- Email: [email protected]
Absolute calibration of 60Co by using sum-peak method and an HPGe detector
Applied Radiation and Isotopes 58 (2003) 227–233
Absolute calibration of 60Co by using sum-peak method and an HPGe detector I.J. Kim*, C.S. Park, H.D. Choi Department of Nuclear Engineering, Seoul National University, Seoul 151-742, South Korea Received 13 May 2002; received in revised form 18 June 2002; accepted 30 August 2002
Abstract The sum-peak method was applied to calibrate four 60Co sources in the range of 25–350 kBq. An HPGe-based g-ray spectroscopy system was used, and the effects of the angular correlation and pulse pile-up were corrected, and are discussed. The correction for the angular correlation was obtained from a theoretical calculation, while the pulse pile-up effect was corrected using a new extrapolation technique based on the pile-up measurements by varying the shaping time of the amplifier. The determined radioactivities were within 2% deviation from the values reported by the supplier and the associated uncertainties were less than 2%. The observed consistency was obtained under the experimental condition of keeping the total counting rate p15 kcps. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Sum-peak method;
60
Co; HPGe; Angular correlation; Pulse pile-up; Shaping time
1. Introduction Sum-peak method is an absolute measurement technique that uses coincidence counting and g-ray spectrometry (Hutchinson et al., 1973). Coincidence counting itself has been used as an absolute method by composing the detection system of pair detectors. The pair detectors register b2g; g2g; X–(X,g), etc. in coincidence and the radioactivity of an unknown source is determined using the counts in coincidence or anticoincidence between the detector signals (NCRP, 1985). The sum-peak method is based on the same principle as coincidence counting, but requires only one g-ray detector with spectroscopy electronics. In this method, the radioactivity is determined using the count rates of the full absorption peaks of a single g-ray, the sum peak count rate in true coincidence and the total count rate of the spectrum.
*Corresponding author. Tel.: +82-2-8807214; fax:+82-28892688. E-mail address: [email protected] (I.J. Kim).
The merit of the sum-peak method lies in the simplicity of both the technique and the detection system. The sum-peak method requires a single detector with spectroscopy electronics, while the coincidence counting method requires two or more detectors with timing modules. The sum-peak method also has an advantage when compared with the relative measurement technique using g-ray spectroscopy, which is frequently used to determine the radioactivity of an unknown source. The relative measurement requires a precise energy-efficiency calibration of the spectroscopy system. Hence, it is influenced by the experimental conditions of the source-to-detector geometry, the g-ray energy, and the source radioactivity. The sum-peak method was originally developed by Brinkman and Aten (1963, 1965) and Brinkman et al. (1963a, b, 1965). They measured 60Co, 46Sc, 22Na, 18F radioactivity with a well type NaI(Tl) detector, and considered the effect of the angular correlation between the cascade g-rays. In measuring the 60Co and 46Sc, which are the b decay isotopes, the effect of angular correlation was canceled out by placing the sources on top of the detector crystal (2p geometry). For 22Na, a
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I.J. Kim et al. / Applied Radiation and Isotopes 58 (2003) 227–233
bþ 2g emitter, the source was placed either on top of the detector crystal or outside the detector well, which enabled the determination of radioactivity free from angular correlation. In addition to measuring the radioactivity, the 22Na source was also placed inside the detector well and the angular correlation effect by the annihilation radiations was determined from the singles, sum peak counts of the 22Na spectrum, and the measured detection efficiencies of the annihilation radiation and the relevant g-rays. This result was used to correct the angular correlation for measuring 18F, a pure bþ emitter. The achieved accuracy was reported to be between 2% and 5%. Another sum-peak method using NaI(Tl) was performed by Zajic (1986). The detection system was composed of two NaI(Tl) crystals and timing electronics, and was operated in the summing, coincidence, anti-coincidence modes. Sumpeak method using two NaI(Tl) crystals had already been applied by Hutchinson et al. (1973). However, Zajic improved the accuracy by correcting for the problems of the dead time, pulse pile-up and random coincidence. 88Y, 207Bi were measured under a 4p geometry, and hence no correction for the angular correlation was required. The overall estimated uncertainties were 1.4% and 2.4% for 88Y and 207Bi, respectively. The use of a Ge detector in the sum-peak method was attempted by Martin and Taylor (1992). 125 I was measured and the problems of the dead time, and pulse pile-up were considered but the angular correlation was not. The measurement was performed for diluted 125I samples with various activities, and the specific activity of the original source was determined by extrapolation to zero mass of 125I per unit sample mass. The accuracy was o2%. Recently, a theoretical correction of the angular correlation was reported by Asano et al. (1996) in their measurement of 60Co with a Ge detector. The source was placed at 8.7 cm away from the detector surface, which was quite different from the 2p geometry. The correction of the angular correlation effect was performed with a Monte Carlo simulation using the theoretical angular correlation function of the cascade g-rays. The effect of the angular correlation increased with increasing source-to-detector distance up to 9%. The problems of the dead time, pulse pile-up, and random coincidence were not mentioned. The achievable uncertainty was expected to be B1%. In this study, the sum-peak method was applied for the absolute calibration of the 60Co sources with activities ranging from 25 to 350 kBq. An HPGe detector was used and the measurements were performed at source-to-detector distances of 0.5–8 cm. Generally, high counting rate causes severe problems of an increased dead time, pulse pile-up and random coincidence summing. Therefore, a longer source-todetector distance is desirable in order to reduce these problems sufficiently. However, a longer source-to-
detector distance was inappropriate due to quite low counting rate of the sum peak. Consequently, both the angular correlation and the high counting rate problems were inevitable in these measurements. The correction for the angular correlation was performed using the theoretical model and a Monte Carlo simulation. The pulse pile-up effect was corrected technically by extrapolating the measured activities to zero shaping time of the amplifier. The results of the measurements and the correction are discussed.
