on the other hand. 3. Numerical calculations The process of generating a synthetic fission spectrum consisted of the following steps:
(ii) (iii) (iv)
U by slow neutrons. Right: Calculated inventory of selected fission products for
3.1. Fission product inventory
2.2. Preparation and measurement of a fission sample
(i)
235
Preparation of a nuclear database file for relevant fission and activation products. Calculation of the time-dependent fission product inventory. Monte Carlo simulations of individual spectra for photons and electrons. Compilation of the simulated spectra with the nuclear data and fission product inventory.
3.2. Monte-Carlo Simulations The response of the HPGe detector to photons and electrons was calculated using the Monte Carlo software GEANT4 (version 4.9.4.p02) [12]. The physics package ‘‘LHEP_EMV’’ was used to model the transport of photons and charged particles through matter.
The nuclear data (half-lives, photon and electron energies and their respective emission probabilities) were retrieved from the libraries Lund/LBNL and LNHB [25,26]. Steps (ii)–(iv) are described in the following. 2
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Nuclear Inst. and Methods in Physics Research, A 968 (2020) 163949
Fig. 2. Scheme of the geometrical setup used in GEANT4 simulations. Labels indicate the main composite materials.
The geometrical configuration of the germanium detector and particle sources (material composition, densities, dimensions and locations in space) were modeled and defined in the simulation input geometry (Fig. 2). The response of the detector system was calculated separately for photons and electrons from a grain of uranium (0.1 mm) positioned 10 cm above the detector endcap. While the starting conditions of the mono-energetic photon source included a random direction in space, the electron source was generated in accordance with momentum conservation laws and angular distribution of beta decay [28]. The initial and final energies of the particles that passed through the germanium crystal were recorded into a text file. Each simulation included 107 primary particles which typically lasted 15 min on a quad-core PC (3.2 GHz). As part of the validation process of the code, the full-energy-peak efficiency was calculated for photons in the energy range of 59.5– 1836.1 keV and emitted by isotropic point-like sources. Fig. 3 shows a comparison between the detection efficiencies obtained from the simulations to those determined from measurements of certified calibration sources (54 Mn, 57 Co, 60 Co, 88 Y, 133 Ba, 137 Cs and 241 Am) positioned 10 cm above the detector endcap on a dedicated plastic holder. The deviations between the simulations and experimental data were found to be below 5% for the entire photon energy range. The simulation output file was converted into a histogram (or spectrum) representing the energy deposited by the impinging particles in the germanium crystal. The histogram had an identical number of bins (or channels) and energy calibration as in the experimental system. While a spectrum resulting from photons was characterized by an energy dependent function having a complex structure (e.g. photopeaks, Compton continuum, escape peaks and backscattering) [29], the resulting spectrum from electrons was characterized by a monotonous function with a considerably low number of events. Photo-peaks in the simulated spectrum were artificially broadened using a Monte Carlo approach [30]. Here, an inverse function was used which corresponds to a Gaussian distribution centered around the photo-peak energy and having a width corresponding to the resolution of the experimental system. As an example, the gamma-ray spectrum of a point-like source of 60 Co positioned at a distance of 10 cm from the detector endcap was simulated and compared to an experimental measurement (shown in Fig. 4). The various features associated with a gamma-ray spectrum as well as the relative intensities of the photo-peaks of 60 Co (shown in the inserts of Fig. 4) were reconstructed well in the simulation.
Fig. 3. Top: Experimental (black) and simulated (red) detection efficiency of a HPGe (model BE5030, Canberra) for point-like sources (54 Mn, 57 Co, 60 Co, 88 Y, 133 Ba, 137 Cs and 241 Am), measured 10 cm above its endcap. Bottom: Relative deviation. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. Experimental (black) and simulated (red) gamma-ray spectrum of a 60 Co point-like source measured at 10 cm above a HPGe (model BE5030, Canberra). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
from Koala. To account for the decay and production of radionuclides during a 24-hour measurement (i.e. as in the experimental procedure), the number of atoms at time t was calculated for 𝑀 = 288 intervals, of duration 𝑚 = 300 s. Therefore, the effective number of the remaining atoms for isotope j is: 𝑁̄ 𝑗 (𝑡) =
𝑀−1 ∑
𝑁𝑗 (𝑡 + 𝑖 ⋅ 𝑚)
(3)
𝑖=0
The counts per energy (or channel — k) in a spectrum for time t after the fission was obtained by summing over gamma spectrum (C)
3.3. Generation of a synthetic fission spectrum
and electron spectrum (c) representing an energy i normalized by the respective probability for emitting gamma-ray (P) or electron (p), and
The synthetic spectra were generated for 1–31 days after the fission time. The number of remaining atoms (or inventory — N ) was obtained
by the effective number of remaining atoms and the respective decay 3
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Nuclear Inst. and Methods in Physics Research, A 968 (2020) 163949
coefficient (𝜆), as shown in Eq. (4). 𝐶 (𝑘, 𝑡) ⎧ ⎡ ⎫ ⎤ ∑ ⎪∑ ∑ ⎪ 𝑝𝑖𝑒 𝑗 ⋅ 𝑐𝑖𝑒 𝑗 (𝑘)⎥ 𝜆𝑗 ⋅ 𝑁 𝑗 (𝑡) + 𝑓1 ⋅ 𝐵(𝑘)⎬ ⋅ 𝑓2 = ⎨ ⎢ 𝑃𝑖𝛾 𝑗 ⋅ 𝐶𝑖𝛾 𝑗 (𝑘) + ⎥ 𝑖𝑒 ⎪ 𝑗 ⎢⎣ 𝑖𝛾 ⎪ ⎦ ⎩ ⎭ (4) A background spectrum (B), being a 24-hour measurement of the HEU sample prior to irradiation, was added to the fission spectrum to account for events originating from the radioisotopes in the sample as well as from the experimental systems background radiation. Among others, the normalization factors 𝑓1 and 𝑓2 account for the sample activity, neutron flux during irradiation and number of fissions, both were determined by the best fit to the experimental data. It is stressed that the same normalization factors (i.e. 𝑓1 and 𝑓2 ) were used to generate the synthetic spectra for different times after fission. Finally, contributions of events originating from activation products (239 Np and 24 Na) in the irradiated HEU sample were also added with proper normalization factors obtained from fits to the experimental data. In order to reduce computer time arising from calculating negligible contributions to the final spectrum, only fission products that meet each of the following criteria were considered: (a) A minimal relative atomic abundance (inventory) of 0.05% at 24 h after fission (e.g. compared to 6.4% for 95 Zr). (b) A minimal emission probability of 0.2% and an energy above 50 keV for photons. (c) A minimal emission probability of 5% and an end-point energy above 200 keV for electrons. (d) Halflife longer than 60 s. Thus, the number of considered fission products was reduced from 561 to 98. Altogether, a library comprising of 1,600 spectra files was compiled. All stages described above were implemented using the MATLAB™ software. The synthetic spectra were exported to text files having a format compatible with the commercial software Genie2k™, which in turn, was used for analysis by standard gamma spectrometry methods. Once the nuclear database files, inventory matrix data and individual simulated spectra files are prepared, producing a synthetic fission spectrum is easy and immediate.
