- Email: [email protected]
On the iteration of coincidence summing correction for determination of gamma-ray intensities
Applied Radiation and Isotopes ∎ (∎∎∎∎) ∎∎∎–∎∎∎
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
On the iteration of coincidence summing correction for determination of gamma-ray intensities Yosuke Shima a, Hiroaki Hayashi b, Yasuaki Kojima c, Ryouta Jyousyou a, Michihiro Shibata c,n a
Department of Materials, Physics and Energy Engineering, Nagoya University, Nagoya 464-8603, Japan Institute of Biomedical Sciences, Tokushima University Graduate School, Tokushima 770-8509, Japan c Radioisotope Research Center, Nagoya University, Nagoya 464-8602, Japan b
H I G H L I G H T S
Summing corrections are required for Iγ evaluation in close geometry measurement. Self-consistent values of coincidence summing corrections are obtained by iteration. The required number of iterations of coincidence summing correction was evaluated. 56 Co, 134Cs and 154Eu were measured in specific solid angle geometries as examples. At least 4 iterations needed to determine Iγ with uncertainties below 5%.
art ic l e i nf o
a b s t r a c t
Article history: Received 31 March 2015 Accepted 19 November 2015
In order to determine the γ-ray emission intensities of nuclei far from the β-stability line with HPGe detectors under large solid-angle geometry, coincidence summing corrections should be performed, even if full energy peak efficiencies of detectors are accurately measured with standard sources. Because the summing effects depend on decay schemes and emission intensities, the correction needs to be iterated several times starting from the initial values of intensities obtained directly from the measured peak counts of γ-rays. Considering 134Cs, 154Eu and 56Co as typical examples, we discuss the number of iterations of summing correction required for self-consistency with respect to the total efficiencies of the detectors. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Coincidence summing correction Monte Carlo simulation 134 Cs 154 Eu 56 Co
1. Introduction For γ-ray emission intensity determination with HPGe detectors, in many cases the short-lived nuclei far from the β-stability line are measured in close-to-detector geometry. This improves the statistics and also gives the possibility to carry out simultaneously the γ–γ coincidence measurements. But in these conditions the apparent γ-ray intensities (obtained directly from the observed peak count rates of γ-rays divided by the peak efficiencies) are affected by large coincidence summing effects, which should be corrected for obtaining unbiased intensities. Because the correction depends on the decay scheme and emission intensities, the summing correction needs to be iterated several times, each time using for correction the newly determined level structure and n
Corresponding author. E-mail address: [email protected] (M. Shibata).
γ-ray intensities. The β-branching ratios and the log-ft values, which are needed for the discussion of the nuclear structure, are calculated from the γ-ray intensity imbalance at each excited level. Summing effects strongly depend on the total efficiency of the detector. It is known empirically from previous studies that summing corrections should be iterated several times before reaching self-consistency; nevertheless, the number of iterations has not been investigated with respect to the total efficiency. In this paper, the number of iterations required for the assessment of reliable γray intensities is discussed with respect to the total efficiencies. For this study the radionuclides 56Co, 134Cs and 154Eu, which have well evaluated, but dissimilar decay schemes, were chosen. The nuclide 134Cs has a relatively simple decay scheme. 154Eu has a more complicated decay scheme including γ-rays and KX-rays in a wide energy range. 56Co is a β þ emitter having high energy γ-rays above 3 MeV. We use the correct level structure and placement of the γ transitions in the schemes of these nuclides, but consider that the emission intensities are unknown. Starting from the
http://dx.doi.org/10.1016/j.apradiso.2015.11.035 0969-8043/& 2015 Elsevier Ltd. All rights reserved.
Please cite this article as: Shima, Y., et al., On the iteration of coincidence summing correction for determination of gamma-ray intensities. Appl. Radiat. Isotopes (2015), http://dx.doi.org/10.1016/j.apradiso.2015.11.035i
Y. Shima et al. / Applied Radiation and Isotopes ∎ (∎∎∎∎) ∎∎∎–∎∎∎
2
apparent intensities and applying the corrections iteratively, we evaluate the corrected intensities and compare them with the reference values.
