Determination of HPGe peak efficiency for voluminous gamma-ray sources by using an effective solid angle method

Author’s Accepted Manuscript Determination of HPGe Peak Efficiency for Voluminous Gamma-ray Sources by Using an Effective Solid Angle Method M.Y. Kang, G.M. Sun, Junhyuck Kim, H.D. Choi www.elsevier.com/locate/apradiso

PII: DOI: Reference:

S0969-8043(16)30384-0 http://dx.doi.org/10.1016/j.apradiso.2016.07.015 ARI7555

To appear in: Applied Radiation and Isotopes Received date: 4 April 2016 Revised date: 13 July 2016 Accepted date: 17 July 2016 Cite this article as: M.Y. Kang, G.M. Sun, Junhyuck Kim and H.D. Choi, Determination of HPGe Peak Efficiency for Voluminous Gamma-ray Sources by Using an Effective Solid Angle Method, Applied Radiation and Isotopes, http://dx.doi.org/10.1016/j.apradiso.2016.07.015 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Determination of HPGe Peak Efficiency for Voluminous Gamma-ray Sources by Using an Effective Solid Angle Method

M.Y. Kanga, G.M. Sunb, Junhyuck Kima,b, H.D. Choia a

b

Seoul National University, Daehak-dong, Gwanak-gu, Seoul, 151-742 Korea

Korea Atomic Energy Research Institute (KAERI), Yuseong, Daejeon, 305-353 Korea Corresponding author. [email protected]

Summary

A code called EXVol has been developed to obtain the absolute peak efficiency for an extended or voluminous -ray source. The method is based on the concept of effective solid angles. Several efficiency curves that have been determined semi-empirically for voluminous sources are compared with the experimental values based on certified reference volume sources. To study the geometric and matrix effects, standard -ray sources of several media, volumes and shapes were measured using HPGe detectors with three different efficiencies. For the n-type detector of 32% relative efficiency, the relative deviations are less than ±10%; this performance is similar to that of existing programs for similar purposes. The EXVol code is able to calculate the detection efficiency within approximately five minutes or less. Systematic errors based on EXVol input parameters, which are mainly due to the inherent uncertainty in the detector’s characteristic dimensions provided by the vendor, are studied to obtain more accurate specifications of the detectors.

Key words: Effective solid angle, Attenuation effect, Detection efficiency, Voluminous -ray source 1 Introduction In -ray spectrometry using HPGe detectors, peak efficiency is one of the important parameters for quantifying the activity of radioactive samples, but is not easy to determine for a real geometry unless standard sources of the same geometry and matrix are used. The voluminous sample and its containers, the complicated detector geometry and the adjacent multiple layers between the sample and the detector cause complex attenuation and self-shielding effects. Multiply scattered radiations should also sometimes be

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considered. It is relatively simple to determine the full-energy peak (FEP) efficiency for a point or smallarea source by using a calibration curve based on several standard point sources. However, real samples typically taken from geology, the environment, radioactive waste, etc. have a variety of volumes, shapes and chemical matrices. This complexity complicates determination of the detection efficiency. One of the major geometrical effects is an extended solid angle effect called the effective solid angle, which results in a significant deviation from the efficiencies based on point sources that varies with the distance of the sample. To consider or correct this effective solid angle effect, a standard voluminous source with the same geometry and chemical matrix as the real sample should be prepared. However, it is costly and tedious to prepare an accurately calibrated voluminous -ray source with the same shape and chemical composition as the sample. For these reasons, methods based on calculation or semi-empirical procedures are preferred to reduce the effort to calibrate the efficiencies for various geometric conditions of detection. The concept of effective solid angle is a semi-empirical approach to determine the detection efficiency for the sample combined with a correction for the attenuation and self-shielding effects. Moens et al. suggested the concept of the effective solid angle by including the attenuation effect of -rays in the source and detector media and developed the code “SOLANG” [1-2]. It was able to determine the FEP efficiency of a volumetric source by calculating the effective solid angles for the geometries of both a point source and the volumetric sample and by using the measured FEP efficiencies based on the point reference sources. The SOLANG code has limitations for the shape of a volume source to a cylindrical form or to a volumetric source with a smaller diameter than that of the detector. Our work has been developed based on the same concept with improvements in the numerical speed and the user interface. In this work, a new code, EXVol (Efficiency calculator for eXtended Voluminous source), which is based on the concept of effective solid angle, is developed and its accuracies are compared and validated experimentally. Several codes can give FEP efficiencies for voluminous sources. Among them, a few commercial codes are known to provide calculated efficiencies at experimental conditions similar to those in this study. The relative deviation of “ANGLE” [3] is reported to be approximately ±3% and that of “LabSOCS” [4] is ±10%, while that of “EXVol” in this study is less than ±10% for a 32% n-type detector. There has been a study to determine the FEP efficiencies for extended cylinders and Marinelli beaker sources with dimensions larger than the detector crystals. The relative deviation of “ESOLAN” [5] is up to 190% for a 450 ml Marinelli beaker, while it was reported that the relative deviation is reduced to less than 4% after the detector parameters, e.g., crystal height and dead layer, were tuned. Here the sizes of the relative deviations cannot be compared with each other only by using the given values because the experimental conditions, such as the size and shape of the detector crystal and of the voluminous source being measured, are different. For example, the relative deviation of “ANGLE” within about ±3% [3] is based on an experiment with a 30% p-type detector measuring a small cylindrical source of 80 ml. The underlying principle of the “LabSOCS” code is based on Monte Carlo simulation and it requires a process of “characterization” of the detector that takes several weeks [4].