Fig. 5. Experimental (black) and simulated (red) spectrum of a 1-day old fission sample. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
4. Results and discussion Figs. 5–9 show a comparison between the measured gamma-ray spectra of the fission sample (black) and the simulated fission spectra (red) for 1–31 days after fission time, where each panel represents a different energy range. Radionuclide associations for several photopeaks are also noted in Figs. 5–9. The structure and complexity level of the spectrum varies with the sample age, exhibiting up to ∼200 photopeaks over the energy range of 50–2000 keV. As expected from the experimental procedure, it was possible to observe short-lived radioisotopes (e.g. 91 Sr, 97 Zr and 135 I) at earlier measurements and photo-peaks associated with long-lived radioisotopes (e.g. 95 Zr, 103 Ru and 140 Ba) were more pronounced at later measurements. Clearly, the general trend of the experimental fission spectra was reconstructed well for all measurement times, including the continuum counts and the various features associated with a high-resolution gamma-ray spectrum. Both major and minor photo-peaks appearing in the various energy ranges were reconstructed by the numerical calculations for all sample ages, including regions with complex patterns (e.g. ‘‘multiplet’’). However, some deviations were observed in the continuum counts at the low energy range. This mismatching is more pronounced at early times and may originate from unaccounted radionuclides (fission and activation products). Moreover, few faint photo-peaks originating from cascade summing effect (e.g. 1622 keV associated with 132 I) do not appear in the simulated spectra, as expected. In addition to a qualitative comparison between the simulated and experimental spectra, a quantitative comparison of the net area for photo-peaks for various radionuclides and along a broad energy
Fig. 6. Experimental (black) and simulated (red) spectrum of a 3-day old fission sample. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
range was performed. The relative deviation is defined as (DATASIM)/DATA and shown in Table 1. The statistical uncertainty of the experimental data is typically 3%. The experimental photo-peak areas were corrected for the cascade summing effect, calculated separately using the commercial software GESPECOR [31], found to be within the range 1.00–1.05. Overall, there is reasonable agreement for particulate radionuclides with deviations usually below 15%. For some photopeaks, there is an overestimation of the net area, which becomes more pronounced at later times. The deviations between the experimental data and simulation are attributed mainly to the applicability of the fission model to the experimental procedure, escape of some of the volatile radionuclides (e.g. iodine) from the HEU sample as well as inaccuracies in the nuclear data. The code presented in this work can be used to produce other synthetic spectra representing different spectral scenarios by modifying specific parameters such as the relative abundance of fission and/or activation products, background level, duration of spectral acquisition and so forth. Moreover, it is possible to generate synthetic spectra representing other sample geometries and compositions (e.g. jar of 4
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Nuclear Inst. and Methods in Physics Research, A 968 (2020) 163949
Table 1 Comparison between the synthetic and experimental photo-peak area obtained from fission spectra at different times after fission. Undetected photo-peaks are marked with ‘‘N.D.’’. Energy (keV)
Main RN
Half-life
𝛾-emission probability
57.4 91.1 140.5 145.4 181.1 228.3 249.8 293.3 364.5 487.0 497.1 529.9 537.4 555.6 630.2 657.9 667.7 739.5 743.4 749.8 756.7 765.8 815.8 954.5 1024.3 1260.4 1596.2 1750.2
Ce-143 Nd-147 Tc-99m Ce-141 Mo-99 Te-132 Xe-135 Ce-143 I-131 La-140 Ru-103 I-133 Ba-140 Y-91m I-132 Nb-97 I-132 Mo-99 Zr-97 Sr-91 Zr-95 Nb-95 La-140 I-132 Sr-91 I-135 La-140 Zr-97
33.0 h 11.0 d 6.0 h 32.5 d 2.7 d 3.2 d 9.1 h 33.0 h 8.0 d 1.7 d 39.2 d 20.9 h 12.7 d 0.8 h 2.3 h 1.2 h 2.3 h 2.7 d 16.8 h 9.7 h 64.0 d 35.0 d 1.7 d 2.3 h 9.7 h 6.6 h 1.7 d 16.8 h
11.7% 28.4% 88.5% 48.3% 6.0% 88.1% 90% 42.8% 81.2% 46.1% 89.5% 86.3% 24.6% 95% 13.3% 98.2% 98.7% 12.1% 94.8% 23.7% 54.4% 99.8% 23.7% 17.6% 33.5% 28.7% 95.4% 1.2%
Relative deviation in photo-peak area 1 d
3 d
10 d
16 d
31 d
13% 2% 6% 1% 4% −5% 3% −3% −9% −1% −13% −4% 2% −11% 4% 1% 4% 0% 1% −1% −3% N.D. 5% 1% 2% 15% −6% −5%
12% −1% 5% −2% −1% −2% −4% −6% −19% −1% −11% −4% 0% −5% 1% 0% 3% −4% −1% −17% −3% −2% −6% −2% 6% N.D. −4% N.D.
15% 0% 4% −6% −6% −6% N.D. −2% −25% −3% −14% N.D. −2% N.D. −2% N.D. −3% −6% N.D. N.D. −6% −4% −4% −10% N.D. N.D. −4% N.D.
N.D. −3% −0% −13% −5% −9% N.D. N.D. −27% −7% −18% N.D. −8% N.D. −4% N.D. −10% −4% N.D. N.D. −6% −8% −9% −13% N.D. N.D. −6% N.D.