2. Experiments A p-type HPGe detector of 22% relative efficiency was used for the experiments. Throughout the measurements, typical energy resolution of the detector was 1.9 keV at 1332 keV. The source-todetector distances were set at 13, 28 and 153 mm, corresponding to 20%, 10% and 0.6% solid angles of the source with respect to the detector surface; here and throughout the paper we denote by x% solid angle a solid angle which equals x% from 4π steradians. The detector was covered with a 5-mm-thick acrylic cap to stop the β -particles. The full energy peak efficiencies ϵp and total efficiencies ϵt of the detector for each measurement configuration, determined experimentally and by Monte Carlo simulation, are shown in Fig. 1. Experimental calibration was done using monoenergetic γ-ray sources of 109Cd, 137Cs and 54Mn. A 60Co source was also measured at 0.6% solid-angle geometry. The nuclear decay data were adopted from the NUCLEIDE Database (2013) database, hosted by the Laboratoire National Henri Becquerel from CEA, Saclay, France. Next, the Monte Carlo simulation code GEANT4 (Agostinelli et al., 2003) was used for the determination of the ϵp and ϵt so as to reproduce the measured ϵp at 0.6% solid angle, by modifying the detector geometry parameters, such as crystal size. The modified parameters were adopted for simulation of the measurements at 10% and 20% solid-angle geometries. As a result, the simulation by GEANT4 reproduced well the experimental ϵp and ϵt ; their uncertainties were evaluated to be 2% and 5%, respectively. The radioactive 134Cs and 154Eu sources were prepared by dropping a small amount of radioactive solution on a thin 5 mm 5 mm square of filter paper. The nuclide 56Co was produced with the 56Fe(p,n) reaction using a TANDEM accelerator at Japan Atomic Energy Agency. Several squares (10 mm 10 mm) of iron foil, 0.7-mm-thick and others 1-mm-thick, were bombarded by 32 MeV proton beams. The nuclide 134Cs was measured at the three solid-angle geometries, whereas 154Eu and 56Co were
measured only in the 20% solid-angle geometry. For the measurement of 56Co, the source was sandwiched between 5-mmthick acrylic plates to stop the β þ particles (Kawade et al., 1991). The activities of the radioisotopes were between 0.4 and 1.5 kBq, with approximate uncertainties of 2%, and the counting rates were kept below one thousand counts per second (kcps). The pile-up and dead time of the ADC were negligible.
3. Analysis of
γ-ray relative intensities and results
We applied the following step by step iteration procedure for obtaining the emission intensities of 134Cs, 154Eu and 56Co. At the beginning, the initial intensity Iγi;0 (uncorrected) was deduced as follows:
Iγi;0=
Cγi;0 ϵp γi
(1)
where Cγi;0 and ϵpγ are the measured count rate and peak efficiency i
for γi, respectively. The summing correction was evaluated for the γi peak by means of the procedure proposed by Shima et al. (2014) using the level structure from the Evaluated Nuclear Structure Data File (ENSDF) (2014). Here the method is described briefly. The decay path from an excited level to the ground state in the decay scheme of each nucleus was randomly sampled using Monte Carlo simulation and then the energy deposited in the detector was also randomly sampled on the basis of ϵp and ϵt , respectively. Sampling the energy deposition in this way, which is rigorously correct for point-like sources, substantially reduces the computation time, by elimination the need to simulate the interaction with the detector for each photon. A number of 107 events were simulated. If the βbranching ratios became negative at some level, they were set to zero. According to the efficiencies and the decay scheme, the energy deposition events without coincidence summing (with one γray) or in the presence of coincidence summing (with cascading γrays), were simulated. The ratio of the number of events in which the total energy of the γi photon was deposited in the detector in the two cases gives the correction factor for coincidence summing . Using the correction factor fγ the corrected intensity I′γi;1 fγ i;0 → 1
i;0 → 1
was deduced as follows:
I′γi;1=fγi;0 → 1 × Iγi;0 εt(Ω=20%)
-1
Efficiency
10
εt(Ω=10%)
εp(Ω=20%)
εp(Ω=10%)
-2
10
εt(Ω=0.6%)
(2)
Next, the corrected emission intensity I′γi;1 was renormalized, obtaining thus Iγi;1. The corrected value Iγ604.7;1 (in the case of 134Cs), and the corresponding values for 1274.4 keV (in the case of 154Eu) and 846.8 keV (in the case of 56Co), were used for normalization. For obtaining the next value of the summing correction fγi;1 → 2 the procedure was repeated using the renormalized values Iγi;1. Successively, the corrected intensities were derived by multiplying the initial intensities Iγi;0 by the correction factor as follows:
I′γi; j +1=fγi; j → j +1 × Iγi;0 εp(Ω=0.6%)
(3)
Fig. 2 shows the trend of the ratio of the current value fγi; j → j +1 to
-3
10
the previous value fγi; j −1 → j of the correction factor for each
γ ray of
134
-4
10
2
3
10
10 Gamma-ray energy (keV)
Fig. 1. Full energy peak and total efficiencies of a 22% relative efficiency p-type HPGe detector for each measurement configuration determined experimentally and by Monte Carlo simulation with GEANT4.