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In this study, we performed detailed experiments by using point standard -sources and five different voluminous certified reference -sources measured with three different sizes of detector crystals, and therefore showed that EXVol provides an accuracy level comparable to those obtained by the existing calculation tools. However, EXVol is simple and fast for calculation of detection efficiencies. EXVol takes less than 5 minutes to calculate detection efficiency for a total of 19 cases by simulating 1000 -events. The advantage of EXVol is that it can handle sources with diameters larger than that of the detector, including extended cylinder and Marinelli beaker sources. Additionally, EXVol can deal with detectors of various shapes including planar, coaxial, and closed-ended coaxial detectors. Bulletization of the detector crystal can also be treated.

2 Theory and run of EXVol code

The EXVol code is based on an effective solid angle concept suggested by Moens et al. [1-2]. The effective solid angle determines the probability of detection for a -photon emitted from the source, and it gives the total efficiency after an appropriate normalization. EXVol was developed to determine the FEP efficiency without the need to prepare a certified source with the same chemical composition and geometry as the sample. Detailed formulae for the geometric solid angle (Ω) and the effective solid angle ̅ ) can be found in the original study by Moens et al. [1], hence we describe here only a brief (Ω introduction. By considering the attenuation effect on rays in any type of material situated between the source and the active detector zone, the effective solid angle of an areal element dA on the detector’s surface A with respect to a point in the source medium is given by [1]

̅=∫ Ω 𝐴

𝐺𝑎𝑡𝑡 𝐻𝑒𝑓𝑓 𝑐𝑜𝑠𝛼 𝑟2

𝑑𝐴

(1)

where Gatt is a -ray’s attenuation factor along the path between the source and the outer surface of detector’s sensitive zone. The attenuation is considered for the geometries of the source, the associated absorbing media including the air between the source and detector, the end cap window, and the insensitive layer of the detector. Heff is the efficiency factor, or the probability of a -ray impinging on the sensitive zone interacting with the detector material along the path before leaving the detector, cos is the directional cosine between the areal element dA and the source position, and r is the distance between the source point and the detector’s active zone element dA. For a volumetric source, the integration of Eq. (1) is extended over the entire volume of the source and

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the detailed expression is given for the cylinder-symmetric sources in Ref. [1]. Therefore, the volume is rendered by a quadruple integration. Instead of numerical integration, we used a Monte Carlo method. For uniform generation of -rays inside the source, a Cartesian coordinate system is adopted and the z-axis is set to the direction from the base of the source to the top of the detector. The geometry of a Marinellishape source and a detector for calculating the effective solid angle is shown in Figure 1. The expression for the effective solid angle presented by an extended voluminous source to the detector is given by

̅=∫ ∫ ∫ ∫ ∫ Ω 𝑧 𝑦 𝑥 𝑦 𝑥 𝑠

𝑠

𝑠

𝑑

𝐺𝑎𝑡𝑡 𝐻𝑒𝑓𝑓 𝑧𝑠 𝑑𝑥𝑑 𝑑𝑦𝑑 𝑑𝑥𝑠 𝑑𝑦𝑠 𝑑𝑧𝑠 𝑑

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[(𝑥𝑠 −𝑥𝑑 )2 +((𝑦𝑠 −𝑦𝑑 )2 +(𝑧𝑠 −𝑧𝑑 )2 ]2

(2)

where the coordinates of the source and those on the detector surface are (xs,ys,zs) and (xd,yd,zd), respectively. Here the -rays are considered to be impinging on the top surface of the detector crystal. A similar but different expression is given for the -rays impinging on the side surface of the detector. The ratio of the effective solid angles for volume and point source is converted to the detection efficiency. The underlying principle here is that the “virtual” peak-to-total ratio, referring to the bare detector, is a constant that is an intrinsic quantity of the detector, and independent of the counting geometry and sample. Then, the efficiency of a volume source can be given as follows:

𝜀𝑣𝑜𝑙𝑢𝑚𝑒 = 𝜀𝑝𝑜𝑖𝑛𝑡 ×

̅ 𝑣𝑜𝑙𝑢𝑚𝑒 𝛺 ̅ 𝑝𝑜𝑖𝑛𝑡 𝛺

(3)

where the efficiency of a point source ɛpoint is obtained by measuring reference point sources at a distance sufficiently large to render the true coincidence summing effects negligible. Usually we take the point sources’ distance to be 25 cm from the detector front face. Effective solid angle is calculated under the following three conditions. 1) Attenuation in the source and the adjacent absorption layers is caused by the self-shielding effect of the volumetric source. 2) An interacting photon deposits all its energy in the sensitive region and is recorded as a full energy absorption event. Any incomplete charge collection interaction is considered to transfer full energy to the detector. 3) The -rays are transported through the detector material, where they undergo various interactions of the photoelectric effect, Compton scattering, and pair production contributing to the FEP. Coherent scattering does not cause energy absorption and its path variation is negligible in the energy range of interest. Hence, the total attenuation coefficient without coherent scattering is used. To calculate the effective solid angle, -rays are generated randomly and uniformly within the sample

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volume by using a Monte Carlo method, in which the -ray energy, generation position and direction of emission are determined. The -rays incident to the solid angle on the detector surface are considered to have undergone a certain amount of attenuation within the source and the layered media between the source and the detector crystal. This attenuation is included in the numerical calculation of multiple integrals. To maintain the same statistical fluctuations for proper normalization, the number of particles incident on the detector crystal is set to be equal for each generation position. The present method has the advantages of minimizing the computational time required for the multiple integrations and of being applicable to various sources with more complex geometries, which can be described as a combination of several simple shapes. The EXVol code calculates the effective solid angles for both the voluminous sample source and the reference calibration source. It can describe the source as a point, a disk, a cylinder, a sphere, a Marinelli container, or an extended voluminous source having a diameter larger than that of the detector. The computable structures of the detector with EXVol are Coaxial, Planar and Well-type. When the calculation is completed, the averages of the attenuation factor, the efficiency factor, the effective solid angle and the FEP efficiencies for point source and voluminous source are saved. NIST X-ray mass attenuation coefficient data [6] are used to calculate the factors Gatt and Heff. To separate the contributions of incoherent scattering and coherent scattering to the photoelectric effect, we use the interaction cross-sectional data obtained from the XCOM code [7]. The EXVol code is written in Matlab language. Figure 1 shows a GUI (Graphical User Interface) of the EXVol code. It requests various input data cards about the detector geometry, source geometry, adjacent media and simulation. Each input card has its own windows for easy editing and checking. The geometric configuration and simulation process are graphically displayed during the operation. The EXVol code generates the effective solid angles for both the point source and the voluminous source, and the absolute FEP efficiency curve for the voluminous source, as shown in Figure 1. The calculation time depends on the computer’s CPU specifications. In this study, we ran the EXVol code on a PC with a single-core 3.6 GHz CPU and 8 GB of RAM. For a coaxial HPGe detector with a relative efficiency of 32% and a 450 ml liquid source in the Marinelli beaker, the calculation times are143 seconds for 1,000 events, 1,045 seconds for 10,000 events and 10,728 seconds for 100,000 events. In this study, the number of events is defined as the multiple of the generation number in the source and the solid angle. This definition means that the event number is not the number of -rays emitting from the source but the number of -rays incident on the detector, and it could maintain statistical stability.

3 Experiments to assess the inaccuracy of EXVol Experiments were performed to verify the accuracy of the EXVol results. IAEA standard -ray sources were used as reference point sources. Five CRM (Certified Reference Materials) volume sources were prepared by KRISS (Korea Research Institute of Standards and Science) and used in this measurement.

