- Email: [email protected]
Determination of the emission probabilities of the principal γ-rays for 134Cs to a high precision
Applied Radiation and Isotopes 56 (2002) 131–135
Determination of the emission probabilities of the principal g-rays for 134Cs to a high precision Hiroshi Miyaharaa,*, Nobuo Hayashib, Kazuo Fujikib, Norio Takeuchic, Yoshio Hinod a
Department of Radiological Technology, School of Health Sciences, Nagoya University, 1-1-20, Daikominami, Higashi-ku, Nagoya 461-8673, Japan b Department of Nuclear Engineering, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan c Department of Radioisotopes, Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan d Quantum Radiation Division, National Institute of Advanced Industrial Science and Technology, 1-1-4 Umezono, Tsukuba, Ibaraki-ken 305-8568, Japan Accepted 30 July 2001
Abstract While multi-g-ray emitting nuclides such as 75Se, 134Cs and 152Eu have reasonably well-defined decay scheme, some inconsistencies still remain. Detailed evaluations and weighted-mean analyses result in the recommendation of g-ray emission probabilities with small uncertainties, although significant deviations exist in the measured values. Therefore, the g-ray emission probabilities of 134Cs have been measured to a high precision after an extremely accurate calibration of detection efficiency. The resulting data agree extremely well with the evaluated values in IAEA-TECDOC-619 (IAEA, X-ray and g-ray standards for detector calibration, IAEA-TECDOC-619, IAEA, Vienna, 1991). r 2002 Elsevier Science Ltd. All rights reserved. Keywords: 134Cs; g-ray emission probability; High precision; Absolute g-ray intensity; Disintegration rate; Highly precise detection efficiency curve
1. Introduction Standardisation and quantification of radionuclides by g-ray detection can be undertaken with relative ease and precision for various applications. Nuclides with precisely evaluated g-ray emission probabilities are used for the efficiency calibration of detectors (IAEA, 1991). If the uncertainty in the disintegration rate is not better than 1%, g-ray emission probabilities need only be defined to modest precision. However, these data need to be known to greater accuracy if the disintegration rate *Corresponding author. Tel.: +81-52-719-1548; fax: +8152-719-1506. E-mail address: [email protected] (H. Miyahara).
is determined with an uncertainty of o0.1%. The decay data of nuclides such as 24Na, 46Sc and 60Co are very precise, because they emit g-rays with probabilities close to 100%. On the other hand, the uncertainties of the decay data for multi-g emitting nuclides such as 75Se, 134 Cs and 152Eu vary between 0.1% and 0.5%. There may be variations in the measurements of decay data, but simple and weighted-mean analyses can result in relatively small uncertainties. Although difficult to measure with an uncertainty o1% (Gehrke et al., 1977; Mehta et al., 1986), an accurately defined g-ray detection efficiency curve is required in order to determine g-ray emission probabilities. Hawari and Fleming (1994) reported that the relative g-ray detection efficiency curve from 900 to 1300 keV could be determined with uncertainty of about
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H. Miyahara et al. / Applied Radiation and Isotopes 56 (2002) 131–135
0.1% by using 46Sc and 60Co. We have found that a similar result can be obtained from 430 to 2750 keV by replacing their linear fit with a polynomial fitting (Hayashi et al., 2000a, b). This approach has been applied to the precise determination of the relative g-ray emission probabilities of 38Cl (Hayashi et al., 2000a). The work described below involves a new application of the highly precise relative g-ray detection efficiency curve to the study of 134Cs.
2. Experimental procedures The experiments were divided into three steps: (a) measurement of the precise relative g-ray detection efficiency curve; (b) determination of the precise absolute detection efficiency curve from the relative data using a 60Co source of known disintegration rate; and (c) measurement of the g-ray emission probabilities for 134 Cs. The method of determining the relative g-ray detection efficiency curve has been described in previous papers (Hayashi et al., 2000a, b), and only a brief outline is given below. Several sources were measured that emitted cascade g-rays with an emission ratio close to unity, and the changing slope of the resulting efficiency curve was determined. Corrections were also made to compensate for the cascade summing effect and selfabsorption of the g-rays by the sources. A second-order polynomial function was fitted to the energy-slope data, and this function was integrated to determine the relative detection efficiencies across the full energy range. The relative g-ray detection efficiency curve was determined by using a covariance matrix method (Brandt, 1976). The disintegration rate of 60Co source was determined with an uncertainty of o0.1% by 4pb2g coincidence
with a live-timed two-dimensional data-acquisition system (Miyahara et al., 1989). This source was also measured by g-ray spectrometry to derive the absolute detection efficiencies of the 1173 and 1333 keV g-rays. Corrections were made for self-absorption of the g-rays and the effect of cascade summing. The resulting data were used to normalise the relative g-ray detection efficiency curve and derive the highly precise absolute detection efficiency curve. Finally, the disintegration rate of 134Cs was measured to an uncertainty of about 0.1% by 4pb g coincidence, and g-ray spectra were accumulated from the same source by g-ray spectrometry. The precise g-ray emission probabilities of 134Cs were calculated from the g-ray intensities and the known disintegration rate. The peak areas were determined by the integration method of Helmer (1982).