Cs versus the number of iterations of the correction, from j¼1 to 10. Most correction factors converged at 6 iterations, except for some weak γ rays. Fig. 3 and Table 1 show the deviation of the deduced values of the emission intensities of 134Cs from the reference values for each measurement configuration. The deduced intensities for most γ rays are in agreement with the reference values of NUCLEIDE Database (2013). The results for 154Eu and 56Co measured in the 20% solid angle configuration are shown in Fig. 4. The 1274.4 eV γ-ray and the 846.8 keV γ-ray were used for
Please cite this article as: Shima, Y., et al., On the iteration of coincidence summing correction for determination of gamma-ray intensities. Appl. Radiat. Isotopes (2015), http://dx.doi.org/10.1016/j.apradiso.2015.11.035i
Y. Shima et al. / Applied Radiation and Isotopes ∎ (∎∎∎∎) ∎∎∎–∎∎∎
475.6 563.2 569.3
1.05
604.7 795.9 802.0
1038.6 1168.0 1365.2
0.1
Ω=0.6%
1 0.95 1.1
Ω=20%
0.05 0 -0.05
154
-0.1
Ω=10%
1.05
f /f
Deviation (%)
1.1
3
0
2
4
6
Eu 10
8
Number of iterations
1
123.7(116) 723.3(57.6) 1004.8(51.7) 873.2(34.7) 996.3(30.1) 247.9(19.8)
0.95 1.1 Ω=20%
1.05
591.8(14.2) 756.8(13.0) 1596.5(5.16) 692.4(5.1) 582.0(2.56) 904.1(2.55)
1246.1(2.46) 1494.0(2.00) 815.5(1.47) 444.5(1.57) 892.8(1.50)
0.1
0.95
2/1
3/2
4/3
5/4
6/5
7/6
(iteration ) / (iteration
8/7
9/8
10/9
)
Fig. 2. The trends of the correction factor versus the number of iterations for the 20%, 10% and 0.6% solid-angle measurements. The vertical axis indicates the ratio of the correction factor at iteration j to the value at iteration j 1.
Deviation (%)
1
Ω=20%
0.05 0 -0.05 56
-0.1
Co
0
2
4
6
8
10
Number of iterations 977.4(1.42) 1037.8(14.0) 1175.1(2.25) 1238.3(66.5) 1360.2(4.28)
0.1 Ω=0.6%
0.05
475.6(1.513) 563.2(8.541) 569.3(15.748)
-0.05 -0.1 0.1 Deviation (%)
3202.0(3.21) 3253.5(7.88) 3273.1(1.86) 3451.2(0.94)
Fig. 4. Deviations of the corrected relative γ-ray intensities from the reference values for 154Eu and 56Co in the Ω¼20% geometry.
0 795.9(87.54) 802.0(8.900) 1038.6(1.014)
1168.0(1.834) 1365.2(3.091)
Ω=10%
0.05 0 -0.05 -0.1 0.1
Ω=20%
0.05 0 -0.05 -0.1
1771.4(15.5) 2015.2(3.02) 2034.8(7.75) 2598.5(17.0) 3009.6(1.04)
0
2
4
6
8
10
Number of iterations Fig. 3. Deviations of the corrected relative γ-ray intensities from the reference values for 134Cs in each geometry.
normalization in 154Eu and 56Co, respectively. Under the condition of the 20% solid angle, it was found that at least 6 iterations are needed for obtaining self-consistent values of the summing correction of the three isotopes. Despite of their different decay properties, similar tendencies were observed among the three radionuclides. It should be mentioned that since 154Eu has many γrays and a complicated level structure, only γ-rays with relative intensities above 1% were taken into account. On the other hand, annihilation γ-rays were taken into account in the case of 56Co. The 3451.2 keV γ-ray in 56Co shows a relatively large deviation; nevertheless, its relative intensity of 0.94% was the smallest in 56 Co. Therefore, it was considered that the deviation does not influence very much the imbalances of the intensities in the decay scheme. For unstable nuclei far from the stability line, the β-branching ratio Iβ and log-ft values were determined from the γ-ray intensity imbalances at each level of excitation. To derive nuclear structure information from the decay scheme, it is considered that uncertainties of the relative intensities below 5% are desirable. To obtain reliable results, at least 4 iterations are required, but it is
Table 1 Comparisons of the corrected relative emission intensities after 10 iterations to the evaluated values. Eγ(keV)
Relative Iγ (%)
Solid angle 20%
475.4 563.2 569.3 604.7a 795.9 802.0 1038.6 1168.0 1365.2 a
1.5137 8.54114 15.74817 100 87.546 8.90016 1.10143 1.8345 3.0918
10%
0.6%
Corrected Iγ (%)
Deviation (%)
Corrected Iγ (%)
Deviation (%)
Corrected Iγ (%)
Deviation (%)
1.542 8.720 16.189 100 88.75 9.081 1.0248 1.853 3.104
1.9 2.1 2.8 0 1.4 2.0 1.1 1.1 0.4
1.530 8.651 15.886 100 87.82 8.896 1.0267 1.869 3.145
1.1 1.3 0.9 0 0.3 0.0 1.2 2.0 1.8
1.523 8.522 15.958 100 88.32 8.965 1.0103 1.849 3.112
0.6 0.2 1.3 0 0.9 0.7 0.4 0.8 0.7
Used as normalization.
