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A simple and versatile data acquisition system for software coincidence and pulse-height discrimination in 4πβ–γ coincidence experiments
Applied Radiation and Isotopes 70 (2012) 2031–2036
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A simple and versatile data acquisition system for software coincidence and pulse-height discrimination in 4pb–g coincidence experiments Y. Kawada a,n, T. Yamada a,b, Y. Unno a, A. Yunoki a, Y. Sato a, Y. Hino a a b
National Metrology Institute of Japan, National Institute of Advanced Industrial Sciences and Technology, Tsukuba Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan Japan Radioisotope Association, 2-28-45, Hon-komagome, Bunkyo, Tokyo 113-3941, Japan
a r t i c l e i n f o
abstract
Available online 1 March 2012
A simple but versatile data acquisition system for software coincidence experiments is described, in which any time stamping and live time controller are not provided. Signals from b- and g-channels are fed to separately two fast ADCs (16 bits, 25 MHz clock maximum) via variable delay circuits and pulse-height stretchers, and also to pulse-height discriminators. The discriminating level was set to just above the electronic noise. Two ADCs were controlled with a common clock signal, and triggered simultaneously by the logic OR pulses from both discriminators. Paired digital signals for each sampling were sent to buffer memories connected to main PC with a FIFO (First-In, First-Out) pipe via USB. After data acquisition in list mode, various processing including pulse-height analyses was performed using MS-Excel (version 2007 and later). The usefulness of this system was demonstrated for 4pb(PS)–4pg coincidence measurements of 60Co, 134Cs and 152Eu. Possibilities of other extended applications will be touched upon. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Software 4pb–g coincidence Efficiency function Excel 60 Co 134 Cs 152 Eu
1. Introduction For several decades, 4pb–g coincidence counting method (Campion, 1959) has been employed as the major technique for radionuclide standardization, in which extrapolation techniques are often used to determine most of efficiency dependent corrections. For the determination of the efficiency functions required in this procedure, it is necessary to perform many 4pb–g coincidence measurements for different b-efficiencies. To change b-efficiencies, adjustments of self-absorption and/or additions of absorber foils have historically been used. As an alternative, electronic discrimination techniques based upon pulse-height discrimination of signals from a pressurized 4pb–counter or a plastic/liquid scintillation detector has come into wide use (Baerg, 1973a). Pulse-height discrimination can be done manually by the adjustments of discrimination level or by the use of ladder type discriminators in a conventional 4pb–g coincidence counting system. In measuring complex decaying nuclides, the slope and shape of the efficiency functions are dependent on the g-window setting, and hence the 4pb–g extrapolation curve should be determined for each of different g-window settings. In order to avoid such tedious procedures, the use of a two dimensional list-mode-measurements (Miyahara et al., 1987) or software coincidence techniques has
n
Corresponding author. E-mail address: [email protected] (Y. Kawada).
0969-8043/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2012.02.060
become more popular instead of the use of a conventional 4pb–g coincidence counting. So far techniques and various applications of such digital coincidence systems were already reported by several authors (e.g.,: Buckman and Ius, 1996; Park et al., 1998; Hwang et al., 1999; Butcher et al., 2000; Hevelka et al., 2002, Chernyshev et al., 2004) and are currently used in some of standardizing institutes (Keightley and Park, 2007; Bobin et al., 2010). In this paper, we will describe a very simple but versatile data acquisition system developed in NMIJ for such purposes. In order to demonstrate the performance and usefulness of this system, 4pb(PS)–4pg coincidence measurements with a detector configuration of a sandwich type plastic scintillator(PS) and a well type NaI(Tl) scintillation detector were carried out for 60Co, 134Cs and 152Eu using this digital coincidence counting system. It should be emphasized that all data analyses including pulse-height analyses, bi-dimensional analyses for making efficiency functions and extrapolations can be performed by the conventional MS Excel from a huge number of list-mode data-pairs.