3. Experiments The g-ray spectrometer consisted of an ORTEC GEM-23195 HPGe detector, ORTEC 571 amplifier and Laboratory Equipment 2201 ADC. The source-todetector distances were set to 30 cm to ensure a small correction for the cascade summing effect. Sources 5 mm in diameter were prepared by drying drops of solution on VYNS film stretched across source mounts for 4pb g coincidence measurements. Corrections for self-absorption involved estimating the source thickness, but with the need to consider absorption in only the forward direction because of the large source-to-detector distance compared to source thickness. The nuclides used to determine the precise relative g-ray detection efficiencies are listed in Table 1, along with half-lives, g-ray energies, g-ray emission
Table 1 Nuclides used to determine the precise relative g-ray detection efficiencies Nuclide
Half-life
g-Ray energy (keV)
g-Ray emission probability
Relative g-ray intensity
Reference
24
14.959 h
Firestone and Shirley (1996)
83.79 d
0.99997 (2)
Firestone and Shirley (1996)
48
43.67 h
0.99983 (12)
NDS (Burrows, 1993)
60
5.27 yr
0.99918 (20)
Firestone and Shirley (1996)
88
106.65 d
0.94605 (301)
94
20300 yr
1.00 0.99944 (4) 0.99984 (1) 0.99987 (1) 0.99976 (12) 0.999931 (9) 0.9990 (2) 0.999820 (10) 0.940 (3) 0.9936 (3) 0.9979 (5) 0.9986 (5) 0.9073 (59) 0.9110 (60)
1.00056 (4)
46
1368.6 2754.0 889.3 1120.5 983.5 1312.1 1173.2 1332.5 898.0 1836.1 702.6 871.1 433.9 722.9
IAEA-TECDOC-619 (IAEA, 1991) IAEA-TECDOC-619 (IAEA, 1991) NDS (Blachot, 1997)
Na Sc Sc Co Y Nb
108
Ag
418 yr
0.99930 (71) 0.99594 (90)
133
H. Miyahara et al. / Applied Radiation and Isotopes 56 (2002) 131–135
5 Detection efficiency (x10-4)
probabilities and relative intensities. The relative intensity of the 108Ag g-ray was calculated from the data in Nuclear Data Sheets (Blachot, 1997). The sources of 60 Co and 134Cs were prepared using commercially available solutions, while 88Y spectra were obtained from a QCRB6721 mixed source (obtained from AEA Technology). Other sources were prepared at JAERI by the (n; g) and (n; a) reactions.
(a)
4 3 2
1
4. Results and discussion 0.4
Deviation (%)
Corrections for self-absorption and the cascade summing effect were necessary in order to determine the relative g-ray detection efficiencies to a high precision. The largest self-absorption of 0.6% occurred with the 94 Nb source (foil thickness of 0.127 mm), but the selfabsorption ratio for the 703 to 871 keV g-rays was only 1.00052. The 88Y source had the largest ratio of 1.00076 because of the large differences in g-ray energies and the thick source. Correction for self-absorption resulted in uncertainties that were a combination of the absorption coefficient (5%), density (1%) and thickness (5%). Corrections for cascade summing required definition of the total detection efficiency curve, which was calculated from the geometrical arrangement and detector size. The largest absolute values were approximately 0.4% for 108Ag, while the smallest ratio was 0.99979 for 24Na with such a large energy differences. These particular corrections were estimated to contribute 10% of the total uncertainty. After this correction, a precise relative g-ray detection efficiency curve was determined by the procedure described in Section 2. The 60Co source was prepared from CoCl2 solution by the Ludox treatment method (Merritt et al., 1959), and the disintegration rate was determined from four measurements of 3000 s each by 4pb g coincidence. An uncertainty of o0.1% was assigned to the disintegration rate, while the correction for self-absorption of g-rays was estimated to be 0.02%. Using these corrected detection efficiencies for the two main g-rays of 60Co, the precise relative g-ray detection efficiency curve was converted to a g-ray detection efficiency curve of high precision. Fig. 1(a) shows the highly precise g-ray detection efficiency curve, and Fig. 1(b) the deviation of the data from the third-order polynomial fitting function and the estimated standard deviation by covariance analysis (Brandt, 1976). Insufficient counts were obtained from the weak 48Sc source, and the uncertainty of the data for this radionuclide was 1.3% (and this error bar was omitted). This high degree of uncertainty did not affect the fitting curve, because a weighted-mean procedure was adopted. As shown in Fig. 1(b), the estimated uncertainty over the energy range 700–1400 keV is only 0.1% because of the many precise data points.