N.D. 2% N.D. −14% N.D. −10% N.D. N.D. −37% −12% −18% N.D. −6% N.D. N.D. N.D. N.D. N.D. N.D. N.D. −10% −11% −4% N.D. N.D. N.D. −8% N.D.
Fig. 7. Experimental (black) and simulated (red) spectrum of a 10-day old fission sample. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 8. Experimental (black) and simulated (red) spectrum of a 16-day old fission sample. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
soil). The developed code can be used in proficiency tests for laborato-
5. Summary
ries [18,32–35], thereby avoiding uncertainties in radionuclide content
Synthetic spectra of a fission sample were calculated by combining GEANT4 (used to calculate the detector response) and the Koala package (used to calculate fission product inventory). The entire code was validated against measurements of an irradiated HEU sample performed with a geometrical configuration similar to the one used in the Monte Carlo simulations. Considering the uncertainties associated with the assumptions of the model and the complexity of the experimental procedure, a fairly good agreement was observed between the calculations and the experimental data, proving the reliability of the numerical model. The developed code may be applied in several fields, including evaluation of the ability of a detector system in
(e.g. due to preparation or radioactive decay) as well as allowing versatile scenarios. In addition, the synthetic spectra may be used to test gamma analysis software in correctly identifying and quantifying radionuclide content (including unfolding of ‘‘multiplets’’). Thus, above 800 synthetic spectra were generated using the code described in this paper to test a method for limiting data in a gamma-ray spectrometer [36]. 5
O. Aviv, A. Lipshtat, S. Vaintraub et al.
Nuclear Inst. and Methods in Physics Research, A 968 (2020) 163949 [6] Y. Shima, et al., Determination of full-energy peak efficiency at the center position of a through-hole-type clover detector between 0.05 MeV and 3.2 MeV by source measurements and Monte Carlo simulations, Appl. Radiat. Isot. 91 (2014) 97–103. [7] R. Britton, et al., Monte Carlo characterisation of a Compton suppressed broad-energy HPGe detector, J. Radioanal. Nucl. Chem. 300 (3) (2014) 1253–1259. [8] R. Britton, et al., Maximising the sensitivity of a gamma spectrometer for lowenergy, low-activity radionuclides using Monte Carlo simulations, J. Environ. Radioact. 134 (2014) 1–5. [9] N.L. Maidana, et al., Experimental HPGe coaxial detector response and efficiency compared to Monte Carlo simulations, Appl. Radiat. Isot. 108 (2016) 64–74. [10] F. Xie, et al., A study on activity determination of volume sources using point-like standard sources and Monte Carlo simulations, Radiat. Phys. Chem. 103 (2014) 53–56. [11] R. Britton, et al., Coincidence corrections for a multi-detector gamma spectrometer, Nucl. Instrum. Methods Phys. Res. A 769 (2015) 20–25. [12] S. Agostinelli, et al., Geant4—a simulation toolkit, Nucl. Instrum. Methods Phys. Res. A 506 (3) (2003) 250–303. [13] F. Salvat, J.M. Fernández-Varea, J. Sempau, PENELOPE-2008: A code system for Monte Carlo simulation of electron and photon transport, in: Workshop Proceedings, 2006. [14] I. Kawrakow, Accurate condensed history Monte Carlo simulation of electron transport. I. EGSnrc, the new EGS4 version, Med. Phys. 27 (3) (2000) 485–498. [15] M.C. Team, MCNP–a general Monte Carlo N-particle transport code, version 5, in: Book MCNP-a General Monte Carlo N-Particle Transport Code Version, 2003, 5. [16] B. Sarusi, et al., Application of the ‘GammaGen’ computer code for NORM synthetic spectra analysis, in: 27th Conference of the Nuclear Societies in Israel, 2014. [17] R. Werzi, The operational status of the IMS radionuclide particulate network, J. Radioanal. Nucl. Chem. 282 (3) (2009) 749. [18] L. Lakosi, et al., Gamma spectrometry in the ITWG CMX-4 exercise, J. Radioanal. Nucl. Chem. 315 (2) (2018) 409–416. [19] M. Stern, A. Baram, S. Pistinner, Time dependent radio-toxicology of fission products, in: 27th Conference of the Nuclear Societies in Israel, 2014. [20] C.-Y. Yi, et al., Calculation of spectrum to dose conversion factors for a HPGe spectrometer, J. Korean Phys. Soc. 30 (2) (1997) 186–193. [21] A. Krakovich, et al., Depletion measurements using a new gamma transparency method of irradiated MTR-type fuel assemblies, Nucl. Instrum. Methods Phys. Res. A 903 (2018) 224–233. [22] Canberra, Genie2k™ user manual, 2011. [23] T. Makmal, O. Aviv, E. Gilad, A simple gamma spectrometry method for evaluating the burnup of MTR-type HEU fuel elements, Nucl. Instrum. Methods Phys. Res. A 834 (2016) 175–182. [24] Y. Nir-El, Production of 177 lu by neutron activation of 176 Lu, J. Radioanal. Nucl. Chem. 262 (3) (2005) 563–567. [25] LNHB, Laboratoire National Henri Becquerel (LNHB), Nuclear and Atomic Data, 2018, Available online at http://www.nucleide.org/Laraweb. [26] LBNL, LBNL/LUND nuclear data search, 2018, Available online at http:// nucleardata.nuclear.lu.se/toi/. [27] Python, Python software foundation, Python Language Reference, version 2.7, 2020, Available at http://www.python.org. [28] S. Vaintraub, et al., Simulations of beta-decay of 6 he in an electrostatic ion trap, 2014, in arXiv:1402.3987. [29] G.F. Knoll, Radiation Detection and Measurement, John Wiley & Sons, 2010. [30] M. Tanabashi, et al., Review of particle physics. Monte-Carlo techniques (p. 542-543), Phys. Rev. D 98 (3) (2018) 030001. [31] O. Sima, D. Arnold, C. Dovlete, GESPECOR: A versatile tool in gamma-ray spectrometry, J. Radioanal. Nucl. Chem. 248 (2001) 359–364. [32] P. Karhu, S.M. Jerome, Proficiency tests for radionuclide laboratories supporting the network of IMS stations, Appl. Radiat. Isot. 61 (2) (2004) 415–419. [33] P. Karhu, et al., Proficiency test for gamma spectroscopic analysis with a simulated fission product reference spectrum, Appl. Radiat. Isot. 64 (10) (2006) 1334–1339. [34] N. Nakashima, E. Duran, Proficiency test exercises for particulate systems at CTBT radionuclide laboratories, Appl. Radiat. Isot. 134 (2018) 35–39. [35] M. Dowdall, et al., An emergency response intercomparison exercise using a synthetically generated gamma-ray spectrum, J. Radioanal. Nucl. Chem. 283 (1) (2010) 31–43. [36] O. Aviv, A. Lipshtat, A method for limiting data acquisition in a highresolution gamma-ray spectrometer during on-site inspection activities under the comprehensive nuclear-test-ban treaty, J. Instrum. 13 (05) (2018) P05006-P05006.