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Three types of polyethylene containers - 450 ml and 1000 ml Marinelli beakers, and a 1000 ml cylindrical beaker - were used. Nine different radionuclides were contained in 0.1 mol of dilute HCl solution or solidified in HCl medium (agar). The geometric details of the voluminous sources, the experimental instruments setup and the detection geometry are shown in Figure 2 and Figure 3. The list of used sources is given in Table 1. We used three detectors of different sizes or types to assess the systematics of the efficiency calculated by the EXVol code. One 17% p-type detector and two n-type detectors having 32% and 63% relative efficiencies were used. Measurements were performed with the p-type and n-type detectors to see the effects of detection efficiency according to the thickness of the dead layer. The detector specifications provided by the vendors are listed in Table 2. To reduce the natural background radiation and the scattered radiation, the -ray measurement system of the detector and source was located inside a large shield chamber made of lead bricks and a copper wall of 3 mm thickness. The outside of the shield chamber was enclosed with a steel plate of 3 mm thickness. The shield chamber’s size was 260 cm (width)  140 cm (length)  160 cm (height). This structure is shown in Figure 3. For sufficient statistics, the minimum peak area was typically set at 10,000 counts. Every spectrum was then acquired for 7,200 seconds while its dead time was kept at less than 2%. The Marinelli beakers were measured on top of the detector head while the cylindrical beakers were measured at source-to-detector distances of 0 cm, 5 cm and 10 cm to see the change in the effective solid angle and the true coincidence effect for multiple gamma emitters with distance. The coincidence effects are large for small source-todetector distances, while these effects can be neglected for large distances [8,9]. The HyperGam [10] was used to acquire the spectrum and to analyze peak areas.

4 Result and discussion Calculated and measured efficiency curves for different detectors and geometries are shown in Figures 4 to 8. Differences between EXVol calculated efficiencies and measured efficiencies are shown by their relative deviations (%) and are shown in Figures 9 to 13. To assess systematic variation, a comparison of the results was carried out according to the volume, medium, and shape of each voluminous CRM source and the source-to-detector distance. The convention for the figure captions is that the first two numbers and a letter (P or N) indicate the %-relative efficiency and the type of Ge detector, the next M or C indicates the Marinelli beaker or cylindrical beaker, the next number 1000 or 450 for the beaker’s volume in ml, and the last letter (S or L) indicate solid or liquid source medium. The measurement analysis of radionuclides that were affected by true coincidence summing are shown by open symbols and the practically coincidence-free nuclides are indicated by full symbols. The error bars in Figures 4 to 8 are based on the uncertainty (1) due to experimental geometry, nuclear data and statistics. The relative uncertainty is less than 5.1% for the cylindrical beaker and less than 6% for the Marinelli beaker measured with the 32% and 63% n-type detectors and the 17% p-type detector,

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respectively. Results of calculated efficiency curves and relative deviations for the 17% p-type detector are shown in Figures 4 and 9. The measurement was performed for only the two sources of solid medium. Because the detector’s crystal and front face faced the horizontal direction, the liquid medium sources could not be measured in this geometry. The calculation and measurement results for the 450 ml Marinelli beaker agree within the relative deviation of ±20%, except for the 255 keV 113Sn data. Due to the small emission ratio of the 255 keV

113

Sn gamma ray (approximately 2.1%) and its low activity of 72 Bq when the

measurement was performed, this data point has poor statistics. The data for the 1000 ml Marinelli beaker also showed differences within ±20% in the energy range of 59 keV - 1332 keV. Comparing the efficiencies of the 450 ml and the 1000 ml Marinelli beakers, the smaller volume has higher detection efficiencies. This result can be explained as due to the self-shielding effect of the voluminous sample and the geometry of the Marinelli beaker. The average Gatt and Heff of the 450 ml Marinelli beaker are 0.82 and 0.72, respectively, and those of the 1000 ml Marinelli beaker are 0.76 and 0.72, respectively, for the entire energy range. Calculated and measured efficiencies of the 32% n-type detector are shown in Figure 5 for the Marinelli beaker and in Figure 6 for the cylindrical beaker, respectively. The relative deviations are shown in Figures 10 and 11, respectively. Calculated efficiencies for the Marinelli beaker with four different combinations of volume and medium exhibit relative deviations of less than ±10%, except at the energies of 1173 keV and 1332 keV (60Co) in a 1000 ml solid source. The discrepancy for the source with multiple gamma emitters – 60Co and 88Y – is likely partially due to the true coincidence effect because the distance of the Marinelli beaker to the detector’s window face was 0 cm. The differences between the calculated and the measured results are less than ±10% for the cylindrical beaker, except for the data from the 255 keV -ray of

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Sn measured at a 5 cm distance. The difference

between the calculation and the measurement is reduced to less than 5% as the source is moved farther from the detector. Abbas performed a comparison of the calculated and the experimental photopeak efficiencies for a coaxial circular disk source (radius=2.3 cm) located at three different distances (0, 5 and 10 cm) from the detector window. His study showed that the overall error is mostly less than ±3% after performing the coincidence corrections [11]. Results for the 63% n-type detector are shown in Figures 7 – 8 and 12 – 13. Compared to the deviations shown for the 32% n-type detector and the 17% p-type detector, the relative deviations are large and apparently increase with gamma-ray energy. A similar trend in the relative deviation is also hinted in the existing studies based on the commercial codes “ANGLE” [3] and “LabSOCS” [4]. The uncertainty of “GESPECOR” [12] is below 4% at the energies of 1173 keV and 1332 keV (60Co) and 898 keV (88Y) after a coincidence summing correction calculation is considered. There are a few studies of the detection efficiency of larger detectors over 50% - 60% in which voluminous sources are measured and compared with those obtained by calculation [13-14]. These works shared the common problem that the detection efficiency is not accurately obtained by calculation.