2. Sum-peak method When the cascade g-rays emitted from 60Co are detected, the count rates of the full absorption peaks for the two g-rays have the relation (Brinkman and Aten, 1965) N1 ¼ N0 ep1 ½1 et2W ð0ÞLp ;
ð1Þ
N2 ¼ N0 ep2 ½1 et1W ð0ÞLp ;
ð2Þ
where N1 ; N2 are the count rates of the full absorption peaks, N0 is the radioactivity of 60Co, ep1 ; ep2 are the full absorption peak efficiencies, et1 ; et2 are the total efficiencies and the subscripts 1, 2 denote the quantity for the corresponding g-rays. W ð0Þ and Lp are correction factors for the angular correlation and the pulse pile-up loss, respectively. The sum peak count rate of the cascade g-rays, N12 ; and the total count rate, Nt ; are given by N12 ¼ N0 ep1 ep2W ð0ÞLp þ G;
ð3Þ
Nt ¼ N0 ½et1 þ et2 et1 et2W ð0Þ;
ð4Þ
where G is the correction factor for the pulse pile-up gain. In Eq. (4), the loss of the total count rate by pulse pile-up is assumed to be negligible. The defining W ð0Þ’s in the relations (1)–(4) are slightly different in a strict sense that a corresponding detection is implied by full energy absorption ðep Þ or by partial energy absorption ðet Þ for each g-ray in the equation. In this study, these W ð0Þ’s were assumed to have the same value for any combination of detections for the two g-rays. This assumption was verified by Kim et al. (2002). Hence, from Eqs. (1)–(4), the radioactivity N0 is given by N1 N2 N0 ¼ þ Nt W ð0Þ: ð5Þ ðN12 GÞLp
3. Angular correlation correction The coincident counting probability of cascade g-rays is dependent on the detection efficiencies and the detection geometries in addition to the angular correlation W ðyÞ of the cascade g-rays. Rose (1953), Camp and
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229
Van Lehn (1969) calculated the effective angular correlation, W ðyÞ; to estimate the effect of the finite angular resolution on the coincidence counting with finite-sized detectors. They showed that W ðyÞ can be written as follows (Rose, 1953; Camp and Van Lehn, 1969): W ðyÞ ¼
kmax X
Akk Pk ðcos yÞQk ð1ÞQk ð2Þ;
ð6Þ
even k
where y is the angle between the two axes of the coincidence counting detectors, Pk is the Legendre polynomial and Akk is the angular correlation coefficient. Qk ð1Þ is the attenuation correction factor for g1 impinging on a detector while Qk ð2Þ is the attenuation correction factor for g2 impinging on the other detector. Qk is given by Qk ðiÞ ¼ Jk ðiÞ=J0 ðiÞ; Jk ðiÞ ¼
Z
Fig. 2. The effective angular correlation at zero degree for detecting the cascade g-rays from 60Co with the HPGe detector used in this study (Kim et al., 2002).
ð7Þ
bmax
db sinðbÞPk ðcos bÞei ðbÞ;
ð8Þ
0
where b is the incident angle of the g-ray with respect to the detector axis, bmax is the maximum incident angle of the g-ray, and ei ðbÞ is the detection efficiency for the i-th g-ray impinging on the detector with an incident angle b: In this study, a single HPGe detector was used without a collimator for the sum-peak method. Therefore, y in Eq. (6) becomes zero and bmax covers the full front face of the Ge crystal. W ð0Þ of the cascade g-rays from 60Co for the detection system used in this study has already been calculated and is reported elsewhere (Kim et al., 2002). In calculating W ð0Þ; the full absorption peak efficiency, ei ðbÞ; calculated by the Monte Carlo method was used, and the location of the 60Co point source was taken on the coaxial detector axis. The angular correlation, W ðyÞ; of the cascade g-rays from 60 Co and W ð0Þ are shown in Figs. 1 and 2, respectively. In Fig. 2, W ð0Þ is plotted as a function of the source-to-
Fig. 1. The decay scheme of 60Co and the angular correlation of the cascade g-rays (Frauenfelder and Steffen, 1966).
detector distance since the angular resolution of the detector is mainly dependent on the source-to-detector distance.