Fig. 9. Experimental (black) and simulated (red) spectrum of a 31-day old fission sample. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
correctly identifying certain fission and/or activation products in a sample retrieved following a radiological event, proficiency tests and professional training for analysts. In order to extend the versatility of the developed code and further improve its reliability, it is planned to include additional fission scenarios, geometrical configurations and incorporate the cascade summing effect. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement O. Aviv: Conceptualization, Methodology, Software, Data curation, Writing - original draft, Investigation, Validation. A. Lipshtat: Conceptualization, Methodology, Software, Data curation, Writing - original draft, Investigation, Validation. S. Vaintraub: Conceptualization, Methodology, Software, Data curation, Writing - original draft, Investigation, Validation. T. Makmal: Conceptualization, Methodology, Software, Data curation, Writing - original draft, Investigation, Validation. References [1] C. Liu, et al., Gamma spectrum and coincidence summation simulations with Geant4 in the analysis of radionuclide using BEGe detector, Appl. Radiat. Isot. 137 (2018) 210–218. [2] G.S. Cebastien Joel, et al., Monte Carlo method for gamma spectrometry based on GEANT4 toolkit: Efficiency calibration of BE6530 detector, J. Environ. Radioact. 189 (2018) 109–119. [3] Y. Unno, R. Furukawa, A. Yunoki, Simulation of a well-type HPGe detector for samples both in the hole and on top of the endcap, Appl. Radiat. Isot. 126 (2017) 154–157. [4] J.G. Guerra, et al., A simple methodology for characterization of germanium coaxial detectors by using Monte Carlo simulation and evolutionary algorithms, J. Environ. Radioact. 149 (2015) 8–18. [5] E. Chham, et al., 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. Radiat. Isot. 95 (2015) 30–35.
6
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Nuclear Inst. and Methods in Physics Research, A journal homepage: www.elsevier.com/locate/nima
A code for simulating a high-resolution gamma-ray spectrum of a fission sample O. Aviv ∗, A. Lipshtat, S. Vaintraub, T. Makmal Soreq Nuclear Research Center, Yavne, 81800, Israel
ARTICLE
INFO
MSC: 00-01 99-00 Keywords: Gamma spectrometry HPGe Fission HEU GEANT4 Monte Carlo simulations
ABSTRACT A numerical model was developed that fully reconstructs a high-resolution gamma-ray spectrum of a fission sample. The code combines GEANT4 Monte Carlo simulations (used to calculate the response of a germanium detector) with the in-house Koala package (used to calculate the fission product inventory). In order to validate the model against experimental data, a highly enriched uranium sample was irradiated in a reactor and measured for up to 31 days later. A comparison between the simulated spectra and the experimental spectra exhibited a good quantitative agreement, demonstrating the high reliability of the model, especially for early times. While a simple source geometry was used for benchmarking the developed code, it can be easily extended to include complex geometries. The synthetic fission spectra can be used in several applications, e.g. assessing the capability of detector systems in identifying certain radionuclides, verification of gamma spectrometry analysis software and proficiency tests for analytical laboratories.
1. Introduction The main characteristics of interest for a High-Purity Germanium (HPGe) detector are its detection efficiency and resolution. Traditionally, the response of HPGe for gamma/X-rays is determined empirically using radioactive sources of known activities. In recent years, there is a growing trend in utilizing Monte Carlo simulations for calculating the detection efficiency of HPGe as well as other properties related to gamma/X-ray detection and quantification [1–11]. The main advantages of using numerical calculations are versatility, reduced cost and avoiding the risks associated with handling of radioactive materials. The common Monte Carlo software used for such applications include GEANT [12], PENELOPE [13], EGS [14] and MCNP [15]. A complementary aspect in using Monte Carlo for modeling the response of a high-resolution germanium detector is simulating a gammaray spectrum. Preceding knowledge of the detailed gamma-ray spectrum structure can be used to predict the capability of a HPGe in detecting certain radionuclides from a sample obtained within a radiological scenario involving multiple radionuclides (e.g. an air filter collected following a reactor accident) [16]. Depending on the scenario, the structure of the gamma-ray spectrum may vary significantly over time in accordance with the radionuclide content. A particular and highly complex study case is a high-resolution gamma-ray spectrum of a fresh fission sample. The ability to detect certain fission and activation products (e.g. 140 Ba and 134 Cs) is essential to the verification regime affiliated to the Comprehensive Test-Ban-Treaty
Organization [17]. Thus, the design of a measurement system, including crystal dimensions and shielding configuration, may be optimized using Monte Carlo simulations. Other fields where preceding knowledge of a detailed fission spectra may be beneficial include nuclear forensics [18], radio-dosimetry [19,20] and certain aspects of nuclear reactor researches [21]. This paper describes a computer code developed for generating scientifically reliable gamma-ray spectra of fission samples of varying ages. The code combines GEANT4 Monte Carlo simulations (used to calculate the response function of a HPGe detector) and the in-house Koala package (used to calculate the time-dependent inventory of fission products). The synthetic spectra were compared to experimental spectra of a Highly Enriched Uranium (HEU) sample measured at different times after irradiation. The experimental system which was used for measurements (and was considered in the model) is described in the following section. The successive section provides details about the numerical calculations used for generating the synthetic spectra, followed by results and concluding remarks. 2. Experimental methods 2.1. Measurement system All measurements were performed using a broad energy HPGe detector (Model BE5030P, Canberra), having a crystal volume of 157 cm3 , a relative detection efficiency of 50% and a resolution of 1.65 keV
∗ Corresponding author. E-mail address: [email protected] (O. Aviv).
https://doi.org/10.1016/j.nima.2020.163949 Received 10 January 2020; Received in revised form 14 February 2020; Accepted 10 April 2020 Available online 18 April 2020 0168-9002/© 2020 Elsevier B.V. All rights reserved.