(b)
0.2 0.0 -0.2 -0.4 400
600
800
1000
2000
3000
Gamma-ray energy (keV)
Fig. 1. (a) Precise g-ray detection efficiency curve; (b) deviation from the fitted curve of third-order polynomial function with estimated standard deviation. The uncertainty bars for 48Sc data were omitted because of the large spread of 1.3%.
Table 2 Correction factors for self-absorption and cascade summing effects of 134Cs g-Ray energy (keV) Correction factor
475.4 563.2 569.3 604.7 795.8 801.9 1038.6 1167.9 1365.2
Self-absorption
Cascade summing
1.00021 1.00018 1.00018 1.00017 1.00014 1.00014 1.00012 1.00011 1.00011
1.00387 1.00410 1.00417 1.00257 1.00252 1.00386 1.00125 0.99901 0.99922
(1) (1) (1) (1) (1) (1) (1) (1) (1)
(39) (41) (42) (26) (25) (39) (13) (10) (8)
The disintegration rates of 134Cs sources were determined from six measurements of 3200 s each by 4pb g coincidence. Gates were set on the 605 and 796 keV g-rays and the results for both settings were in good agreement. Uncertainties in the disintegration rates were o0.1%. The emission probabilities of the g-rays ranging in energy from 475 to 1365 keV were determined by using the precise g-ray detection efficiency curve from 430 to 2750 keV. Absolute g-ray emission probabilities were determined after correction for selfabsorption and cascade summing in a similar manner to 60 Co. Table 2 shows the correction factors for selfabsorption (10 mm thick planar source) and cascade
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H. Miyahara et al. / Applied Radiation and Isotopes 56 (2002) 131–135
summing. The maximum correction factor for selfabsorption was 0.02% for the 475.3 keV g-ray, with an uncertainty of o0.01%; the maximum correction factor for cascade summing was 0.42% for the 569.3 keV g-ray, with an uncertainty of approximately 0.04%. Table 3 lists the measured g-ray emission probabilities, and compares these data with other published values. The uncertainties of the 475.4 and 604.7 keV g-rays are 0.7% and 0.13%, respectively. Debertin et al. (1976) estimated a smaller uncertainty for the 604.7 keV g-ray than obtained in the current study, while the uncertainties reported by Yoshizawa et al. (1980) for the 604.7 and 795.8 keV g-rays are o0.1%. However, these values were calculated by normalisation of the 604.7 and 1167.9 keV transitions feeding the ground state, with no direct b decay to the ground state. Relative g-ray intensities determined in previous studies are listed in Table 4, and compared with our results calculated from the g-ray emission probabilities. The relative intensities of the main g-rays are in good agreement, and our data exhibit the lower uncertainties. Assuming that the internal conversion coefficients for the 604.7 and 1167.9 keV transitions are 0.00599 and 0.00131 (Sergeenkov, 1994), respectively, the calculated sum of both
transitions is 100.028% in the present study. Our high precision measurements of the absolute g-ray emission probabilities agree with the data evaluated within an IAEA Co-ordinated Research Program (IAEA, 1991).