4. Pile-up correction The g-ray pulses from a radiation detector have random distribution in time space. Hence, the consecutive g-ray pulses may introduce a dead time and pulse pile-up. In processing the precedent g-ray pulse, the detection system is insensitive to the g-ray pulses during the dead time. The dead time results in a loss of the g-ray peak counts and the total counts. The consecutive g-ray pulses can also be piled up on one another due to the limit of time resolution. This ‘‘pulse pile-up’’ may distort the g-ray spectrum in any region, and result in either the loss or gain of counts in each g-ray peak. Assuming that the dead time is corrected during the measurements by using the ADC in the live time mode, pulse pile-up loss can be described by the effective dead time tp (Debertin and Helmer, 1988b). tp is defined as the time interval between the consecutive pulses leading to the removal of the count from the g-ray peak. To account for the pulse pile-up gain, the effective coincidence resolving time tR (Knoll, 1989a) is also defined as the time interval between the consecutive pulses leading to gain in the sum peak counts. Therefore, the correction factors Lp and G can be written as LP ¼ 1 tP N;
ð9Þ
G ¼ 2tR N1 N2 ;
ð10Þ
where N1 and N2 were defined in Eqs. (1) and (2), N is the detector count rate, and it is assumed that all nonrecorded counts below the lower threshold or above the upper threshold can be neglected. Both tP and tR are
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closely related to the pulse width. The g-ray pulse shaped by (CR)(RC)2 circuit in the amplifier is expressed in analytic form by (Weinzierl and Drosg, 1970) t 1 t 2 V ðtÞ ¼ exp ; ð11Þ 2 t t where V ðtÞ is the g-ray pulse height at time t and t is the RC-time constant of the (CR)(RC)2 circuit. Here, the output signal at the preamplifier was assumed to be a step function and the pole-zero cancellation of the amplifier was assumed to be complete. By using Eq. (11), the pile-up pulses can be written in mathematical form. A single g-ray pulse and the pile-up pulses are shown in Fig. 3 for various cases of the interaction interval. From the figure, it is obvious that tP and tR are the parameters depending on t; and the pulse pile-up can be relieved by reducing t: In the measurements, t was adjusted by the shaping time of the amplifier. The reduction in the shaping time was limited so as not to spoil the relevant energy resolution of the spectroscopy system. Pulse pile-up was inevitable even at the smallest permissible t; which resulted in an underestimation of the radioactivity. The
Fig. 3. The single g-ray pulse and the pile-up pulses after the (CR)(RC)2 circuit. Dt is the time interval between consecutive pulses.
radioactivity measured at the shaping time t without a pile-up correction was N1 ðtÞN2 ðtÞ N0 ðtÞ ¼ þ Nt ðtÞ W ð0Þ; ð12Þ N12 ðtÞ where the count rates N1 ðtÞ; N2 ðtÞ; Nt ðtÞ are measured at the shaping time t: N0 ðtÞ is similar to N0 in Eq. (5), but does not include the pile-up corrections. The pile-up free radioactivity N0 is equivalent to N0 ðtÞ at zero shaping time, N0 ð0Þ: Although a direct measurement of N0 ð0Þ is impossible, the extrapolation technique allows N0 ð0Þ to be determined. The N0 ðtÞ’s were measured at the various t permitted, and a linear relationship of N0 ðtÞ versus t was obtained. The pile-up free radioactivity N0 was determined by extrapolating the line of best fit down to t ¼ 0:
5. Experiment and analysis 60
Co g-ray spectra were measured using the g-ray spectroscopy system based on an HPGe detector. The set up of the system is shown schematically in Fig. 4. The relative detection efficiency of the HPGe is 17.8% and the energy resolution is 1.73 keV for the 1.33 MeV gray peak from 60Co. The Ge crystal is a closed-ended coaxial type with 5.05 cm diameter and 3.65 cm length. The electronics system is comprised of a linear spectroscopy amplifier, a Wilkinson ADC and an MCA. The gray pulses from the preamplifier are shaped into semiGaussian form by the (CR)(RC)2 circuit in the amplifier. The measurement was performed for four 60 Co sources by varying the source-to-detector distance and the shaping time. Each source has a point-like area and a detailed specification is listed in Table 1. The pole-zero cancellation was fine-tuned for each measurement in order to maintain the best energy resolution of the relevant peaks. The shaping time was varied in the 1.5–8 ms range. The spectra were accumulated with operating ADC in the live time mode, but the pile-up rejection (PUR) mode was not used. The percentage dead time in the ADC was 5–54%. The
Fig. 4. The schematic arrangement of the g-ray spectroscopy system in this study.
I.J. Kim et al. / Applied Radiation and Isotopes 58 (2003) 227–233
231
Table 1 Standard calibration sources Sourcea
Radioactivity (kBq) (1 December 2000)
S1 S2 S3
25.5270.34 29.4370.07 42.0670.15
S4
354.1374.64
a
Active diameter (mm)
Calibration method
Calibration date
1 5 Unknown
Unknown Unknown Calibrated 4p ionization chamber Calibrated HPGe detector at 1173.24 keV
1 June 1996 1 October 1993 1 July 1983
1
28 December 2000
Manufactured by: S1: Amersham Buchler GmbH & Co KG, S2: Korea Research Institute of Standards and Science, S3: International Atomic Energy Agency, S4: North American Scientific, Inc.
6. Result and discussion
Fig. 5. The coincidence sum peak spectrum and the result of the HYPERMET analysis. It was measured with a S3 source located at 2.8 cm source-to-detector distance, and the shaping time of the amplifier was 4 ms.
low-level discriminator (LLD) of the ADC was set at approximately 40 keV.The loss of the total count rate below the LLD was compensated for by extrapolating the LLD level down to 0 keV. Here the total count rates were plotted as a function of the LLD level in the range of 40 to 200 keV, and then fitted to a line of best fit. The LLD corrections were approximately 4% of the total count rate. The peaks were analyzed by HYPERMET (Phillips and Marlow, 1976). Fig. 5 shows an example of the sum peak analysis. In one exceptional case, the Debertin method (Debertin and Helmer, 1988a) was used to analyze the spectra measured with a S4 source located at 3.6 cm. For these spectra, the count rate was so high, about 25 kcps, that the pulse pile-up formed a shoulder on the high-energy tail in each g-ray peak. HYPERMET was unable to analyze these deformed peaks.