Please cite this article as: Shima, Y., et al., On the iteration of coincidence summing correction for determination of gamma-ray intensities. Appl. Radiat. Isotopes (2015), http://dx.doi.org/10.1016/j.apradiso.2015.11.035i
4
Y. Shima et al. / Applied Radiation and Isotopes ∎ (∎∎∎∎) ∎∎∎–∎∎∎
σϵp and σϵt at each correction, and the uncertainty σγi: j − 1 of the previous correction factor. The value of σγi: j − 1 is also affected by σϵp and σϵt . It is considered that the σγi associated with ϵt is at most 2% when the uncertainty of ϵt is approximately 5%. The uncertainty introduced by the Monte Carlo calculation is negligibly small in this calculation. Then, the components of the uncertainties of intensities are roughly evaluated to be the uncertainties of peak efficiencies σϵp of 2% and the previous σγi: j − 1 of 2%, namely 0.022 + 0.022 ≈0.03 at each iteration. Then, the uncertainty n brought by n iterations is considered to be ∑1 0.03n . Therefore, the uncertainty due to the iteration procedure is at most 0.031 in total when there are 6 iterations.
4. Conclusion Fig. 5. Correction factors at 10 iterations versus the average total efficiencies for 134 Cs, 154Eu and 56Co.
considered that weak γ-rays having relative intensities less than 1% do not need to be taken into account for the coincidence summing correction. The magnitude of the correction depends mainly on the total efficiencies. Since it is difficult to introduce a definite parameter to represent the influence factors on the summing effects, the ∑ ϵt × Iγ weighted mean total efficiency ϵt , defined as , was pro∑ Iγ
posed as a measure of the correction. The final correction factors versus ϵt are shown in Fig. 5 for the three nuclides. The value of the correction factor is specific to each γ-ray, but Fig. 5 shows that the range of the magnitude of these factors is of the order of ϵt . It is considered that the uncertainties brought by the correction depend mainly on the magnitude of the total efficiencies. The reliability of the relative intensities increases but the uncertainties also increase as the number of iterations of correction increases. In studies that processed the correction by an analytical method (e.g. Debertin and Helmer (1988)), the uncertainties could be calculated by the error propagation equation. In the present method by Monte Carlo calculation, this analytical estimation could not be applied. Nevertheless, it is considered that the uncertainties increase when the peak and total efficiencies increase. The uncertainty σγi: j for Iγi after iteration j was evaluated as follows. From the deviation of the deduced results from the reference values, the uncertainties by the summing correction were evaluated to be about 3% for the 20% solid-angle measurements as shown in Figs. 3 and 4. The uncertainties due to the correction depend actually on the nuclide and gamma-ray, but an approximate global estimation can be obtained as follows. It is considered that σγi: j includes the statistical uncertainty σγi:stat. of peak counts and the uncertainty related to the correction factor for iteration j. The uncertainty of the correction factor σ fi: j includes the statistical uncertainties of the Monte Carlo calculation, the uncertainties of
In conclusion, for the determination of γ-ray emission intensities of unstable nuclei by measurements in close-to-detector geometrical configurations, the correction for coincidence summing requires several iterations. The number of iterations depends on the decay scheme, namely the γ-ray energy, cascade relation and on the peak and total efficiencies. Nevertheless, our study shows that the results converge at 6 iterations, and that at least 4 iterations are needed in order to determine the emission intensities with 5% uncertainty in the case of the 20% solid-angle measurement. It is considered that the required number of iterations becomes larger in larger solid angle configuration. In addition, in this paper, we discuss the ideal case in which the γ-ray peaks are clearly observed without contaminants. In practice, it is important to analyze γ-ray spectra carefully and determine the peak counts as initial conditions reliably.
References Agostinelli, A., et al., 2003. GEANT4-a simulation toolkit. Nucl. Instrum. Methods Phys. Res. A 503, 250–303. Debertin, K., Helmer, R.G., 1988. Gamma- and X-ray Spectrometry with Semiconductor Detectors. Elsevier Science Publishers, North-Holland, Amsterdam. Evaluated Nuclear Structure Data File (ENSDF), 2014. Retrieval 〈http://www.nndc. bnl.gov/ensdf/〉. Last updated 2014-07-10. (Published: 2004 Nuclear Data Sheets). Kawade, K., Katou, K., Osa, A., Shibata, M., Yamamoto, H., Katoh, T., 1991. Measurements of β þ -activity by detecting 511 keV annihilation γ-rays. Nucl. Instrum. Methods Phys. Res. A 301, 594–595. NUCLEIDE Database, 2013. Recommended data by the Decay Data Evaluation Project. 〈http://www.nucleide.org/DDEP_WG/DDEPdata.htm〉; Nuclear Decay Data Evaluations of: 134Cs (author: Marie-Martine Bé, LNHB, CEA, France, 2012), 109Cd (Marie-Martine Bé (LNHB) and E. Schönfeld (PTB, Germany), 1996), 137Cs (R.G. Helmer (INEEL, USA) and V. Chechev (KRI, Russia), 1998, updated in 2006), 54Mn (R.G. Helmer (INEEL, USA) and E. Schönfeld (PTB, Germany), 2001), 60Co (R.G. Helmer, 1996, updated in 2006) (updated 20 December 2013). Shima, Y., Hayashi, H., Kojima, Y., Shibata, M., 2014. 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, 97–103.