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Here, our data for gamma energies over 800 keV are based on multiple-gamma emitters 88Y and 60Co, but no correction for the coincidence summing has been performed in this study even if their magnitudes are known to be large. For example, the relative deviation of the calculated detection efficiency from the measured efficiency for a 2000 ml Marinelli beaker measured with a 98% detector is shown to be as large as 30% even after correcting for the true coincidence summing effect [15]. Without correcting for the coincidence summing effect, the relative deviation of the calculated efficiency is larger than 50 - 60%. Hence, assessing the magnitudes of the calculated efficiencies with a reasonable accuracy is another issue that needs to be resolved in future studies, even though some methods exist and some studies have dealt with this topic [12-14]. In comparison with the above studies, EXVol code is versatile in that it can give the detection efficiency for a variety of forms, geometries and distances for a voluminous source and detector. EXVol can produce more accurate results by adjusting the detector parameters through standards measurement and also by correcting for the true coincidence summing effect. Mainly due to the inherent uncertainty in the detector’s characteristic dimensions provided by the vendor, systematic errors based on EXVol input parameters are studied to obtain a better specification of the detectors. We assume maximum magnitudes of the inaccurate values as follows: ±10% for the detector crystal radius, height and the distance between the source and the detector crystal, ±20% for the dead layer thickness. From the deviated value of each detector parameter, the change in the calculated efficiencies from those based on the nominal values is obtained and shown in a continuous curve in Figure 14. This was performed for each of the 17% p-type, 32% n-type and 63% n-type HPGe detectors. The source was taken as the Marinelli beaker of 450 ml of solid medium. The most sensitive parameter is the radius of the crystal and the systematic errors are less than ±7.5%; this result is the same obtained by Moens et al. [1]. Another study of the tuning of the geometrical parameters was performed by Vukotic et al [16]. Two cylindrical sources (191 ml of liquid medium and 509 ml of powder medium) were considered. The systematic error was reduced by artificially changing some input parameters and the results obtained fall in the ±5% range. In Vukotic’s study, it is concluded that the detector dead layer thickness is a critical parameter to obtain the best result for FEP efficiency, which was similarly studied by Wang et al [17]. We have not attempted to tune the parameters to improve the deviation of the calculated efficiency in this study for two reasons. First, the effect of systematic errors in the parameters of detector specification shows complicated behavior and hence an automatic search for the best-tuned parameters set is required. In addition, the measured efficiencies in the region of energies greater than approximately 700 keV are based on multiple gamma emitters. They must be corrected for the coincidence summing effect before they can be used for tuning the parameters.

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Most previous studies in the discussion above [1,3,4,17] used cylindrical sources with small volumes (less than 80 ml) and small-volume detectors (under 50% rel. eff.). However, in this study, we use cylindrical sources with large volumes (1000 ml) and Marinelli beaker sources with a large volumedetector (63%), none of which were used in previous studies. In a comparison with a previous study of similar experimental conditions [5], we have shown the effects of the detector variables on the relative deviations vs. the -energy.

5 Conclusion and further work We developed the EXVol code, based on the effective solid angle concept, to determine the energyefficiency curve of a voluminous source and to apply the self-attenuation effect and a coincidence summing correction. To assess the performance of the code, several CRM volume sources were measured with three detectors of different sizes and types, and the measured efficiencies were compared with the calculated values. The EXVol code efficiencies for a 17% p-type detector show an error range of ±20% from the measured values. In the mid-energy region, the calculated values and experimental data agree well, but in the high- and low-energy regions, the calculation seems to overestimate the efficiencies compared with the measured values. With the exception of the 1173 keV region, the relative deviation for the 32% n-type detector is less than ±10%. For the 63% detector, the magnitude of the relative deviation is further increased. Compared to other research results, EXVol is shown to provide an accuracy level similar to those obtainable by the existing programs. EXVol is versatile in that it can give the detection efficiency for a variety of forms, geometries and distances for a voluminous source and detector.