From the result of the spectrum analysis and the angular correlation factor, the N0 ðtÞ’s were obtained and are shown in Fig. 6 for all the sources and source-todetector distances. The N0;exp ’s were determined from Fig. 6 by extrapolating the N0 ðtÞ’s to t ¼ 0 through the line of best fit (Fig. 7). In the figure, the N0;exp ’s were normalized by the nominal radioactivity, N0;std ’s, provided by the manufacturer. Most were within 2% deviation from the N0;std ’s, while the value of S4 at 3.6 cm showed an approximate 6% discrepancy. The pulse pile-up correction was successful enough to reduce both the uncertainty and the relative deviation to approximately 2% for the total count rate up to 15 kcps. However, when the total count rate approached 25 kcps, the correction was incomplete as indicated by the most deviating case of S4. Fig. 7 shows the systematic increase in the uncertainty and relative deviation of the S4 source, as the total count rate was increased by reducing the source-to-detector distance. At 3.6 cm, the relative deviation and the uncertainty were approximately 6% and 5%, respectively. Several reasons can be deduced for incomplete correction at the 25 kcps total count rate. The first is the limitation in the dead time correction by operating the ADC in the live time mode. It is not guaranteed that the live time correction will be sufficient at the percentage dead time of an ADC higher than 30–40% (Knoll, 1989b; Gilmore and Hemingway, 1995). In measuring S4 at 3.6 cm, the dead time of the ADC exceeded 30% even at the smallest shaping time, and it was observed that the dead times at the shaping time above 4 ms decreased compared to that at 4.6 cm with the same source, while the detector count rate increased. This implies that the dead time correction in the ADC was incomplete at the high total count rate of 25 kcps. The second reason is the distortion of the g-ray peaks by
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I.J. Kim et al. / Applied Radiation and Isotopes 58 (2003) 227–233
Fig. 6. N0 ðtÞ measured at every t and the linear fit of N0 ðtÞ as a function of t: The symbols are the measured data and the lines are lines of best fit.
exceeding 2% by using a single HPGe detector and the sum-peak method by keeping total counting rate at p15 kcps. In practical measurements with a strong source, simply moving the source further away from the detector at the expense of a reduced count rate for the sum peak can reduce the total count rate. Therefore, the limitation on the total count rate is not a significant factor. The implemented corrections for the angular correlation and the pulse pile-up were successful in obtaining reliable activities for the sources in this study.
Fig. 7. The result of the radioactivity calibration for each source.
pulse pile-up. As the pulse pile-up increases, the distortion of the g-ray peak becomes severe, which enhances the uncertainty in the analysis of g-ray peak area. The uncertainty of the g-ray peak area propagates to that of N0;exp : Therefore, the distorted peak shape increases the uncertainty of N0;exp : The third reason is the random coincidence occurring during the charge collection period in the detector. This may be a minor factor since the charge collection time in an HPGe detector is a few hundred nanoseconds at most. However, this cannot be neglected at high counting rates even with the annihilating shaping time. A proper prescription is left to a further study. In conclusion, this study showed that the radioactivity of 60Co could be calibrated with excellent accuracy not
Acknowledgements This work has been supported in part by Electrical Engineering & Science Research Institute grant, 99-j-03 which is funded by Korea Electric Power Co.
References Asano, Y., Mori, S., Ohta, Y., Tsujita, Y., 1996. Sum-peak method and angular correlation correction for a 60Co source by a Ge(Tl) detector. Jpn. J. Appl. Phys. 35, 4117–4120. Brinkman, G.A., Aten Jr., A.H.W., 1963. Absolute standardization with a NaI(Tl) crystal-III. Int. J. Appl. Radiat. Isot. 14, 503–510. Brinkman, G.A., Aten Jr., A.H.W., 1965. Absolute standardization with a NaI(Tl) crystal-V. Int. J. Appl. Radiat. Isot. 16, 177–181.
I.J. Kim et al. / Applied Radiation and Isotopes 58 (2003) 227–233 Brinkman, G.A., Aten Jr., A.H.W., Veenboer, J.Th., 1963a. Absolute standardization with a NaI(Tl) crystal-I. Int. J. Appl. Radiat. Isot. 14, 153–157. Brinkman, G.A., Aten Jr., A.H.W., Veenboer, J.Th., 1963b. Absolute standardization with a NaI(Tl) crystal-II. Int. J. Appl. Radiat. Isot. 14, 433–437. Brinkman, G.A., Aten Jr., A.H.W., Veenboer, J.Th., 1965. Absolute standardization with a NaI(Tl) crystal-IV. Int. J. Appl. Radiat. Isot. 16, 15–18. Camp, D.C., Van Lehn, A.L., 1969. Finite solid-angle corrections for Ge(Li) detectors. Nucl. Instrum. Methods 76, 192–240. Debertin, K., Helmer, R.G., 1988a. Gamma-and X-ray Spectrometry with Semiconductor Detectors. North-Holland, Amsterdam, pp. 175–177. Debertin, K., Helmer, R.G., 1988b. Gamma- and X-ray Spectrometry with Semiconductor Detectors. North-Holland, Amsterdam, pp. 271–281. Frauenfelder, H., Steffen, R.M., 1966. In: Siegbahn, K. (Ed.), Alpha-, Beta- and Gamma Ray Spectroscopy, Vol. 2. North-Holland, Amsterdam, pp. 1027–1044. Gilmore, G., Hemingway, J.D., 1995. Practical gamma-ray spectrometry. John Wiley & Sons, Chichester, pp. 84–103. Hutchinson, J.M.R., Mann, W.B., Mullen, P.A., 1973. Sumpeak counting with two crystals. Nucl. Instrum. Methods 112, 187–196.