O. Aviv, A. Lipshtat, S. Vaintraub et al.
Nuclear Inst. and Methods in Physics Research, A 968 (2020) 163949
Fig. 1. Left: Calculated atomic abundance (inventory) of fission products 24 h after fission of different times after fission.
for a gamma-ray energy of 1332.5 keV. The detector is housed in a low background shielding cell (Model ULB777, Canberra), consisting of low activity lead (100 mm) and an inner layer of high-purity copper (1.6 mm). In addition, a plastic scintillator (CosmicGuard™, Canberra) operated in anti-coincidence with the germanium detector was used to further reduce background events caused by cosmic radiation. The detector signal was fed into a digital processing unit (Lynx™, Canberra), which includes a multi-channel analyzer with 16,384 channels. Data acquisition and spectral analysis were performed using the software Genie2k™ [22]. The measurement system was calibrated for energy, resolution and detection efficiency in a wide range of photon energies using a set of certified point-like sources (54 Mn, 57 Co, 60 Co, 88 Y, 133 Ba, 137 Cs and 241 Am), measured separately at 10 cm from the center of the detector endcap.
The Koala code was used to calculate the inventory at various times after fission. The Koala package is a set of Python scripts [27], aimed at calculating and visualizing time-dependent inventory of fission products [19]. It consists of a branching matrix of 561 isotopes and is based on an efficient solver for the Bateman equation: ∑ 𝑑𝑁𝑖 = −𝜆𝑖 𝑁𝑖 + 𝛼𝑗𝑖 𝜆𝑗 𝑁𝑗 (1) 𝑑𝑡 𝑗 Where 𝑁𝑖 (𝑡) is the number of atoms of isotope i at time t with respect to the time of fission, 𝜆𝑖 is the respective decay constant and 𝛼𝑗𝑖 is the branching fraction from the parent isotope j to the considered daughter. The solver is based on writing the Bateman equation in a vector form: 𝑑 | ⟩ | ⟩ (2) | = C| | 𝑑𝑡 | ⎛ 𝑁1 (𝑡) ⎞ ⎟ ⎜ 𝑁2 (𝑡) ⎟ is the inventory state vector and C𝑖𝑗 ≡ where | (𝑡)⟩ = ⎜ ⎟ ⎜ ⋮ ⎜ 𝑁 (𝑡) ⎟ 𝑛 ⎝ ⎠ 𝜆𝑖 (𝛼𝑖𝑗 − 1). The major challenge is to diagonalize the matrix C. However, this step needs to be done only once. The diagonalized matrix enables practically immediate solution of the equation for any initial condition (0) and for any time t. Thus, the typical duration of the calculation for the inventory of all 561 fission products and for 10 different times is only few minutes. The advantage of this approach is that both the duration of calculation and its accumulated error do not increase with t. The Koala package includes sets of standard initial conditions for uranium and plutonium isotopes irradiated by either fast or slow neutrons. Other sets of initial conditions can be easily defined. In this work, the option of a pure 235 U isotope that was irradiated by slow neutrons was selected. This option represents the experimental procedure rather well as the HEU (U900) sample used in this work was irradiated in a ‘‘Rabbit’’ system, which is characterized mainly by thermal neutrons [24]. As an example, Fig. 1 (left) shows the atomic abundance (inventory) of fission products (both stable and radioactive isotopes) calculated to 24 h after irradiation of 235 U by slow neutrons. The time dependent inventory for selected fission products is shown Fig. 1 (right).
A sample of 0.2 mg of the Certified Reference Material U900 (highly purified U3 O8 fine powder, with 235 U enriched to 90%) was inserted into a quartz ampule. The sample was irradiated at the Israeli Research Reactor#1 (IRR1) during 20 s using a pneumatic transfer device (‘‘Rabbit’’) [23,24]. The sample was positioned at a distance of 10 cm from the HPGe endcap in a rigid plastic holder to ensure identical measurement geometry throughout the experimental campaign. Sample measurements were performed prior to irradiation and up to 31 days later, where each measurement lasted 24 h. The entire experimental procedure balanced between the requirement for sufficient statistics for both the short-lived and long-lived fission products on the one hand, and the requirements for low system dead time, low cascade summing effects and low random summing effects, on the other hand. 3. Numerical calculations The process of generating a synthetic fission spectrum consisted of the following steps:
(ii) (iii) (iv)
U by slow neutrons. Right: Calculated inventory of selected fission products for
3.1. Fission product inventory
2.2. Preparation and measurement of a fission sample
(i)
235
Preparation of a nuclear database file for relevant fission and activation products. Calculation of the time-dependent fission product inventory. Monte Carlo simulations of individual spectra for photons and electrons. Compilation of the simulated spectra with the nuclear data and fission product inventory.
3.2. Monte-Carlo Simulations The response of the HPGe detector to photons and electrons was calculated using the Monte Carlo software GEANT4 (version 4.9.4.p02) [12]. The physics package ‘‘LHEP_EMV’’ was used to model the transport of photons and charged particles through matter.
The nuclear data (half-lives, photon and electron energies and their respective emission probabilities) were retrieved from the libraries Lund/LBNL and LNHB [25,26]. Steps (ii)–(iv) are described in the following. 2
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Fig. 2. Scheme of the geometrical setup used in GEANT4 simulations. Labels indicate the main composite materials.