5. Conclusions Hawari and Fleming (1994) used a linear function approximation to determine a relative detection efficiency curve of high precision between 890 and 1330 keV that has been extended to cover the energy range from 430 to 2750 keV by a polynomial approximation (Hayashi et al., 2000b). This curve was used to develop a precise g-ray detection efficiency curve by determining the disintegration rate of 60Co source to an uncertainty of o0.1% by 4pb g coincidence measurements. The estimated standard deviation of the detection efficiency ranged from 0.1% to 0.2%, based on a covariance matrix analysis. The disintegration rate of a series of 134Cs sources was measured with an uncertainty of 0.1%, and these data were used to determine the g-ray emission probabilities with high precision. The resulting 604.7 keV g-ray was
Table 3 Measured g-ray emission probabilities and previously published values g-Ray energy (keV)
Van Hise et al. (1975)
Debertin et al. (1976)
Yoshizawa et al. (1980)
IAEA TECDOC (1991)
Present result
475.4 563.2 569.3 604.7 795.8 801.9 1038.6 1167.9 1365.2
0.01465 (40) 0.0838 (5) 0.1543 (11) 0.9756 (32) 0.8544 (38) 0.0873 (4) 0.0100 (1) 0.01805 (26) 0.0304 (4)
0.0151 (3) 0.0834 (12) 0.1538 (22) 0.976 (1) 0.853 (9) 0.0864 (12) 0.00998 (13) 0.01800 (20) 0.0302 (3)
F 0.0837 (5) 0.1540 (8) 0.9764 (6) 0.8552 (5) 0.0868 (4) 0.00984 (6) 0.01783 (10) 0.03001 (17)
0.0149 (2) 0.0836 (3) 0.1539 (6) 0.9763 (6) 0.854 (3) 0.0869 (3) 0.00990 (5) 0.01792 (7) 0.03016 (11)
0.01469 (11) 0.08328 (20) 0.15333 (28) 0.9765 (13) 0.8549 (11) 0.08691 (23) 0.00998 (7) 0.01792 (7) 0.03023 (10)
Table 4 Calculated relative g-ray intensities compared with measured data g-Ray energy (keV)
Van Hise et al. (1975)
Debertin et al. (1976)
Yoshizawa et al. (1980)
Wang et al. (1987)
Present result
475.4 563.2 569.3 604.7 795.8 801.9 1038.6 1167.9 1365.2
1.50 (4) 8.59 (9) 15.8 (2) 100.0 (3) 87.5 (8) 8.95 (9) 1.02 (2) 1.85 (3) 3.11 (4)
8.55 (12) 15.76 (23) 100.0 87.4 (9) 8.85 (12) 1.023 (13) 1.844 (20) 3.09 (3)
8.57 (3) 15.87 (6) 100.0 (4) 87.5 (3) 8.89 (3) 1.008 (5) 1.827 (8) 3.074 (13)
1.520 (10) 8.53 (6) 15.71 (10) 100.0 (7) 87.5 (6) 8.97 (8) 1.016 (7) 1.841 (13) 3.109 (20)
1.503 (11) 8.530 (18) 15.728 (23) 100.00 (8) 87.54 (6) 8.898 (20) 1.021 (8) 1.834 (7) 3.094 (10)
H. Miyahara et al. / Applied Radiation and Isotopes 56 (2002) 131–135
measured to an uncertainty of 0.13%, which is higher than the uncertainty derived by Debertin et al. (1976) and Yoshizawa et al. (1980) from calculations of decay to the ground state; this g-ray emission probability was measured directly in our studies rather than defined through calculations of level population. Our measured g-ray emission probabilities are in good agreement with the evaluated data of IAEA-CRP (IAEA, 1991).
Acknowledgements This work was carried out at the Radioisotope Research Center (RIC), Nagoya University and JAERI. The authors would like to express their thanks to Prof. K. Nishizawa of RIC for suggestions, and Mr. H. Matsuoka and Mr. R. Motoki of JAERI for source preparation. This work was partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture, Japan.
References Blachot, J., 1997. Nuclear data sheets for A=108. Nucl. Data Sheets 81, 599–752. Brandt, S., 1976. Statistical and Computation Methods in Data Analysis. North-Holland, Amsterdam. Burrows, T.W., 1993. Nuclear data sheets update for A=48. Nucl. Data Sheets 68, 1–115. Debertin, K., Schotzig, U., Walz, K.F., 1976. PTB Jahresbericht 160 (see also Yoshizawa et al., 1980). Firestone, R.B., Shirley, V.S., 1996. Table of Isotopes,, 8th Edition.. Wiley, New York. Gehrke, R.J., Helmer, R.G., Greenwood, R.C., 1977. Precise relative g-ray intensities for calibration of Ge semiconductor detectors. Nucl. Instrum. Methods 147, 405–423.