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Kim, I.J., Sun, G.M., Choi, H.D., Bae, Y.-D., 2002. Calculation of effective angular correlation in the HPGe spectroscopy of Co-60 g-rays. J. Korean. Ncul. Soc. 34, 22–29. Knoll, G.F., 1989a. Radiation Detection and Measurement, 2nd Edition. John Wiley & Sons, New York, pp. 625–647. Knoll, G.F., 1989b. Radiation Detection and Measurement, 2nd Edition. John Wiley & Sons, New York, pp. 660–662. Martin, R.H., Taylor, J.G.V., 1992. The standardization of 125I: a comparison of three methods. Nucl. Instrum. Methods A 312, 64–66. NCRP report No. 58, 1985. A Handbook of Radioactivity Measurements Procedures, 2nd Edition, National Council on Radiation Protection and Measurements, Bethesda, pp. 74–93. Phillips, G.W., Marlow, K.W., 1976. Automatic analysis of gamma-ray spectra from germanium detectors. Ncul. Instrum. Methods 137, 525–536. Rose, M.E., 1953. The analysis of angular correlation and angular distribution data. Phys. Rev. 91, 610–615. Weinzierl, P., Drosg, M., 1970. Lehrbuch der nuklear-electronik. Springer-Verlag, Wien, pp. 117–126. Zajic, D., 1986. Insturmental corrections of peak areas in gamma-ray sum-peak counting. Appl. Radiat. Isot. 37, 1225–1233.
Absolute calibration of 60Co by using sum-peak method and an HPGe detector I.J. Kim*, C.S. Park, H.D. Choi Department of Nuclear Engineering, Seoul National University, Seoul 151-742, South Korea Received 13 May 2002; received in revised form 18 June 2002; accepted 30 August 2002
Abstract The sum-peak method was applied to calibrate four 60Co sources in the range of 25–350 kBq. An HPGe-based g-ray spectroscopy system was used, and the effects of the angular correlation and pulse pile-up were corrected, and are discussed. The correction for the angular correlation was obtained from a theoretical calculation, while the pulse pile-up effect was corrected using a new extrapolation technique based on the pile-up measurements by varying the shaping time of the amplifier. The determined radioactivities were within 2% deviation from the values reported by the supplier and the associated uncertainties were less than 2%. The observed consistency was obtained under the experimental condition of keeping the total counting rate p15 kcps. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Sum-peak method;
60
Co; HPGe; Angular correlation; Pulse pile-up; Shaping time
1. Introduction Sum-peak method is an absolute measurement technique that uses coincidence counting and g-ray spectrometry (Hutchinson et al., 1973). Coincidence counting itself has been used as an absolute method by composing the detection system of pair detectors. The pair detectors register b2g; g2g; X–(X,g), etc. in coincidence and the radioactivity of an unknown source is determined using the counts in coincidence or anticoincidence between the detector signals (NCRP, 1985). The sum-peak method is based on the same principle as coincidence counting, but requires only one g-ray detector with spectroscopy electronics. In this method, the radioactivity is determined using the count rates of the full absorption peaks of a single g-ray, the sum peak count rate in true coincidence and the total count rate of the spectrum.
*Corresponding author. Tel.: +82-2-8807214; fax:+82-28892688. E-mail address: [email protected] (I.J. Kim).