The geometrical configuration of the germanium detector and particle sources (material composition, densities, dimensions and locations in space) were modeled and defined in the simulation input geometry (Fig. 2). The response of the detector system was calculated separately for photons and electrons from a grain of uranium (0.1 mm) positioned 10 cm above the detector endcap. While the starting conditions of the mono-energetic photon source included a random direction in space, the electron source was generated in accordance with momentum conservation laws and angular distribution of beta decay [28]. The initial and final energies of the particles that passed through the germanium crystal were recorded into a text file. Each simulation included 107 primary particles which typically lasted 15 min on a quad-core PC (3.2 GHz). As part of the validation process of the code, the full-energy-peak efficiency was calculated for photons in the energy range of 59.5– 1836.1 keV and emitted by isotropic point-like sources. Fig. 3 shows a comparison between the detection efficiencies obtained from the simulations to those determined from measurements of certified calibration sources (54 Mn, 57 Co, 60 Co, 88 Y, 133 Ba, 137 Cs and 241 Am) positioned 10 cm above the detector endcap on a dedicated plastic holder. The deviations between the simulations and experimental data were found to be below 5% for the entire photon energy range. The simulation output file was converted into a histogram (or spectrum) representing the energy deposited by the impinging particles in the germanium crystal. The histogram had an identical number of bins (or channels) and energy calibration as in the experimental system. While a spectrum resulting from photons was characterized by an energy dependent function having a complex structure (e.g. photopeaks, Compton continuum, escape peaks and backscattering) [29], the resulting spectrum from electrons was characterized by a monotonous function with a considerably low number of events. Photo-peaks in the simulated spectrum were artificially broadened using a Monte Carlo approach [30]. Here, an inverse function was used which corresponds to a Gaussian distribution centered around the photo-peak energy and having a width corresponding to the resolution of the experimental system. As an example, the gamma-ray spectrum of a point-like source of 60 Co positioned at a distance of 10 cm from the detector endcap was simulated and compared to an experimental measurement (shown in Fig. 4). The various features associated with a gamma-ray spectrum as well as the relative intensities of the photo-peaks of 60 Co (shown in the inserts of Fig. 4) were reconstructed well in the simulation.
Fig. 3. Top: Experimental (black) and simulated (red) detection efficiency of a HPGe (model BE5030, Canberra) for point-like sources (54 Mn, 57 Co, 60 Co, 88 Y, 133 Ba, 137 Cs and 241 Am), measured 10 cm above its endcap. Bottom: Relative deviation. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. Experimental (black) and simulated (red) gamma-ray spectrum of a 60 Co point-like source measured at 10 cm above a HPGe (model BE5030, Canberra). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
from Koala. To account for the decay and production of radionuclides during a 24-hour measurement (i.e. as in the experimental procedure), the number of atoms at time t was calculated for 𝑀 = 288 intervals, of duration 𝑚 = 300 s. Therefore, the effective number of the remaining atoms for isotope j is: 𝑁̄ 𝑗 (𝑡) =
𝑀−1 ∑
𝑁𝑗 (𝑡 + 𝑖 ⋅ 𝑚)
(3)
𝑖=0
The counts per energy (or channel — k) in a spectrum for time t after the fission was obtained by summing over gamma spectrum (C)
3.3. Generation of a synthetic fission spectrum
and electron spectrum (c) representing an energy i normalized by the respective probability for emitting gamma-ray (P) or electron (p), and
The synthetic spectra were generated for 1–31 days after the fission time. The number of remaining atoms (or inventory — N ) was obtained
by the effective number of remaining atoms and the respective decay 3
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coefficient (𝜆), as shown in Eq. (4). 𝐶 (𝑘, 𝑡) ⎧ ⎡ ⎫ ⎤ ∑ ⎪∑ ∑ ⎪ 𝑝𝑖𝑒 𝑗 ⋅ 𝑐𝑖𝑒 𝑗 (𝑘)⎥ 𝜆𝑗 ⋅ 𝑁 𝑗 (𝑡) + 𝑓1 ⋅ 𝐵(𝑘)⎬ ⋅ 𝑓2 = ⎨ ⎢ 𝑃𝑖𝛾 𝑗 ⋅ 𝐶𝑖𝛾 𝑗 (𝑘) + ⎥ 𝑖𝑒 ⎪ 𝑗 ⎢⎣ 𝑖𝛾 ⎪ ⎦ ⎩ ⎭ (4) A background spectrum (B), being a 24-hour measurement of the HEU sample prior to irradiation, was added to the fission spectrum to account for events originating from the radioisotopes in the sample as well as from the experimental systems background radiation. Among others, the normalization factors 𝑓1 and 𝑓2 account for the sample activity, neutron flux during irradiation and number of fissions, both were determined by the best fit to the experimental data. It is stressed that the same normalization factors (i.e. 𝑓1 and 𝑓2 ) were used to generate the synthetic spectra for different times after fission. Finally, contributions of events originating from activation products (239 Np and 24 Na) in the irradiated HEU sample were also added with proper normalization factors obtained from fits to the experimental data. In order to reduce computer time arising from calculating negligible contributions to the final spectrum, only fission products that meet each of the following criteria were considered: (a) A minimal relative atomic abundance (inventory) of 0.05% at 24 h after fission (e.g. compared to 6.4% for 95 Zr). (b) A minimal emission probability of 0.2% and an energy above 50 keV for photons. (c) A minimal emission probability of 5% and an end-point energy above 200 keV for electrons. (d) Halflife longer than 60 s. Thus, the number of considered fission products was reduced from 561 to 98. Altogether, a library comprising of 1,600 spectra files was compiled. All stages described above were implemented using the MATLAB™ software. The synthetic spectra were exported to text files having a format compatible with the commercial software Genie2k™, which in turn, was used for analysis by standard gamma spectrometry methods. Once the nuclear database files, inventory matrix data and individual simulated spectra files are prepared, producing a synthetic fission spectrum is easy and immediate.