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Hawari, A.I., Fleming, R.F., 1994. High accuracy determination of the shape of efficiency curve of the HPGe detector in the energy range 900–1300 keV. Nucl. Instrum. Methods A 353, 106–108. Hayashi, N., Miyahara, H., Mori, C., Takeuchi, N., Iwamoto, S., Ishikawa, I., 2000a. High accuracy measurement of the relative efficiency curve and determination of gamma-ray relative intensity for 38Cl. Appl. Radiat. Isot. 52, 733–737. Hayashi, N., Miyahara, H., Mori, C., 2000b. Highly precise measurement of the relative gamma-ray detection efficiency curve. J. Nucl. Sci. Technol. 37, 139–143. Helmer, R.G., 1982. Efficiency calibration of a Ge detector for 30–2800 keV g rays. Nucl. Instrum. Methods 199, 521–529. IAEA, 1991. X-ray and gamma-ray standards for detector calibration. IAEA-TECDOC-619, IAEA, Vienna. Mehta, D., Garg, M.L., Singh, J., Singh, N., Cheema, T.S., Trehan, P.N., 1986. Precision measurements of X- and gamma-ray intensities in 192Ir, 160Tb, 169Yb and 152Eu decays. Nucl. Instrum. Methods A 245, 447–454. Merritt, J.S., Taylor, J.G.V., Campion, P.J., 1959. Selfabsorption in sources prepared for 4p beta counting. Can. J. Chem. 37, 1109–1114. Miyahara, H., Kitaori, S., Nozue, S., Watanabe, T., 1989. A 4pb(ppc)–g(HPGe) coincidence apparatus using a live-timed bi-dimensional data acquisition system and its application to measurement of gamma ray emission probability. Appl. Radiat. Isot. 40, 343–345. Sergeenkov, Yu.V., 1994. Nuclear data sheets update for A=134. Nucl. Data Sheets 71, 557–658. Van Hise, J.R., Camp, P.C., Meyer, R.C., 1975. Decay of the 134 Cs isomers and the levels of 134Xe, 134Cs and 134Ba. Z. Phys. A 274, 383–389. Wang, G., Alburger, D.E., Warburton, E.K., 1987. Precise energy and intensity measurements for g transitions from 134 Cs decay. Nucl. Instrum. Methods A 260, 413–417. Yoshizawa, Y., Iwata, Y., Kaku, T., Katoh, T., Ruan, J., Kojima, T., Kawada, Y., 1980. Precision measurements of gamma-ray intensities. 1 56Co, 88Y, 110mAg, 134Cs and 207Bi. Nucl. Instrum. Methods 174, 109–131.
Determination of the emission probabilities of the principal g-rays for 134Cs to a high precision Hiroshi Miyaharaa,*, Nobuo Hayashib, Kazuo Fujikib, Norio Takeuchic, Yoshio Hinod a
Department of Radiological Technology, School of Health Sciences, Nagoya University, 1-1-20, Daikominami, Higashi-ku, Nagoya 461-8673, Japan b Department of Nuclear Engineering, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan c Department of Radioisotopes, Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki-ken 319-1195, Japan d Quantum Radiation Division, National Institute of Advanced Industrial Science and Technology, 1-1-4 Umezono, Tsukuba, Ibaraki-ken 305-8568, Japan Accepted 30 July 2001
Abstract While multi-g-ray emitting nuclides such as 75Se, 134Cs and 152Eu have reasonably well-defined decay scheme, some inconsistencies still remain. Detailed evaluations and weighted-mean analyses result in the recommendation of g-ray emission probabilities with small uncertainties, although significant deviations exist in the measured values. Therefore, the g-ray emission probabilities of 134Cs have been measured to a high precision after an extremely accurate calibration of detection efficiency. The resulting data agree extremely well with the evaluated values in IAEA-TECDOC-619 (IAEA, X-ray and g-ray standards for detector calibration, IAEA-TECDOC-619, IAEA, Vienna, 1991). r 2002 Elsevier Science Ltd. All rights reserved. Keywords: 134Cs; g-ray emission probability; High precision; Absolute g-ray intensity; Disintegration rate; Highly precise detection efficiency curve
1. Introduction Standardisation and quantification of radionuclides by g-ray detection can be undertaken with relative ease and precision for various applications. Nuclides with precisely evaluated g-ray emission probabilities are used for the efficiency calibration of detectors (IAEA, 1991). If the uncertainty in the disintegration rate is not better than 1%, g-ray emission probabilities need only be defined to modest precision. However, these data need to be known to greater accuracy if the disintegration rate *Corresponding author. Tel.: +81-52-719-1548; fax: +8152-719-1506. E-mail address: [email protected] (H. Miyahara).
is determined with an uncertainty of o0.1%. The decay data of nuclides such as 24Na, 46Sc and 60Co are very precise, because they emit g-rays with probabilities close to 100%. On the other hand, the uncertainties of the decay data for multi-g emitting nuclides such as 75Se, 134 Cs and 152Eu vary between 0.1% and 0.5%. There may be variations in the measurements of decay data, but simple and weighted-mean analyses can result in relatively small uncertainties. Although difficult to measure with an uncertainty o1% (Gehrke et al., 1977; Mehta et al., 1986), an accurately defined g-ray detection efficiency curve is required in order to determine g-ray emission probabilities. Hawari and Fleming (1994) reported that the relative g-ray detection efficiency curve from 900 to 1300 keV could be determined with uncertainty of about
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H. Miyahara et al. / Applied Radiation and Isotopes 56 (2002) 131–135
0.1% by using 46Sc and 60Co. We have found that a similar result can be obtained from 430 to 2750 keV by replacing their linear fit with a polynomial fitting (Hayashi et al., 2000a, b). This approach has been applied to the precise determination of the relative g-ray emission probabilities of 38Cl (Hayashi et al., 2000a). The work described below involves a new application of the highly precise relative g-ray detection efficiency curve to the study of 134Cs.