The merit of the sum-peak method lies in the simplicity of both the technique and the detection system. The sum-peak method requires a single detector with spectroscopy electronics, while the coincidence counting method requires two or more detectors with timing modules. The sum-peak method also has an advantage when compared with the relative measurement technique using g-ray spectroscopy, which is frequently used to determine the radioactivity of an unknown source. The relative measurement requires a precise energy-efficiency calibration of the spectroscopy system. Hence, it is influenced by the experimental conditions of the source-to-detector geometry, the g-ray energy, and the source radioactivity. The sum-peak method was originally developed by Brinkman and Aten (1963, 1965) and Brinkman et al. (1963a, b, 1965). They measured 60Co, 46Sc, 22Na, 18F radioactivity with a well type NaI(Tl) detector, and considered the effect of the angular correlation between the cascade g-rays. In measuring the 60Co and 46Sc, which are the b decay isotopes, the effect of angular correlation was canceled out by placing the sources on top of the detector crystal (2p geometry). For 22Na, a
0969-8043/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 4 3 ( 0 2 ) 0 0 2 9 5 - 6
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I.J. Kim et al. / Applied Radiation and Isotopes 58 (2003) 227–233
bþ 2g emitter, the source was placed either on top of the detector crystal or outside the detector well, which enabled the determination of radioactivity free from angular correlation. In addition to measuring the radioactivity, the 22Na source was also placed inside the detector well and the angular correlation effect by the annihilation radiations was determined from the singles, sum peak counts of the 22Na spectrum, and the measured detection efficiencies of the annihilation radiation and the relevant g-rays. This result was used to correct the angular correlation for measuring 18F, a pure bþ emitter. The achieved accuracy was reported to be between 2% and 5%. Another sum-peak method using NaI(Tl) was performed by Zajic (1986). The detection system was composed of two NaI(Tl) crystals and timing electronics, and was operated in the summing, coincidence, anti-coincidence modes. Sumpeak method using two NaI(Tl) crystals had already been applied by Hutchinson et al. (1973). However, Zajic improved the accuracy by correcting for the problems of the dead time, pulse pile-up and random coincidence. 88Y, 207Bi were measured under a 4p geometry, and hence no correction for the angular correlation was required. The overall estimated uncertainties were 1.4% and 2.4% for 88Y and 207Bi, respectively. The use of a Ge detector in the sum-peak method was attempted by Martin and Taylor (1992). 125 I was measured and the problems of the dead time, and pulse pile-up were considered but the angular correlation was not. The measurement was performed for diluted 125I samples with various activities, and the specific activity of the original source was determined by extrapolation to zero mass of 125I per unit sample mass. The accuracy was o2%. Recently, a theoretical correction of the angular correlation was reported by Asano et al. (1996) in their measurement of 60Co with a Ge detector. The source was placed at 8.7 cm away from the detector surface, which was quite different from the 2p geometry. The correction of the angular correlation effect was performed with a Monte Carlo simulation using the theoretical angular correlation function of the cascade g-rays. The effect of the angular correlation increased with increasing source-to-detector distance up to 9%. The problems of the dead time, pulse pile-up, and random coincidence were not mentioned. The achievable uncertainty was expected to be B1%. In this study, the sum-peak method was applied for the absolute calibration of the 60Co sources with activities ranging from 25 to 350 kBq. An HPGe detector was used and the measurements were performed at source-to-detector distances of 0.5–8 cm. Generally, high counting rate causes severe problems of an increased dead time, pulse pile-up and random coincidence summing. Therefore, a longer source-todetector distance is desirable in order to reduce these problems sufficiently. However, a longer source-to-
detector distance was inappropriate due to quite low counting rate of the sum peak. Consequently, both the angular correlation and the high counting rate problems were inevitable in these measurements. The correction for the angular correlation was performed using the theoretical model and a Monte Carlo simulation. The pulse pile-up effect was corrected technically by extrapolating the measured activities to zero shaping time of the amplifier. The results of the measurements and the correction are discussed.
2. Sum-peak method When the cascade g-rays emitted from 60Co are detected, the count rates of the full absorption peaks for the two g-rays have the relation (Brinkman and Aten, 1965) N1 ¼ N0 ep1 ½1 et2W ð0ÞLp ;
ð1Þ
N2 ¼ N0 ep2 ½1 et1W ð0ÞLp ;
ð2Þ
where N1 ; N2 are the count rates of the full absorption peaks, N0 is the radioactivity of 60Co, ep1 ; ep2 are the full absorption peak efficiencies, et1 ; et2 are the total efficiencies and the subscripts 1, 2 denote the quantity for the corresponding g-rays. W ð0Þ and Lp are correction factors for the angular correlation and the pulse pile-up loss, respectively. The sum peak count rate of the cascade g-rays, N12 ; and the total count rate, Nt ; are given by N12 ¼ N0 ep1 ep2W ð0ÞLp þ G;
ð3Þ
Nt ¼ N0 ½et1 þ et2 et1 et2W ð0Þ;
ð4Þ
where G is the correction factor for the pulse pile-up gain. In Eq. (4), the loss of the total count rate by pulse pile-up is assumed to be negligible. The defining W ð0Þ’s in the relations (1)–(4) are slightly different in a strict sense that a corresponding detection is implied by full energy absorption ðep Þ or by partial energy absorption ðet Þ for each g-ray in the equation. In this study, these W ð0Þ’s were assumed to have the same value for any combination of detections for the two g-rays. This assumption was verified by Kim et al. (2002). Hence, from Eqs. (1)–(4), the radioactivity N0 is given by N1 N2 N0 ¼ þ Nt W ð0Þ: ð5Þ ðN12 GÞLp
3. Angular correlation correction The coincident counting probability of cascade g-rays is dependent on the detection efficiencies and the detection geometries in addition to the angular correlation W ðyÞ of the cascade g-rays. Rose (1953), Camp and
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229
Van Lehn (1969) calculated the effective angular correlation, W ðyÞ; to estimate the effect of the finite angular resolution on the coincidence counting with finite-sized detectors. They showed that W ðyÞ can be written as follows (Rose, 1953; Camp and Van Lehn, 1969): W ðyÞ ¼
kmax X
Akk Pk ðcos yÞQk ð1ÞQk ð2Þ;
ð6Þ
even k
where y is the angle between the two axes of the coincidence counting detectors, Pk is the Legendre polynomial and Akk is the angular correlation coefficient. Qk ð1Þ is the attenuation correction factor for g1 impinging on a detector while Qk ð2Þ is the attenuation correction factor for g2 impinging on the other detector. Qk is given by Qk ðiÞ ¼ Jk ðiÞ=J0 ðiÞ; Jk ðiÞ ¼
Z
Fig. 2. The effective angular correlation at zero degree for detecting the cascade g-rays from 60Co with the HPGe detector used in this study (Kim et al., 2002).