Please cite this article as: Shima, Y., et al., On the iteration of coincidence summing correction for determination of gamma-ray intensities. Appl. Radiat. Isotopes (2015), http://dx.doi.org/10.1016/j.apradiso.2015.11.035i
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
On the iteration of coincidence summing correction for determination of gamma-ray intensities Yosuke Shima a, Hiroaki Hayashi b, Yasuaki Kojima c, Ryouta Jyousyou a, Michihiro Shibata c,n a
Department of Materials, Physics and Energy Engineering, Nagoya University, Nagoya 464-8603, Japan Institute of Biomedical Sciences, Tokushima University Graduate School, Tokushima 770-8509, Japan c Radioisotope Research Center, Nagoya University, Nagoya 464-8602, Japan b
H I G H L I G H T S
Summing corrections are required for Iγ evaluation in close geometry measurement. Self-consistent values of coincidence summing corrections are obtained by iteration. The required number of iterations of coincidence summing correction was evaluated. 56 Co, 134Cs and 154Eu were measured in specific solid angle geometries as examples. At least 4 iterations needed to determine Iγ with uncertainties below 5%.
art ic l e i nf o
a b s t r a c t
Article history: Received 31 March 2015 Accepted 19 November 2015
In order to determine the γ-ray emission intensities of nuclei far from the β-stability line with HPGe detectors under large solid-angle geometry, coincidence summing corrections should be performed, even if full energy peak efficiencies of detectors are accurately measured with standard sources. Because the summing effects depend on decay schemes and emission intensities, the correction needs to be iterated several times starting from the initial values of intensities obtained directly from the measured peak counts of γ-rays. Considering 134Cs, 154Eu and 56Co as typical examples, we discuss the number of iterations of summing correction required for self-consistency with respect to the total efficiencies of the detectors. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Coincidence summing correction Monte Carlo simulation 134 Cs 154 Eu 56 Co
1. Introduction For γ-ray emission intensity determination with HPGe detectors, in many cases the short-lived nuclei far from the β-stability line are measured in close-to-detector geometry. This improves the statistics and also gives the possibility to carry out simultaneously the γ–γ coincidence measurements. But in these conditions the apparent γ-ray intensities (obtained directly from the observed peak count rates of γ-rays divided by the peak efficiencies) are affected by large coincidence summing effects, which should be corrected for obtaining unbiased intensities. Because the correction depends on the decay scheme and emission intensities, the summing correction needs to be iterated several times, each time using for correction the newly determined level structure and n
Corresponding author. E-mail address: [email protected] (M. Shibata).
γ-ray intensities. The β-branching ratios and the log-ft values, which are needed for the discussion of the nuclear structure, are calculated from the γ-ray intensity imbalance at each excited level. Summing effects strongly depend on the total efficiency of the detector. It is known empirically from previous studies that summing corrections should be iterated several times before reaching self-consistency; nevertheless, the number of iterations has not been investigated with respect to the total efficiency. In this paper, the number of iterations required for the assessment of reliable γray intensities is discussed with respect to the total efficiencies. For this study the radionuclides 56Co, 134Cs and 154Eu, which have well evaluated, but dissimilar decay schemes, were chosen. The nuclide 134Cs has a relatively simple decay scheme. 154Eu has a more complicated decay scheme including γ-rays and KX-rays in a wide energy range. 56Co is a β þ emitter having high energy γ-rays above 3 MeV. We use the correct level structure and placement of the γ transitions in the schemes of these nuclides, but consider that the emission intensities are unknown. Starting from the
http://dx.doi.org/10.1016/j.apradiso.2015.11.035 0969-8043/& 2015 Elsevier Ltd. All rights reserved.
Please cite this article as: Shima, Y., et al., On the iteration of coincidence summing correction for determination of gamma-ray intensities. Appl. Radiat. Isotopes (2015), http://dx.doi.org/10.1016/j.apradiso.2015.11.035i
Y. Shima et al. / Applied Radiation and Isotopes ∎ (∎∎∎∎) ∎∎∎–∎∎∎
2
apparent intensities and applying the corrections iteratively, we evaluate the corrected intensities and compare them with the reference values.