Fig. 5. Experimental (black) and simulated (red) spectrum of a 1-day old fission sample. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
4. Results and discussion Figs. 5–9 show a comparison between the measured gamma-ray spectra of the fission sample (black) and the simulated fission spectra (red) for 1–31 days after fission time, where each panel represents a different energy range. Radionuclide associations for several photopeaks are also noted in Figs. 5–9. The structure and complexity level of the spectrum varies with the sample age, exhibiting up to ∼200 photopeaks over the energy range of 50–2000 keV. As expected from the experimental procedure, it was possible to observe short-lived radioisotopes (e.g. 91 Sr, 97 Zr and 135 I) at earlier measurements and photo-peaks associated with long-lived radioisotopes (e.g. 95 Zr, 103 Ru and 140 Ba) were more pronounced at later measurements. Clearly, the general trend of the experimental fission spectra was reconstructed well for all measurement times, including the continuum counts and the various features associated with a high-resolution gamma-ray spectrum. Both major and minor photo-peaks appearing in the various energy ranges were reconstructed by the numerical calculations for all sample ages, including regions with complex patterns (e.g. ‘‘multiplet’’). However, some deviations were observed in the continuum counts at the low energy range. This mismatching is more pronounced at early times and may originate from unaccounted radionuclides (fission and activation products). Moreover, few faint photo-peaks originating from cascade summing effect (e.g. 1622 keV associated with 132 I) do not appear in the simulated spectra, as expected. In addition to a qualitative comparison between the simulated and experimental spectra, a quantitative comparison of the net area for photo-peaks for various radionuclides and along a broad energy
Fig. 6. Experimental (black) and simulated (red) spectrum of a 3-day old fission sample. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
range was performed. The relative deviation is defined as (DATASIM)/DATA and shown in Table 1. The statistical uncertainty of the experimental data is typically 3%. The experimental photo-peak areas were corrected for the cascade summing effect, calculated separately using the commercial software GESPECOR [31], found to be within the range 1.00–1.05. Overall, there is reasonable agreement for particulate radionuclides with deviations usually below 15%. For some photopeaks, there is an overestimation of the net area, which becomes more pronounced at later times. The deviations between the experimental data and simulation are attributed mainly to the applicability of the fission model to the experimental procedure, escape of some of the volatile radionuclides (e.g. iodine) from the HEU sample as well as inaccuracies in the nuclear data. The code presented in this work can be used to produce other synthetic spectra representing different spectral scenarios by modifying specific parameters such as the relative abundance of fission and/or activation products, background level, duration of spectral acquisition and so forth. Moreover, it is possible to generate synthetic spectra representing other sample geometries and compositions (e.g. jar of 4
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Table 1 Comparison between the synthetic and experimental photo-peak area obtained from fission spectra at different times after fission. Undetected photo-peaks are marked with ‘‘N.D.’’. Energy (keV)
Main RN
Half-life
𝛾-emission probability
57.4 91.1 140.5 145.4 181.1 228.3 249.8 293.3 364.5 487.0 497.1 529.9 537.4 555.6 630.2 657.9 667.7 739.5 743.4 749.8 756.7 765.8 815.8 954.5 1024.3 1260.4 1596.2 1750.2
Ce-143 Nd-147 Tc-99m Ce-141 Mo-99 Te-132 Xe-135 Ce-143 I-131 La-140 Ru-103 I-133 Ba-140 Y-91m I-132 Nb-97 I-132 Mo-99 Zr-97 Sr-91 Zr-95 Nb-95 La-140 I-132 Sr-91 I-135 La-140 Zr-97
33.0 h 11.0 d 6.0 h 32.5 d 2.7 d 3.2 d 9.1 h 33.0 h 8.0 d 1.7 d 39.2 d 20.9 h 12.7 d 0.8 h 2.3 h 1.2 h 2.3 h 2.7 d 16.8 h 9.7 h 64.0 d 35.0 d 1.7 d 2.3 h 9.7 h 6.6 h 1.7 d 16.8 h
11.7% 28.4% 88.5% 48.3% 6.0% 88.1% 90% 42.8% 81.2% 46.1% 89.5% 86.3% 24.6% 95% 13.3% 98.2% 98.7% 12.1% 94.8% 23.7% 54.4% 99.8% 23.7% 17.6% 33.5% 28.7% 95.4% 1.2%
Relative deviation in photo-peak area 1 d
3 d
10 d
16 d
31 d
13% 2% 6% 1% 4% −5% 3% −3% −9% −1% −13% −4% 2% −11% 4% 1% 4% 0% 1% −1% −3% N.D. 5% 1% 2% 15% −6% −5%
12% −1% 5% −2% −1% −2% −4% −6% −19% −1% −11% −4% 0% −5% 1% 0% 3% −4% −1% −17% −3% −2% −6% −2% 6% N.D. −4% N.D.
15% 0% 4% −6% −6% −6% N.D. −2% −25% −3% −14% N.D. −2% N.D. −2% N.D. −3% −6% N.D. N.D. −6% −4% −4% −10% N.D. N.D. −4% N.D.
N.D. −3% −0% −13% −5% −9% N.D. N.D. −27% −7% −18% N.D. −8% N.D. −4% N.D. −10% −4% N.D. N.D. −6% −8% −9% −13% N.D. N.D. −6% N.D.
N.D. 2% N.D. −14% N.D. −10% N.D. N.D. −37% −12% −18% N.D. −6% N.D. N.D. N.D. N.D. N.D. N.D. N.D. −10% −11% −4% N.D. N.D. N.D. −8% N.D.
Fig. 7. Experimental (black) and simulated (red) spectrum of a 10-day old fission sample. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 8. Experimental (black) and simulated (red) spectrum of a 16-day old fission sample. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
soil). The developed code can be used in proficiency tests for laborato-
5. Summary
ries [18,32–35], thereby avoiding uncertainties in radionuclide content
Synthetic spectra of a fission sample were calculated by combining GEANT4 (used to calculate the detector response) and the Koala package (used to calculate fission product inventory). The entire code was validated against measurements of an irradiated HEU sample performed with a geometrical configuration similar to the one used in the Monte Carlo simulations. Considering the uncertainties associated with the assumptions of the model and the complexity of the experimental procedure, a fairly good agreement was observed between the calculations and the experimental data, proving the reliability of the numerical model. The developed code may be applied in several fields, including evaluation of the ability of a detector system in
(e.g. due to preparation or radioactive decay) as well as allowing versatile scenarios. In addition, the synthetic spectra may be used to test gamma analysis software in correctly identifying and quantifying radionuclide content (including unfolding of ‘‘multiplets’’). Thus, above 800 synthetic spectra were generated using the code described in this paper to test a method for limiting data in a gamma-ray spectrometer [36]. 5