2. Data acquisition system The basic concept of our system succeeds to the first design described by Buckman and Ius (1996). However, since no time stamping system or live time controller are provided in our system, the system becomes simpler in both of hard- and softwares, and is very easy to operate.
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Fig. 1. Schematic diagram of our bi-dimensional data acquisition system with a 4pb 4pg detector configuration composed of a sandwich type 4p plastic scintillation detector and a well-type NaI(Tl) scintillation detector.
The basic diagram of our data acquisition system is shown in Fig. 1. In order to demonstrate the performance of this system, we used a 4pb 4pg detector configuration composed of a 127 mmf 127 mm well type NaI(Tl) scintillation detector (well diameter: 30 mm) as the g-detector and a slender plastic scintillation detector as 4pb–detector (Kawada et al., 2004; Yamada et al., 2006). The source was sandwiched between two 1 mm thick plastic scintillators. In both of the b- and g-channels, the amplified pulses from an amplifier (Canberra 2024 for b-channel, ORTEC 572 for g-channel) are fed to separately to a fast ADC (16 bits, 25 MHz clock in maximum) via a pulse-peak-height stretcher (ORTEC 542) and an attenuator. To meet the requirement for the input voltage level of the ADC (2V maximum) and to accept the saturated pulses especially in the b-channel, use of a variable attenuator in the final stage of the analog electronics is important. In the output of the linear amplifier a conventional pulse-height discriminator (ORTEC 551 timing single channel analyzer as an integral mode) was connected whose discrimination level was set for slightly higher than the noise level. The output logic pulses from both discriminators were fed to a mixer circuit (logic OR) after passing a dead-time controller and a variable delay. Most of logic circuits including dead-time circuits, variable delay circuits etc. are laboratory made by the use of TTL ICs, and installed in a two span IEC module. These two ADCs (manufactured by Turtle Industries Co. Ltd. Japan together with the USB interface) in both channels are controlled with a common clock signal (25 MHz in maximum), and triggered simultaneously by the logic pulses from the mixer. In the use of this system, timing adjustments between the two analog pulses and two trigger signals are very important. Different time constant settings of the two linear amplifiers of b- and g-channels are therefore not recommended, and critical timing of the relative delay can be adjustable with ORTEC 542 pulse stretcher in a range within 5 ms. A variable delay circuit and dead-time controller were provided prior to digitization. The resolving time of the OR circuit was usually chosen as 1 ms. The width of stretched analog pulses can be also adjusted up to 5 ms in a case of ORTEC 542. The delay in the process of pulse-height stretching was somewhat dependent on the pulse-height especially for the saturated pulses, considerably large relative time jitter being observed. In order to avoid inadequate samplings, the pulse width of stretched analog pulse was chosen as 4 ms, but this pulse-width can be shortened
Fig. 2. Examples of data-pairs obtained in an Excel table. Only first and last parts are shown for illustration.
by the use of a strobe technique including clock pulses. In order to suppress the effect of after-pulses in the use of plastic scintillator, the dead-time of b- and g-channel were set equal to 10 ms or more in the present experiments. If a pressurized 4pb–counter is used, however, shorter dead times are permissible. Paired digitized signals obtained with both ADCs in each sampling are sent to a temporary buffer-memories (2 MB each) which are connected to the main PC with FIFO (First-In, First-Out) pipes via USB in a form of binary code. By the use of this system, the total acquisition number of the data-sets has no limits in practice. However, when MS Excel is used, the total triggering number is restricted below 220 ¼1,048,576 for one data acquisition. This will be solved by using multiple columns in the Excel spreadsheet, in which many more acquisition numbers can be treated. After finishing data acquisition, the binary code files are converted to CSV files for use with MS Excel, as shown in Fig. 2, where the column A is for b-channel, column B for g-channel, respectively. In this figure, only the first and last parts are shown for the illustration. The data pairs can be classified the following three categories; (1) Only a b-channel event is detected. In this case, a pulse-height information was recorded in the column A, and column B showed a small pulse-height near the noise level for the g-channel (see rows 8 in Fig. 2). (2) The converse of (case 1). (see rows 1 and 11).