2. Experiments A p-type HPGe detector of 22% relative efficiency was used for the experiments. Throughout the measurements, typical energy resolution of the detector was 1.9 keV at 1332 keV. The source-todetector distances were set at 13, 28 and 153 mm, corresponding to 20%, 10% and 0.6% solid angles of the source with respect to the detector surface; here and throughout the paper we denote by x% solid angle a solid angle which equals x% from 4π steradians. The detector was covered with a 5-mm-thick acrylic cap to stop the β -particles. The full energy peak efficiencies ϵp and total efficiencies ϵt of the detector for each measurement configuration, determined experimentally and by Monte Carlo simulation, are shown in Fig. 1. Experimental calibration was done using monoenergetic γ-ray sources of 109Cd, 137Cs and 54Mn. A 60Co source was also measured at 0.6% solid-angle geometry. The nuclear decay data were adopted from the NUCLEIDE Database (2013) database, hosted by the Laboratoire National Henri Becquerel from CEA, Saclay, France. Next, the Monte Carlo simulation code GEANT4 (Agostinelli et al., 2003) was used for the determination of the ϵp and ϵt so as to reproduce the measured ϵp at 0.6% solid angle, by modifying the detector geometry parameters, such as crystal size. The modified parameters were adopted for simulation of the measurements at 10% and 20% solid-angle geometries. As a result, the simulation by GEANT4 reproduced well the experimental ϵp and ϵt ; their uncertainties were evaluated to be 2% and 5%, respectively. The radioactive 134Cs and 154Eu sources were prepared by dropping a small amount of radioactive solution on a thin 5 mm 5 mm square of filter paper. The nuclide 56Co was produced with the 56Fe(p,n) reaction using a TANDEM accelerator at Japan Atomic Energy Agency. Several squares (10 mm 10 mm) of iron foil, 0.7-mm-thick and others 1-mm-thick, were bombarded by 32 MeV proton beams. The nuclide 134Cs was measured at the three solid-angle geometries, whereas 154Eu and 56Co were
measured only in the 20% solid-angle geometry. For the measurement of 56Co, the source was sandwiched between 5-mmthick acrylic plates to stop the β þ particles (Kawade et al., 1991). The activities of the radioisotopes were between 0.4 and 1.5 kBq, with approximate uncertainties of 2%, and the counting rates were kept below one thousand counts per second (kcps). The pile-up and dead time of the ADC were negligible.
3. Analysis of
γ-ray relative intensities and results
We applied the following step by step iteration procedure for obtaining the emission intensities of 134Cs, 154Eu and 56Co. At the beginning, the initial intensity Iγi;0 (uncorrected) was deduced as follows:
Iγi;0=
Cγi;0 ϵp γi
(1)
where Cγi;0 and ϵpγ are the measured count rate and peak efficiency i
for γi, respectively. The summing correction was evaluated for the γi peak by means of the procedure proposed by Shima et al. (2014) using the level structure from the Evaluated Nuclear Structure Data File (ENSDF) (2014). Here the method is described briefly. The decay path from an excited level to the ground state in the decay scheme of each nucleus was randomly sampled using Monte Carlo simulation and then the energy deposited in the detector was also randomly sampled on the basis of ϵp and ϵt , respectively. Sampling the energy deposition in this way, which is rigorously correct for point-like sources, substantially reduces the computation time, by elimination the need to simulate the interaction with the detector for each photon. A number of 107 events were simulated. If the βbranching ratios became negative at some level, they were set to zero. According to the efficiencies and the decay scheme, the energy deposition events without coincidence summing (with one γray) or in the presence of coincidence summing (with cascading γrays), were simulated. The ratio of the number of events in which the total energy of the γi photon was deposited in the detector in the two cases gives the correction factor for coincidence summing . Using the correction factor fγ the corrected intensity I′γi;1 fγ i;0 → 1
i;0 → 1
was deduced as follows:
I′γi;1=fγi;0 → 1 × Iγi;0 εt(Ω=20%)
-1
Efficiency
10
εt(Ω=10%)
εp(Ω=20%)
εp(Ω=10%)
-2
10
εt(Ω=0.6%)
(2)
Next, the corrected emission intensity I′γi;1 was renormalized, obtaining thus Iγi;1. The corrected value Iγ604.7;1 (in the case of 134Cs), and the corresponding values for 1274.4 keV (in the case of 154Eu) and 846.8 keV (in the case of 56Co), were used for normalization. For obtaining the next value of the summing correction fγi;1 → 2 the procedure was repeated using the renormalized values Iγi;1. Successively, the corrected intensities were derived by multiplying the initial intensities Iγi;0 by the correction factor as follows:
I′γi; j +1=fγi; j → j +1 × Iγi;0 εp(Ω=0.6%)
(3)
Fig. 2 shows the trend of the ratio of the current value fγi; j → j +1 to
-3
10
the previous value fγi; j −1 → j of the correction factor for each
γ ray of
134
-4
10
2
3
10
10 Gamma-ray energy (keV)
Fig. 1. Full energy peak and total efficiencies of a 22% relative efficiency p-type HPGe detector for each measurement configuration determined experimentally and by Monte Carlo simulation with GEANT4.