2. Experimental procedures The experiments were divided into three steps: (a) measurement of the precise relative g-ray detection efficiency curve; (b) determination of the precise absolute detection efficiency curve from the relative data using a 60Co source of known disintegration rate; and (c) measurement of the g-ray emission probabilities for 134 Cs. The method of determining the relative g-ray detection efficiency curve has been described in previous papers (Hayashi et al., 2000a, b), and only a brief outline is given below. Several sources were measured that emitted cascade g-rays with an emission ratio close to unity, and the changing slope of the resulting efficiency curve was determined. Corrections were also made to compensate for the cascade summing effect and selfabsorption of the g-rays by the sources. A second-order polynomial function was fitted to the energy-slope data, and this function was integrated to determine the relative detection efficiencies across the full energy range. The relative g-ray detection efficiency curve was determined by using a covariance matrix method (Brandt, 1976). The disintegration rate of 60Co source was determined with an uncertainty of o0.1% by 4pb2g coincidence
with a live-timed two-dimensional data-acquisition system (Miyahara et al., 1989). This source was also measured by g-ray spectrometry to derive the absolute detection efficiencies of the 1173 and 1333 keV g-rays. Corrections were made for self-absorption of the g-rays and the effect of cascade summing. The resulting data were used to normalise the relative g-ray detection efficiency curve and derive the highly precise absolute detection efficiency curve. Finally, the disintegration rate of 134Cs was measured to an uncertainty of about 0.1% by 4pb g coincidence, and g-ray spectra were accumulated from the same source by g-ray spectrometry. The precise g-ray emission probabilities of 134Cs were calculated from the g-ray intensities and the known disintegration rate. The peak areas were determined by the integration method of Helmer (1982).
3. Experiments The g-ray spectrometer consisted of an ORTEC GEM-23195 HPGe detector, ORTEC 571 amplifier and Laboratory Equipment 2201 ADC. The source-todetector distances were set to 30 cm to ensure a small correction for the cascade summing effect. Sources 5 mm in diameter were prepared by drying drops of solution on VYNS film stretched across source mounts for 4pb g coincidence measurements. Corrections for self-absorption involved estimating the source thickness, but with the need to consider absorption in only the forward direction because of the large source-to-detector distance compared to source thickness. The nuclides used to determine the precise relative g-ray detection efficiencies are listed in Table 1, along with half-lives, g-ray energies, g-ray emission
Table 1 Nuclides used to determine the precise relative g-ray detection efficiencies Nuclide
Half-life
g-Ray energy (keV)
g-Ray emission probability
Relative g-ray intensity
Reference
24
14.959 h
Firestone and Shirley (1996)
83.79 d
0.99997 (2)
Firestone and Shirley (1996)
48
43.67 h
0.99983 (12)
NDS (Burrows, 1993)
60
5.27 yr
0.99918 (20)
Firestone and Shirley (1996)
88
106.65 d
0.94605 (301)
94
20300 yr
1.00 0.99944 (4) 0.99984 (1) 0.99987 (1) 0.99976 (12) 0.999931 (9) 0.9990 (2) 0.999820 (10) 0.940 (3) 0.9936 (3) 0.9979 (5) 0.9986 (5) 0.9073 (59) 0.9110 (60)
1.00056 (4)
46
1368.6 2754.0 889.3 1120.5 983.5 1312.1 1173.2 1332.5 898.0 1836.1 702.6 871.1 433.9 722.9
IAEA-TECDOC-619 (IAEA, 1991) IAEA-TECDOC-619 (IAEA, 1991) NDS (Blachot, 1997)
Na Sc Sc Co Y Nb
108
Ag
418 yr
0.99930 (71) 0.99594 (90)
133
H. Miyahara et al. / Applied Radiation and Isotopes 56 (2002) 131–135
5 Detection efficiency (x10-4)
probabilities and relative intensities. The relative intensity of the 108Ag g-ray was calculated from the data in Nuclear Data Sheets (Blachot, 1997). The sources of 60 Co and 134Cs were prepared using commercially available solutions, while 88Y spectra were obtained from a QCRB6721 mixed source (obtained from AEA Technology). Other sources were prepared at JAERI by the (n; g) and (n; a) reactions.