References 1. L. Moens, J. De Donder, Lin Xi-lei, F. De Corte, A. De Wiselaere, A. Simonits and J. Hoste, “Calculation of the absolute peak efficiency of gamma-ray detectors for different counting geometries,” Nucl. Instr. and Meth. 187 (1981) 451. 2. L. Moens, F. De Corte, A. Simonits, Lin Xilei, A. De Wispelaere, F. De Donder and J. Hoste, “Calculation of the absolute peak efficiency of Ge and Ge(Li) detectors for different counting geometries,” Journal of Radioanalytical Chemistry. 70 (1982) 539. 3. Maurice Miller, Mitko Voutchkov, “Modeling the impact of uncertainty in detector specification on efficiency values of a HPGe detector using ANGLE software,” Nuclear Technology & Radiation Protection. 28 (2013) 169. 4. K. Abbas, F. Simonelli, F. D’Alberti, M. Forte, M. F. Stroosnijder, “Reliability of two calculation codes for efficiency calibrations of HPGe detectors,” Applied Radiation and Isotopes 56 (2002) 703. 5. Tien-ko Wang, Wei-yang Mar, Tzung-hua Ying, Chia-lian Tseng, Chi-hung Liao and Mei-ya Wang, “HPGe Detector Efficiency Calibration for Extended Cylinder and Marinelli–beaker Sources using the ESOLAN Program,” Applied Radiation & Isotopes 48 (1997) 83-95. 6. J. H. Hubbell and S. M. Seltzer, “Tables of X-Ray Mass Attenuation Coefficients and Mass EnergyAbsorption Coefficients from 1 keV to 20 MeV for Elements Z = 1 to 92 and 48 Additional Substances of Dosimetric Interest,” Applied Radiation and Isotopes 33 (1982) 1269, http://physics.nist.gov/PhysRefData /XrayMassCoef/tab3.html 7. M. J. Berger, J. H. Hubbell, S.M. Seltzer, J. Chang, J.S. Coursey, R. Sukumar, D.S. Zucker, and K. Olsen, “XCOM : Photon Cross Sections Database,” NIST Standard Reference Database 8, XGAM (1990),

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http://www.nist.gov/pml/data/xcom/index.cfm 8. Graham J. McCallum, Graeme E. Coote, “Influence of source-detector distance on relative intensity and angular correlation measurements with Ge(Li) spectrometer,” Nucl. Instr. and Meth. 130 (1975) 189. 9. Klaus Debertin, Ulrich Schotzig, “Coincidence summing corrections in Ge(Li)-spectrometry at low source-to-detector distances,” Nucl. Instr. and Meth. 158 (1979) 471. 10. C. S. Park, H. D. Choi, G. M. Sun and J. H. Whang, “Status of Developing HPGe γ-ray Spectrum Analysis Code HYPERGAM,” J. Prog. Nucl. Energy 50 (2008) 389. 11. Mahmoud I. Abbas, “Direct mathematical method for calculation full-energy peak efficiency and coincidence corrections of HPGe detectors for extended sources,” Nucl. Instr. and Meth. 256 (2007) 554. 12. Dirk Arnold and Octavian Sima, “Extension of the efficiency calibration of germanium detectors using the GESPECOR software,” Applied Radiation and Isotopes 61 (2004) 117-121. 13. V. P. Kolotov et al., “Estimation of true coincidence corrections for voluminous sources,” J. Radioanal. Nucl. Chem. 210 (1996) 183. 14. V. P. Kolotov, M. J. Koskelo, “Testing of different true coincidence correction approaches for gamma-ray spectrometry of voluminous sources,” J. Radioanal. Nucl. Chem. 233 (1998) 95. 15. J. Rodenas, A. Pascual, I. Zarza, V. Serradell, J. Ortiz, L. Ballesteros, “Analysis of the influence of germanium dead layer on detector calibration simulation for environmental radioactive samples using the Monte Carlo method,” Nucl. Instr. and Meth. 496 (2003) 390. 16. P. Vukotic, N. Mihaljevic, S. Jovanovic, S. Dapcevic, F. Boreli, “On the applicability of the effective solid angle concept in activity determination of large cylindrical source,” Journal of Radioanalytical Chemistry. 218 (1997) 21. 17. Tien-ko Wang, Wei-yang Mar, Tzung-hua Ying, Chi-hung Liao and Chia-Lian Tseng, “HPGe Detector Absolute-peak-efficiency Calibration by Using the ESOLAN Program,” Applied Radiation & Isotopes 46 (1995) 933.