Cs versus the number of iterations of the correction, from j¼1 to 10. Most correction factors converged at 6 iterations, except for some weak γ rays. Fig. 3 and Table 1 show the deviation of the deduced values of the emission intensities of 134Cs from the reference values for each measurement configuration. The deduced intensities for most γ rays are in agreement with the reference values of NUCLEIDE Database (2013). The results for 154Eu and 56Co measured in the 20% solid angle configuration are shown in Fig. 4. The 1274.4 eV γ-ray and the 846.8 keV γ-ray were used for
Please cite this article as: Shima, Y., et al., On the iteration of coincidence summing correction for determination of gamma-ray intensities. Appl. Radiat. Isotopes (2015), http://dx.doi.org/10.1016/j.apradiso.2015.11.035i
Y. Shima et al. / Applied Radiation and Isotopes ∎ (∎∎∎∎) ∎∎∎–∎∎∎
475.6 563.2 569.3
1.05
604.7 795.9 802.0
1038.6 1168.0 1365.2
0.1
Ω=0.6%
1 0.95 1.1
Ω=20%
0.05 0 -0.05
154
-0.1
Ω=10%
1.05
f /f
Deviation (%)
1.1
3
0
2
4
6
Eu 10
8
Number of iterations
1
123.7(116) 723.3(57.6) 1004.8(51.7) 873.2(34.7) 996.3(30.1) 247.9(19.8)
0.95 1.1 Ω=20%
1.05
591.8(14.2) 756.8(13.0) 1596.5(5.16) 692.4(5.1) 582.0(2.56) 904.1(2.55)
1246.1(2.46) 1494.0(2.00) 815.5(1.47) 444.5(1.57) 892.8(1.50)
0.1
0.95
2/1
3/2
4/3
5/4
6/5
7/6
(iteration ) / (iteration
8/7
9/8
10/9
)
Fig. 2. The trends of the correction factor versus the number of iterations for the 20%, 10% and 0.6% solid-angle measurements. The vertical axis indicates the ratio of the correction factor at iteration j to the value at iteration j 1.
Deviation (%)
1
Ω=20%
0.05 0 -0.05 56
-0.1
Co
0
2
4
6
8
10
Number of iterations 977.4(1.42) 1037.8(14.0) 1175.1(2.25) 1238.3(66.5) 1360.2(4.28)
0.1 Ω=0.6%
0.05
475.6(1.513) 563.2(8.541) 569.3(15.748)
-0.05 -0.1 0.1 Deviation (%)
3202.0(3.21) 3253.5(7.88) 3273.1(1.86) 3451.2(0.94)
Fig. 4. Deviations of the corrected relative γ-ray intensities from the reference values for 154Eu and 56Co in the Ω¼20% geometry.
0 795.9(87.54) 802.0(8.900) 1038.6(1.014)
1168.0(1.834) 1365.2(3.091)
Ω=10%
0.05 0 -0.05 -0.1 0.1
Ω=20%
0.05 0 -0.05 -0.1
1771.4(15.5) 2015.2(3.02) 2034.8(7.75) 2598.5(17.0) 3009.6(1.04)
0
2
4
6
8
10
Number of iterations Fig. 3. Deviations of the corrected relative γ-ray intensities from the reference values for 134Cs in each geometry.
normalization in 154Eu and 56Co, respectively. Under the condition of the 20% solid angle, it was found that at least 6 iterations are needed for obtaining self-consistent values of the summing correction of the three isotopes. Despite of their different decay properties, similar tendencies were observed among the three radionuclides. It should be mentioned that since 154Eu has many γrays and a complicated level structure, only γ-rays with relative intensities above 1% were taken into account. On the other hand, annihilation γ-rays were taken into account in the case of 56Co. The 3451.2 keV γ-ray in 56Co shows a relatively large deviation; nevertheless, its relative intensity of 0.94% was the smallest in 56 Co. Therefore, it was considered that the deviation does not influence very much the imbalances of the intensities in the decay scheme. For unstable nuclei far from the stability line, the β-branching ratio Iβ and log-ft values were determined from the γ-ray intensity imbalances at each level of excitation. To derive nuclear structure information from the decay scheme, it is considered that uncertainties of the relative intensities below 5% are desirable. To obtain reliable results, at least 4 iterations are required, but it is
Table 1 Comparisons of the corrected relative emission intensities after 10 iterations to the evaluated values. Eγ(keV)
Relative Iγ (%)
Solid angle 20%
475.4 563.2 569.3 604.7a 795.9 802.0 1038.6 1168.0 1365.2 a
1.5137 8.54114 15.74817 100 87.546 8.90016 1.10143 1.8345 3.0918
10%
0.6%
Corrected Iγ (%)
Deviation (%)
Corrected Iγ (%)
Deviation (%)
Corrected Iγ (%)
Deviation (%)
1.542 8.720 16.189 100 88.75 9.081 1.0248 1.853 3.104
1.9 2.1 2.8 0 1.4 2.0 1.1 1.1 0.4
1.530 8.651 15.886 100 87.82 8.896 1.0267 1.869 3.145
1.1 1.3 0.9 0 0.3 0.0 1.2 2.0 1.8
1.523 8.522 15.958 100 88.32 8.965 1.0103 1.849 3.112
0.6 0.2 1.3 0 0.9 0.7 0.4 0.8 0.7
Used as normalization.
Please cite this article as: Shima, Y., et al., On the iteration of coincidence summing correction for determination of gamma-ray intensities. Appl. Radiat. Isotopes (2015), http://dx.doi.org/10.1016/j.apradiso.2015.11.035i
4
Y. Shima et al. / Applied Radiation and Isotopes ∎ (∎∎∎∎) ∎∎∎–∎∎∎
σϵp and σϵt at each correction, and the uncertainty σγi: j − 1 of the previous correction factor. The value of σγi: j − 1 is also affected by σϵp and σϵt . It is considered that the σγi associated with ϵt is at most 2% when the uncertainty of ϵt is approximately 5%. The uncertainty introduced by the Monte Carlo calculation is negligibly small in this calculation. Then, the components of the uncertainties of intensities are roughly evaluated to be the uncertainties of peak efficiencies σϵp of 2% and the previous σγi: j − 1 of 2%, namely 0.022 + 0.022 ≈0.03 at each iteration. Then, the uncertainty n brought by n iterations is considered to be ∑1 0.03n . Therefore, the uncertainty due to the iteration procedure is at most 0.031 in total when there are 6 iterations.