O. Aviv, A. Lipshtat, S. Vaintraub et al.
Nuclear Inst. and Methods in Physics Research, A 968 (2020) 163949 [6] Y. Shima, et al., Determination of full-energy peak efficiency at the center position of a through-hole-type clover detector between 0.05 MeV and 3.2 MeV by source measurements and Monte Carlo simulations, Appl. Radiat. Isot. 91 (2014) 97–103. [7] R. Britton, et al., Monte Carlo characterisation of a Compton suppressed broad-energy HPGe detector, J. Radioanal. Nucl. Chem. 300 (3) (2014) 1253–1259. [8] R. Britton, et al., Maximising the sensitivity of a gamma spectrometer for lowenergy, low-activity radionuclides using Monte Carlo simulations, J. Environ. Radioact. 134 (2014) 1–5. [9] N.L. Maidana, et al., Experimental HPGe coaxial detector response and efficiency compared to Monte Carlo simulations, Appl. Radiat. Isot. 108 (2016) 64–74. [10] F. Xie, et al., A study on activity determination of volume sources using point-like standard sources and Monte Carlo simulations, Radiat. Phys. Chem. 103 (2014) 53–56. [11] R. Britton, et al., Coincidence corrections for a multi-detector gamma spectrometer, Nucl. Instrum. Methods Phys. Res. A 769 (2015) 20–25. [12] S. Agostinelli, et al., Geant4—a simulation toolkit, Nucl. Instrum. Methods Phys. Res. A 506 (3) (2003) 250–303. [13] F. Salvat, J.M. Fernández-Varea, J. Sempau, PENELOPE-2008: A code system for Monte Carlo simulation of electron and photon transport, in: Workshop Proceedings, 2006. [14] I. Kawrakow, Accurate condensed history Monte Carlo simulation of electron transport. I. EGSnrc, the new EGS4 version, Med. Phys. 27 (3) (2000) 485–498. [15] M.C. Team, MCNP–a general Monte Carlo N-particle transport code, version 5, in: Book MCNP-a General Monte Carlo N-Particle Transport Code Version, 2003, 5. [16] B. Sarusi, et al., Application of the ‘GammaGen’ computer code for NORM synthetic spectra analysis, in: 27th Conference of the Nuclear Societies in Israel, 2014. [17] R. Werzi, The operational status of the IMS radionuclide particulate network, J. Radioanal. Nucl. Chem. 282 (3) (2009) 749. [18] L. Lakosi, et al., Gamma spectrometry in the ITWG CMX-4 exercise, J. Radioanal. Nucl. Chem. 315 (2) (2018) 409–416. [19] M. Stern, A. Baram, S. Pistinner, Time dependent radio-toxicology of fission products, in: 27th Conference of the Nuclear Societies in Israel, 2014. [20] C.-Y. Yi, et al., Calculation of spectrum to dose conversion factors for a HPGe spectrometer, J. Korean Phys. Soc. 30 (2) (1997) 186–193. [21] A. Krakovich, et al., Depletion measurements using a new gamma transparency method of irradiated MTR-type fuel assemblies, Nucl. Instrum. Methods Phys. Res. A 903 (2018) 224–233. [22] Canberra, Genie2k™ user manual, 2011. [23] T. Makmal, O. Aviv, E. Gilad, A simple gamma spectrometry method for evaluating the burnup of MTR-type HEU fuel elements, Nucl. Instrum. Methods Phys. Res. A 834 (2016) 175–182. [24] Y. Nir-El, Production of 177 lu by neutron activation of 176 Lu, J. Radioanal. Nucl. Chem. 262 (3) (2005) 563–567. [25] LNHB, Laboratoire National Henri Becquerel (LNHB), Nuclear and Atomic Data, 2018, Available online at http://www.nucleide.org/Laraweb. [26] LBNL, LBNL/LUND nuclear data search, 2018, Available online at http:// nucleardata.nuclear.lu.se/toi/. [27] Python, Python software foundation, Python Language Reference, version 2.7, 2020, Available at http://www.python.org. [28] S. Vaintraub, et al., Simulations of beta-decay of 6 he in an electrostatic ion trap, 2014, in arXiv:1402.3987. [29] G.F. Knoll, Radiation Detection and Measurement, John Wiley & Sons, 2010. [30] M. Tanabashi, et al., Review of particle physics. Monte-Carlo techniques (p. 542-543), Phys. Rev. D 98 (3) (2018) 030001. [31] O. Sima, D. Arnold, C. Dovlete, GESPECOR: A versatile tool in gamma-ray spectrometry, J. Radioanal. Nucl. Chem. 248 (2001) 359–364. [32] P. Karhu, S.M. Jerome, Proficiency tests for radionuclide laboratories supporting the network of IMS stations, Appl. Radiat. Isot. 61 (2) (2004) 415–419. [33] P. Karhu, et al., Proficiency test for gamma spectroscopic analysis with a simulated fission product reference spectrum, Appl. Radiat. Isot. 64 (10) (2006) 1334–1339. [34] N. Nakashima, E. Duran, Proficiency test exercises for particulate systems at CTBT radionuclide laboratories, Appl. Radiat. Isot. 134 (2018) 35–39. [35] M. Dowdall, et al., An emergency response intercomparison exercise using a synthetically generated gamma-ray spectrum, J. Radioanal. Nucl. Chem. 283 (1) (2010) 31–43. [36] O. Aviv, A. Lipshtat, A method for limiting data acquisition in a highresolution gamma-ray spectrometer during on-site inspection activities under the comprehensive nuclear-test-ban treaty, J. Instrum. 13 (05) (2018) P05006-P05006.
Fig. 9. Experimental (black) and simulated (red) spectrum of a 31-day old fission sample. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
correctly identifying certain fission and/or activation products in a sample retrieved following a radiological event, proficiency tests and professional training for analysts. In order to extend the versatility of the developed code and further improve its reliability, it is planned to include additional fission scenarios, geometrical configurations and incorporate the cascade summing effect. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement O. Aviv: Conceptualization, Methodology, Software, Data curation, Writing - original draft, Investigation, Validation. A. Lipshtat: Conceptualization, Methodology, Software, Data curation, Writing - original draft, Investigation, Validation. S. Vaintraub: Conceptualization, Methodology, Software, Data curation, Writing - original draft, Investigation, Validation. T. Makmal: Conceptualization, Methodology, Software, Data curation, Writing - original draft, Investigation, Validation. References [1] C. Liu, et al., Gamma spectrum and coincidence summation simulations with Geant4 in the analysis of radionuclide using BEGe detector, Appl. Radiat. Isot. 137 (2018) 210–218. [2] G.S. Cebastien Joel, et al., Monte Carlo method for gamma spectrometry based on GEANT4 toolkit: Efficiency calibration of BE6530 detector, J. Environ. Radioact. 189 (2018) 109–119. [3] Y. Unno, R. Furukawa, A. Yunoki, Simulation of a well-type HPGe detector for samples both in the hole and on top of the endcap, Appl. Radiat. Isot. 126 (2017) 154–157. [4] J.G. Guerra, et al., A simple methodology for characterization of germanium coaxial detectors by using Monte Carlo simulation and evolutionary algorithms, J. Environ. Radioact. 149 (2015) 8–18. [5] E. Chham, et al., 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. Radiat. Isot. 95 (2015) 30–35.
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