ð7Þ
bmax
db sinðbÞPk ðcos bÞei ðbÞ;
ð8Þ
0
where b is the incident angle of the g-ray with respect to the detector axis, bmax is the maximum incident angle of the g-ray, and ei ðbÞ is the detection efficiency for the i-th g-ray impinging on the detector with an incident angle b: In this study, a single HPGe detector was used without a collimator for the sum-peak method. Therefore, y in Eq. (6) becomes zero and bmax covers the full front face of the Ge crystal. W ð0Þ of the cascade g-rays from 60Co for the detection system used in this study has already been calculated and is reported elsewhere (Kim et al., 2002). In calculating W ð0Þ; the full absorption peak efficiency, ei ðbÞ; calculated by the Monte Carlo method was used, and the location of the 60Co point source was taken on the coaxial detector axis. The angular correlation, W ðyÞ; of the cascade g-rays from 60 Co and W ð0Þ are shown in Figs. 1 and 2, respectively. In Fig. 2, W ð0Þ is plotted as a function of the source-to-
Fig. 1. The decay scheme of 60Co and the angular correlation of the cascade g-rays (Frauenfelder and Steffen, 1966).
detector distance since the angular resolution of the detector is mainly dependent on the source-to-detector distance.
4. Pile-up correction The g-ray pulses from a radiation detector have random distribution in time space. Hence, the consecutive g-ray pulses may introduce a dead time and pulse pile-up. In processing the precedent g-ray pulse, the detection system is insensitive to the g-ray pulses during the dead time. The dead time results in a loss of the g-ray peak counts and the total counts. The consecutive g-ray pulses can also be piled up on one another due to the limit of time resolution. This ‘‘pulse pile-up’’ may distort the g-ray spectrum in any region, and result in either the loss or gain of counts in each g-ray peak. Assuming that the dead time is corrected during the measurements by using the ADC in the live time mode, pulse pile-up loss can be described by the effective dead time tp (Debertin and Helmer, 1988b). tp is defined as the time interval between the consecutive pulses leading to the removal of the count from the g-ray peak. To account for the pulse pile-up gain, the effective coincidence resolving time tR (Knoll, 1989a) is also defined as the time interval between the consecutive pulses leading to gain in the sum peak counts. Therefore, the correction factors Lp and G can be written as LP ¼ 1 tP N;
ð9Þ
G ¼ 2tR N1 N2 ;
ð10Þ
where N1 and N2 were defined in Eqs. (1) and (2), N is the detector count rate, and it is assumed that all nonrecorded counts below the lower threshold or above the upper threshold can be neglected. Both tP and tR are
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closely related to the pulse width. The g-ray pulse shaped by (CR)(RC)2 circuit in the amplifier is expressed in analytic form by (Weinzierl and Drosg, 1970) t 1 t 2 V ðtÞ ¼ exp ; ð11Þ 2 t t where V ðtÞ is the g-ray pulse height at time t and t is the RC-time constant of the (CR)(RC)2 circuit. Here, the output signal at the preamplifier was assumed to be a step function and the pole-zero cancellation of the amplifier was assumed to be complete. By using Eq. (11), the pile-up pulses can be written in mathematical form. A single g-ray pulse and the pile-up pulses are shown in Fig. 3 for various cases of the interaction interval. From the figure, it is obvious that tP and tR are the parameters depending on t; and the pulse pile-up can be relieved by reducing t: In the measurements, t was adjusted by the shaping time of the amplifier. The reduction in the shaping time was limited so as not to spoil the relevant energy resolution of the spectroscopy system. Pulse pile-up was inevitable even at the smallest permissible t; which resulted in an underestimation of the radioactivity. The
Fig. 3. The single g-ray pulse and the pile-up pulses after the (CR)(RC)2 circuit. Dt is the time interval between consecutive pulses.
radioactivity measured at the shaping time t without a pile-up correction was N1 ðtÞN2 ðtÞ N0 ðtÞ ¼ þ Nt ðtÞ W ð0Þ; ð12Þ N12 ðtÞ where the count rates N1 ðtÞ; N2 ðtÞ; Nt ðtÞ are measured at the shaping time t: N0 ðtÞ is similar to N0 in Eq. (5), but does not include the pile-up corrections. The pile-up free radioactivity N0 is equivalent to N0 ðtÞ at zero shaping time, N0 ð0Þ: Although a direct measurement of N0 ð0Þ is impossible, the extrapolation technique allows N0 ð0Þ to be determined. The N0 ðtÞ’s were measured at the various t permitted, and a linear relationship of N0 ðtÞ versus t was obtained. The pile-up free radioactivity N0 was determined by extrapolating the line of best fit down to t ¼ 0:
5. Experiment and analysis 60
Co g-ray spectra were measured using the g-ray spectroscopy system based on an HPGe detector. The set up of the system is shown schematically in Fig. 4. The relative detection efficiency of the HPGe is 17.8% and the energy resolution is 1.73 keV for the 1.33 MeV gray peak from 60Co. The Ge crystal is a closed-ended coaxial type with 5.05 cm diameter and 3.65 cm length. The electronics system is comprised of a linear spectroscopy amplifier, a Wilkinson ADC and an MCA. The gray pulses from the preamplifier are shaped into semiGaussian form by the (CR)(RC)2 circuit in the amplifier. The measurement was performed for four 60 Co sources by varying the source-to-detector distance and the shaping time. Each source has a point-like area and a detailed specification is listed in Table 1. The pole-zero cancellation was fine-tuned for each measurement in order to maintain the best energy resolution of the relevant peaks. The shaping time was varied in the 1.5–8 ms range. The spectra were accumulated with operating ADC in the live time mode, but the pile-up rejection (PUR) mode was not used. The percentage dead time in the ADC was 5–54%. The
Fig. 4. The schematic arrangement of the g-ray spectroscopy system in this study.