(a)
4 3 2
1
4. Results and discussion 0.4
Deviation (%)
Corrections for self-absorption and the cascade summing effect were necessary in order to determine the relative g-ray detection efficiencies to a high precision. The largest self-absorption of 0.6% occurred with the 94 Nb source (foil thickness of 0.127 mm), but the selfabsorption ratio for the 703 to 871 keV g-rays was only 1.00052. The 88Y source had the largest ratio of 1.00076 because of the large differences in g-ray energies and the thick source. Correction for self-absorption resulted in uncertainties that were a combination of the absorption coefficient (5%), density (1%) and thickness (5%). Corrections for cascade summing required definition of the total detection efficiency curve, which was calculated from the geometrical arrangement and detector size. The largest absolute values were approximately 0.4% for 108Ag, while the smallest ratio was 0.99979 for 24Na with such a large energy differences. These particular corrections were estimated to contribute 10% of the total uncertainty. After this correction, a precise relative g-ray detection efficiency curve was determined by the procedure described in Section 2. The 60Co source was prepared from CoCl2 solution by the Ludox treatment method (Merritt et al., 1959), and the disintegration rate was determined from four measurements of 3000 s each by 4pb g coincidence. An uncertainty of o0.1% was assigned to the disintegration rate, while the correction for self-absorption of g-rays was estimated to be 0.02%. Using these corrected detection efficiencies for the two main g-rays of 60Co, the precise relative g-ray detection efficiency curve was converted to a g-ray detection efficiency curve of high precision. Fig. 1(a) shows the highly precise g-ray detection efficiency curve, and Fig. 1(b) the deviation of the data from the third-order polynomial fitting function and the estimated standard deviation by covariance analysis (Brandt, 1976). Insufficient counts were obtained from the weak 48Sc source, and the uncertainty of the data for this radionuclide was 1.3% (and this error bar was omitted). This high degree of uncertainty did not affect the fitting curve, because a weighted-mean procedure was adopted. As shown in Fig. 1(b), the estimated uncertainty over the energy range 700–1400 keV is only 0.1% because of the many precise data points.
(b)
0.2 0.0 -0.2 -0.4 400
600
800
1000
2000
3000
Gamma-ray energy (keV)
Fig. 1. (a) Precise g-ray detection efficiency curve; (b) deviation from the fitted curve of third-order polynomial function with estimated standard deviation. The uncertainty bars for 48Sc data were omitted because of the large spread of 1.3%.
Table 2 Correction factors for self-absorption and cascade summing effects of 134Cs g-Ray energy (keV) Correction factor
475.4 563.2 569.3 604.7 795.8 801.9 1038.6 1167.9 1365.2
Self-absorption
Cascade summing
1.00021 1.00018 1.00018 1.00017 1.00014 1.00014 1.00012 1.00011 1.00011
1.00387 1.00410 1.00417 1.00257 1.00252 1.00386 1.00125 0.99901 0.99922
(1) (1) (1) (1) (1) (1) (1) (1) (1)
(39) (41) (42) (26) (25) (39) (13) (10) (8)
The disintegration rates of 134Cs sources were determined from six measurements of 3200 s each by 4pb g coincidence. Gates were set on the 605 and 796 keV g-rays and the results for both settings were in good agreement. Uncertainties in the disintegration rates were o0.1%. The emission probabilities of the g-rays ranging in energy from 475 to 1365 keV were determined by using the precise g-ray detection efficiency curve from 430 to 2750 keV. Absolute g-ray emission probabilities were determined after correction for selfabsorption and cascade summing in a similar manner to 60 Co. Table 2 shows the correction factors for selfabsorption (10 mm thick planar source) and cascade
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H. Miyahara et al. / Applied Radiation and Isotopes 56 (2002) 131–135
summing. The maximum correction factor for selfabsorption was 0.02% for the 475.3 keV g-ray, with an uncertainty of o0.01%; the maximum correction factor for cascade summing was 0.42% for the 569.3 keV g-ray, with an uncertainty of approximately 0.04%. Table 3 lists the measured g-ray emission probabilities, and compares these data with other published values. The uncertainties of the 475.4 and 604.7 keV g-rays are 0.7% and 0.13%, respectively. Debertin et al. (1976) estimated a smaller uncertainty for the 604.7 keV g-ray than obtained in the current study, while the uncertainties reported by Yoshizawa et al. (1980) for the 604.7 and 795.8 keV g-rays are o0.1%. However, these values were calculated by normalisation of the 604.7 and 1167.9 keV transitions feeding the ground state, with no direct b decay to the ground state. Relative g-ray intensities determined in previous studies are listed in Table 4, and compared with our results calculated from the g-ray emission probabilities. The relative intensities of the main g-rays are in good agreement, and our data exhibit the lower uncertainties. Assuming that the internal conversion coefficients for the 604.7 and 1167.9 keV transitions are 0.00599 and 0.00131 (Sergeenkov, 1994), respectively, the calculated sum of both
transitions is 100.028% in the present study. Our high precision measurements of the absolute g-ray emission probabilities agree with the data evaluated within an IAEA Co-ordinated Research Program (IAEA, 1991).