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Fig. 1 An operation GUI screen of the EXVol code. Fig. 2 Schematic diagram of 450 ml, 1000 ml Marinelli beakers and a 1000 ml cylindrical beaker. Fig. 3. Top view of the experimental instruments and detection geometry. (Dimension: mm) Fig. 4. Comparison of the efficiencies between the calculational (lines) and the experimental (symbols) values for Marinelli beakers measured with the 17% p-type detector. The sources are 450 ml solid medium (full line and square symbols) and 1000 ml solid medium (dashed line and triangle symbols). Fig. 5. Comparison of the efficiencies between the calculational (lines) and the experimental (symbols) values for Marinelli beakers measured with the 32% n-type detector. The sources are 450 ml solid medium (full line and triangle symbols), 450 ml liquid medium (dashed-dotted line circle symbols), 1000 ml solid medium (dotted line and square symbols) and 1000 ml liquid medium (dashed line and inverted triangle symbols). Fig. 6. Comparison of the efficiencies between the calculational (lines) and the experimental (symbols) values for cylindrical beaker measured with the 32% n-type detector. The source is 1000 ml liquid medium and source-to-detector distance is 0 cm (dashed line and circle symbols), 5 cm (full line and triangle symbols) and 10 cm (dotted line and square symbols). Fig. 7. Comparison of the efficiencies between the calculational (lines) and the experimental (symbols) values for Marinelli beakers measured with the 63% n-type detector. The sources are 450 ml solid medium (dotted line and square symbols), 450 ml liquid medium (dashed line and circle symbols), 1000 ml solid medium (full line and triangle symbols) and 1000 ml liquid medium (dashed-dotted line and inverted triangle symbols). Fig. 8. Comparison of the efficiencies between the calculational (lines) and the experimental (symbols) values for cylindrical beaker measured with the 63% n-type detector. The source is 1000 ml liquid medium and source-to-detector distance is 0 cm (dashed line and square symbols), 5 cm (full line and circle symbols) and 10 cm (dotted and triangle symbols). Fig. 9. Relative deviation of the calculated efficiency from the measured value by the 17% p-type HPGe detector, for Marinelli beaker of 450 ml solid medium (square symbols) and 1000 ml solid medium (triangle symbols). Fig. 10. Relative deviation of the calculated efficiency from the measured value by the 32% n-type HPGe detector, for Marinelli beaker of 450 ml solid medium (triangle symbols), 450 ml liquid medium (circle symbols), 1000 ml solid medium (square symbols) and 1000 ml liquid medium (inverted triangle symbols). Fig. 11. Relative deviation of the calculated efficiency from the measured value by the 32% n-type HPGe detector, for cylindrical beaker of 1000 ml liquid medium and the source-to-detector distance is 0 cm (circle symbols), 5 cm (triangle symbols) and 10 cm (square symbols).

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Fig. 12. Relative deviation of the calculated efficiency from the measured value by the 63% n-type HPGe detector, for Marinelli beaker of 450 ml solid medium (square symbols), 450 ml liquid medium (circle symbols), 1000 ml solid medium (triangle symbols) and 1000 ml liquid medium (inverted triangle symbols). Fig. 13. Relative deviation of the calculated efficiency from the measured value by the 63% n-type HPGe detector, for cylindrical beaker of 1000 ml liquid medium and the source-to-detector distance is 0 cm (square symbols), 5 cm (circle symbols) and 10 cm (triangle symbols). Fig. 14. Percentile systematic error of the efficiency from the calculated one for the 17% p-type (dashed lines), 32% n-type (full lines) and 63% n-type (dotted lines) HPGe detectors in this study, introduced by inaccurate values of “(a)crystal diameter”, “(b)crystal height”, “(c)source-to-crystal distance” and “(d)dead layer”. The source is Marinelli beaker of 450 ml solid medium. Table 1. Information of source used in this study.

Circular casing

Marinelli beaker

Cylindrical beaker

[Point]

[Volume]

[Volume]

Type

Authority

IAEA

Volume [ml]

-

Medium

Al

KRISS 450, 1000

1000

Liquid, Solid

Liquid

Practically coincidence-free gamma lines: E [keV]

Nuclide

241

Am

133

Ba

60

241

Am

59.54

109

Cd

88.04

57

Co

137

Cs

152

Eu

Co

139

Ce

165.85

113

Sn

255.13, 391.69

85

Sr

137

12

122.06, 136.47

Cs

514.00 661.64

Coincident gamma lines : E [keV] 60

Co

1173.23, 1332.50

88

Y

898.04, 1836.06

Table 2. Specifications of the detectors.

Relative Paramete r

Type

Model

Efficienc y

Resolutio n [FWHM]

Crystal length / diamete r

window thickne ss [mm]

Dead layer [μm]

Detecto r bias voltage

[mm] GC1518 (CAN p

36.5/ 17%

1.92 keV

BERRA)

Contents

n

n

GMX25P 4 (ORTEC )

GMX60P 4-83 (ORTEC )

Research highlights

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50.5

0.2 (kapton )

1.96 keV

0.5 (Be) 52.9

1.86 keV

-4200 V Ge/Li: 700 Ge/B: 0.3,

73.7/ 63%

Ge/B: 0.3

0.5 (Be) 67.7

+1700 V

Ge/B: 0.3,

79.5/ 32%

Ge/Li: 400,

-4900 V Ge/Li: 700



Most previous studies used cylindrical sources of small volume and small volume detectors. But in this study, we use cylindrical sources of large volume and Marinelli beaker sources and a big volume detector, which were not dealt in previous studies



Comparing to a study of similar experimental conditions, we have shown the effects of the detector variables on the relative deviations vs. the -energy.