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Table 1 Standard calibration sources Sourcea
Radioactivity (kBq) (1 December 2000)
S1 S2 S3
25.5270.34 29.4370.07 42.0670.15
S4
354.1374.64
a
Active diameter (mm)
Calibration method
Calibration date
1 5 Unknown
Unknown Unknown Calibrated 4p ionization chamber Calibrated HPGe detector at 1173.24 keV
1 June 1996 1 October 1993 1 July 1983
1
28 December 2000
Manufactured by: S1: Amersham Buchler GmbH & Co KG, S2: Korea Research Institute of Standards and Science, S3: International Atomic Energy Agency, S4: North American Scientific, Inc.
6. Result and discussion
Fig. 5. The coincidence sum peak spectrum and the result of the HYPERMET analysis. It was measured with a S3 source located at 2.8 cm source-to-detector distance, and the shaping time of the amplifier was 4 ms.
low-level discriminator (LLD) of the ADC was set at approximately 40 keV.The loss of the total count rate below the LLD was compensated for by extrapolating the LLD level down to 0 keV. Here the total count rates were plotted as a function of the LLD level in the range of 40 to 200 keV, and then fitted to a line of best fit. The LLD corrections were approximately 4% of the total count rate. The peaks were analyzed by HYPERMET (Phillips and Marlow, 1976). Fig. 5 shows an example of the sum peak analysis. In one exceptional case, the Debertin method (Debertin and Helmer, 1988a) was used to analyze the spectra measured with a S4 source located at 3.6 cm. For these spectra, the count rate was so high, about 25 kcps, that the pulse pile-up formed a shoulder on the high-energy tail in each g-ray peak. HYPERMET was unable to analyze these deformed peaks.
From the result of the spectrum analysis and the angular correlation factor, the N0 ðtÞ’s were obtained and are shown in Fig. 6 for all the sources and source-todetector distances. The N0;exp ’s were determined from Fig. 6 by extrapolating the N0 ðtÞ’s to t ¼ 0 through the line of best fit (Fig. 7). In the figure, the N0;exp ’s were normalized by the nominal radioactivity, N0;std ’s, provided by the manufacturer. Most were within 2% deviation from the N0;std ’s, while the value of S4 at 3.6 cm showed an approximate 6% discrepancy. The pulse pile-up correction was successful enough to reduce both the uncertainty and the relative deviation to approximately 2% for the total count rate up to 15 kcps. However, when the total count rate approached 25 kcps, the correction was incomplete as indicated by the most deviating case of S4. Fig. 7 shows the systematic increase in the uncertainty and relative deviation of the S4 source, as the total count rate was increased by reducing the source-to-detector distance. At 3.6 cm, the relative deviation and the uncertainty were approximately 6% and 5%, respectively. Several reasons can be deduced for incomplete correction at the 25 kcps total count rate. The first is the limitation in the dead time correction by operating the ADC in the live time mode. It is not guaranteed that the live time correction will be sufficient at the percentage dead time of an ADC higher than 30–40% (Knoll, 1989b; Gilmore and Hemingway, 1995). In measuring S4 at 3.6 cm, the dead time of the ADC exceeded 30% even at the smallest shaping time, and it was observed that the dead times at the shaping time above 4 ms decreased compared to that at 4.6 cm with the same source, while the detector count rate increased. This implies that the dead time correction in the ADC was incomplete at the high total count rate of 25 kcps. The second reason is the distortion of the g-ray peaks by
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Fig. 6. N0 ðtÞ measured at every t and the linear fit of N0 ðtÞ as a function of t: The symbols are the measured data and the lines are lines of best fit.
exceeding 2% by using a single HPGe detector and the sum-peak method by keeping total counting rate at p15 kcps. In practical measurements with a strong source, simply moving the source further away from the detector at the expense of a reduced count rate for the sum peak can reduce the total count rate. Therefore, the limitation on the total count rate is not a significant factor. The implemented corrections for the angular correlation and the pulse pile-up were successful in obtaining reliable activities for the sources in this study.
Fig. 7. The result of the radioactivity calibration for each source.
pulse pile-up. As the pulse pile-up increases, the distortion of the g-ray peak becomes severe, which enhances the uncertainty in the analysis of g-ray peak area. The uncertainty of the g-ray peak area propagates to that of N0;exp : Therefore, the distorted peak shape increases the uncertainty of N0;exp : The third reason is the random coincidence occurring during the charge collection period in the detector. This may be a minor factor since the charge collection time in an HPGe detector is a few hundred nanoseconds at most. However, this cannot be neglected at high counting rates even with the annihilating shaping time. A proper prescription is left to a further study. In conclusion, this study showed that the radioactivity of 60Co could be calibrated with excellent accuracy not
Acknowledgements This work has been supported in part by Electrical Engineering & Science Research Institute grant, 99-j-03 which is funded by Korea Electric Power Co.
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