5. Conclusions Hawari and Fleming (1994) used a linear function approximation to determine a relative detection efficiency curve of high precision between 890 and 1330 keV that has been extended to cover the energy range from 430 to 2750 keV by a polynomial approximation (Hayashi et al., 2000b). This curve was used to develop a precise g-ray detection efficiency curve by determining the disintegration rate of 60Co source to an uncertainty of o0.1% by 4pb g coincidence measurements. The estimated standard deviation of the detection efficiency ranged from 0.1% to 0.2%, based on a covariance matrix analysis. The disintegration rate of a series of 134Cs sources was measured with an uncertainty of 0.1%, and these data were used to determine the g-ray emission probabilities with high precision. The resulting 604.7 keV g-ray was
Table 3 Measured g-ray emission probabilities and previously published values g-Ray energy (keV)
Van Hise et al. (1975)
Debertin et al. (1976)
Yoshizawa et al. (1980)
IAEA TECDOC (1991)
Present result
475.4 563.2 569.3 604.7 795.8 801.9 1038.6 1167.9 1365.2
0.01465 (40) 0.0838 (5) 0.1543 (11) 0.9756 (32) 0.8544 (38) 0.0873 (4) 0.0100 (1) 0.01805 (26) 0.0304 (4)
0.0151 (3) 0.0834 (12) 0.1538 (22) 0.976 (1) 0.853 (9) 0.0864 (12) 0.00998 (13) 0.01800 (20) 0.0302 (3)
F 0.0837 (5) 0.1540 (8) 0.9764 (6) 0.8552 (5) 0.0868 (4) 0.00984 (6) 0.01783 (10) 0.03001 (17)
0.0149 (2) 0.0836 (3) 0.1539 (6) 0.9763 (6) 0.854 (3) 0.0869 (3) 0.00990 (5) 0.01792 (7) 0.03016 (11)
0.01469 (11) 0.08328 (20) 0.15333 (28) 0.9765 (13) 0.8549 (11) 0.08691 (23) 0.00998 (7) 0.01792 (7) 0.03023 (10)
Table 4 Calculated relative g-ray intensities compared with measured data g-Ray energy (keV)
Van Hise et al. (1975)
Debertin et al. (1976)
Yoshizawa et al. (1980)
Wang et al. (1987)
Present result
475.4 563.2 569.3 604.7 795.8 801.9 1038.6 1167.9 1365.2
1.50 (4) 8.59 (9) 15.8 (2) 100.0 (3) 87.5 (8) 8.95 (9) 1.02 (2) 1.85 (3) 3.11 (4)
8.55 (12) 15.76 (23) 100.0 87.4 (9) 8.85 (12) 1.023 (13) 1.844 (20) 3.09 (3)
8.57 (3) 15.87 (6) 100.0 (4) 87.5 (3) 8.89 (3) 1.008 (5) 1.827 (8) 3.074 (13)
1.520 (10) 8.53 (6) 15.71 (10) 100.0 (7) 87.5 (6) 8.97 (8) 1.016 (7) 1.841 (13) 3.109 (20)
1.503 (11) 8.530 (18) 15.728 (23) 100.00 (8) 87.54 (6) 8.898 (20) 1.021 (8) 1.834 (7) 3.094 (10)
H. Miyahara et al. / Applied Radiation and Isotopes 56 (2002) 131–135
measured to an uncertainty of 0.13%, which is higher than the uncertainty derived by Debertin et al. (1976) and Yoshizawa et al. (1980) from calculations of decay to the ground state; this g-ray emission probability was measured directly in our studies rather than defined through calculations of level population. Our measured g-ray emission probabilities are in good agreement with the evaluated data of IAEA-CRP (IAEA, 1991).
Acknowledgements This work was carried out at the Radioisotope Research Center (RIC), Nagoya University and JAERI. The authors would like to express their thanks to Prof. K. Nishizawa of RIC for suggestions, and Mr. H. Matsuoka and Mr. R. Motoki of JAERI for source preparation. This work was partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture, Japan.
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