4. Conclusion Fig. 5. Correction factors at 10 iterations versus the average total efficiencies for 134 Cs, 154Eu and 56Co.
considered that weak γ-rays having relative intensities less than 1% do not need to be taken into account for the coincidence summing correction. The magnitude of the correction depends mainly on the total efficiencies. Since it is difficult to introduce a definite parameter to represent the influence factors on the summing effects, the ∑ ϵt × Iγ weighted mean total efficiency ϵt , defined as , was pro∑ Iγ
posed as a measure of the correction. The final correction factors versus ϵt are shown in Fig. 5 for the three nuclides. The value of the correction factor is specific to each γ-ray, but Fig. 5 shows that the range of the magnitude of these factors is of the order of ϵt . It is considered that the uncertainties brought by the correction depend mainly on the magnitude of the total efficiencies. The reliability of the relative intensities increases but the uncertainties also increase as the number of iterations of correction increases. In studies that processed the correction by an analytical method (e.g. Debertin and Helmer (1988)), the uncertainties could be calculated by the error propagation equation. In the present method by Monte Carlo calculation, this analytical estimation could not be applied. Nevertheless, it is considered that the uncertainties increase when the peak and total efficiencies increase. The uncertainty σγi: j for Iγi after iteration j was evaluated as follows. From the deviation of the deduced results from the reference values, the uncertainties by the summing correction were evaluated to be about 3% for the 20% solid-angle measurements as shown in Figs. 3 and 4. The uncertainties due to the correction depend actually on the nuclide and gamma-ray, but an approximate global estimation can be obtained as follows. It is considered that σγi: j includes the statistical uncertainty σγi:stat. of peak counts and the uncertainty related to the correction factor for iteration j. The uncertainty of the correction factor σ fi: j includes the statistical uncertainties of the Monte Carlo calculation, the uncertainties of
In conclusion, for the determination of γ-ray emission intensities of unstable nuclei by measurements in close-to-detector geometrical configurations, the correction for coincidence summing requires several iterations. The number of iterations depends on the decay scheme, namely the γ-ray energy, cascade relation and on the peak and total efficiencies. Nevertheless, our study shows that the results converge at 6 iterations, and that at least 4 iterations are needed in order to determine the emission intensities with 5% uncertainty in the case of the 20% solid-angle measurement. It is considered that the required number of iterations becomes larger in larger solid angle configuration. In addition, in this paper, we discuss the ideal case in which the γ-ray peaks are clearly observed without contaminants. In practice, it is important to analyze γ-ray spectra carefully and determine the peak counts as initial conditions reliably.
References Agostinelli, A., et al., 2003. GEANT4-a simulation toolkit. Nucl. Instrum. Methods Phys. Res. A 503, 250–303. Debertin, K., Helmer, R.G., 1988. Gamma- and X-ray Spectrometry with Semiconductor Detectors. Elsevier Science Publishers, North-Holland, Amsterdam. Evaluated Nuclear Structure Data File (ENSDF), 2014. Retrieval 〈http://www.nndc. bnl.gov/ensdf/〉. Last updated 2014-07-10. (Published: 2004 Nuclear Data Sheets). Kawade, K., Katou, K., Osa, A., Shibata, M., Yamamoto, H., Katoh, T., 1991. Measurements of β þ -activity by detecting 511 keV annihilation γ-rays. Nucl. Instrum. Methods Phys. Res. A 301, 594–595. NUCLEIDE Database, 2013. Recommended data by the Decay Data Evaluation Project. 〈http://www.nucleide.org/DDEP_WG/DDEPdata.htm〉; Nuclear Decay Data Evaluations of: 134Cs (author: Marie-Martine Bé, LNHB, CEA, France, 2012), 109Cd (Marie-Martine Bé (LNHB) and E. Schönfeld (PTB, Germany), 1996), 137Cs (R.G. Helmer (INEEL, USA) and V. Chechev (KRI, Russia), 1998, updated in 2006), 54Mn (R.G. Helmer (INEEL, USA) and E. Schönfeld (PTB, Germany), 2001), 60Co (R.G. Helmer, 1996, updated in 2006) (updated 20 December 2013). Shima, Y., Hayashi, H., Kojima, Y., Shibata, M., 2014. 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, 97–103.
Please cite this article as: Shima, Y., et al., On the iteration of coincidence summing correction for determination of gamma-ray intensities. Appl. Radiat. Isotopes (2015), http://dx.doi.org/10.1016/j.apradiso.2015.11.035i