Comparing to other research results, EXVol is shown to provide an accuracy level similar with those obtainable by the existing programs and calculation time of detection efficiency takes less than 5 minutes.



The EXVol is versatile that it can give the detection efficiency for variety of forms, geometry and distance of voluminous source and detector

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Fig. 1. An operation GUI screen of the EXVol code.

Fig. 2. Schematic diagram of 450 ml, 1000 ml Marinelli beakers and a 1000 ml cylindrical beaker.

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Fig. 3. Top view of the experimental instruments and detection geometry. (Dimension: mm)

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Fig. 4. Comparison of the efficiencies between the calculational (lines) and the experimental (symbols) values for Marinelli beakers measured with the 17% p-type detector. The sources are 450 ml solid medium (full line and square symbols) and 1000 ml solid medium (dashed line and triangle symbols).

17

Fig. 5. Comparison of the efficiencies between the calculational (lines) and the experimental (symbols) values for Marinelli beakers measured with the 32% n-type detector. The sources are 450 ml solid medium (full line and triangle symbols), 450 ml liquid medium (dashed-dotted line circle symbols), 1000 ml solid medium (dotted line and square symbols) and 1000 ml liquid medium (dashed line and inverted triangle symbols).

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Fig. 6. Comparison of the efficiencies between the calculational (lines) and the experimental (symbols) values for cylindrical beaker measured with the 32% n-type detector. The source is 1000 ml liquid medium and source-to-detector distance is 0 cm (dashed line and circle symbols), 5 cm (full line and triangle symbols) and 10 cm (dotted line and square symbols).

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Fig. 7. Comparison of the efficiencies between the calculational (lines) and the experimental (symbols) values for Marinelli beakers measured with the 63% n-type detector. The sources are 450 ml solid medium (dotted line and square symbols), 450 ml liquid medium (dashed line and circle symbols), 1000 ml solid medium (full line and triangle symbols) and 1000 ml liquid medium (dashed-dotted line and inverted triangle symbols).

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Fig. 8. Comparison of the efficiencies between the calculational (lines) and the experimental (symbols) values for cylindrical beaker measured with the 63% n-type detector. The source is 1000 ml liquid medium and source-to-detector distance is 0 cm (dashed line and square symbols), 5 cm (full line and circle symbols) and 10 cm (dotted and triangle symbols).

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Fig. 9. Relative deviation of the calculated efficiency from the measured value by the 17% ptype HPGe detector, for Marinelli beaker of 450 ml solid medium (square symbols) and 1000 ml solid medium (triangle symbols).

22

Fig. 10. Relative deviation of the calculated efficiency from the measured value by the 32% ntype HPGe detector, for Marinelli beaker of 450 ml solid medium (triangle symbols), 450 ml liquid medium (circle symbols), 1000 ml solid medium (square symbols) and 1000 ml liquid medium (inverted triangle symbols). .

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Fig. 11. Relative deviation of the calculated efficiency from the measured value by the 32% ntype HPGe detector, for cylindrical beaker of 1000 ml liquid medium and the source-to-detector distance is 0 cm (circle symbols), 5 cm (triangle symbols) and 10 cm (square symbols).

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Fig. 12. Relative deviation of the calculated efficiency from the measured value by the 63% ntype HPGe detector, for Marinelli beaker of 450 ml solid medium (square symbols), 450 ml liquid medium (circle symbols), 1000 ml solid medium (triangle symbols) and 1000 ml liquid medium (inverted triangle symbols).

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Fig. 13. Relative deviation of the calculated efficiency from the measured value by the 63% ntype HPGe detector, for cylindrical beaker of 1000 ml liquid medium and the source-to-detector distance is 0 cm (square symbols), 5 cm (circle symbols) and 10 cm (triangle symbols).

26

28

29

Fig. 14. Percentile systematic error of the efficiency from the calculated one for the 17% p-type (dashed lines), 32% n-type (full lines) and 63% n-type (dotted lines) HPGe detectors in this study, introduced by inaccurate values of “(a)crystal diameter”, “(b)crystal height”, “(c)sourceto-crystal distance” and “(d)dead layer”. The source is Marinelli beaker of 450 ml solid medium.

30