Y. Kawada et al. / Applied Radiation and Isotopes 70 (2012) 2031–2036
3. Data processing In this system, the count-rates, nb, ng and nc, of b- and g- and coincidence channels, respectively, for various b-discrimination levels and any g-window settings are easily determined by a simple computer software as will be mentioned in the Section 3.2. The 4pb–g efficiency function is prepared from the relationship between apparent disintegration rate n¼ nbng/nc versus (1 eb)/eb, where eb ¼ nc/ng. Of course, these data processing and extrapolation procedures can be made by the use of FORTRAN or Cþþ etc., but in this work we will show that all these data processing can be easily performed by the use of an elementary MS Excel. 3.1. Display of pulse-height spectra Pulse-height distributions of the b- and g-channels can be obtained easily by using an Excel function ‘‘FREQUENCY’’ (after appropriate data binning) and the spectra are readily displayed in the spreadsheet to aid the setting of g-windows and b-channel discrimination levels. Examples of pulse-height spectra thus obtained can be seen in Figs. 3, 5 and 7. 3.2. Computer discrimination/window-setting and coincidence counting From the huge number of data, we can count promptly the number of events which satisfy the decided conditions by using a function ‘‘COUNTIFS’’. For example, the number of g-pulses whose pulse-height lies between channel 22,000 and 25,000 can be readily determined as ¼COUNTIFS(B:B,‘‘4 ¼22,000’’, B:B,‘‘o25,000’’). The same procedure can be extended for coincidence counting. The result of calculation by ¼ COUNTIFS(A:A,‘‘ 4 ¼2000’’, B:B,‘‘ 4=22,000’’, B:B,‘‘ o25,000’’) implies the total number of b-pulses having pulse-heights over 2000 channels which are coincident with g-pulses whose pulse-height lying in the pulseheight-window of 22,000–25,000 channels. From above three simple steps, we can determine instantly, from a huge number of raw list data, precise 4pb–g efficiency functions for any choice of g-window settings even for separate plural g-windows.
4. Example of applications 4.1. Activity measurements of
60
Co
First we will show radioactivity measurements of 60Co with 4pb(PS)–4pg coincidence counting by the use of this system. The detector part was already mentioned in full detail in our previous
10x103
1.17 MeV Peak
60
8
Counts/200 Channel
In this system, as the AD conversion time is less than submicro seconds and FIFO pipes are employed, the resolving time of the system is mostly decided by the dead-time circuit, and the small effects due to the dead-times and accidental coincidences can be corrected. The live-time controller was not therefore used in the present experiments, but such live-time mode can be usable if required. The sampling numbers after each trigger can be selected in the range of 1–1,048,576 in this system, but the sampling number for each trigger was usually chosen as 1 in most of our 4pb–g experiments.
reports (Kawada et al., 2004; Yamada et al., 2006). A 60Co source of activity approximately 1 kBq was dropped onto 1 mm thick plastic scintillator sheets, and a diluted solution of Ludox-SM30 was added. The source was covered with another plastic scintillator sheet after drying, making a 4p sandwich counter. The pulse-height spectrum of g-channel is shown in Fig. 3, where a dominant 1.17 þ1.33 MeV sum peak and Compton continuum at higher pulse-height region (Compton sum effect) were observed. Coincidence absorption functions obtained for three different g-window settings are shown in Fig. 4. In the determination of each data point, the effects due to the dead-times of individual channels, and accidental coincidences were corrected for using an approximate formula proposed by Keightley and Watt (2002) derived from Campion’s formula (Campion, 1959). The extrapolations of n ¼nbng/nc to (1 eb)/eb ¼0 agreed within 0.2% for three different g-window settings; 1007.4 70.4 Bq (1.33 MeV peak gate), 1006.3 70.5 Bq (1.17 and 1.33 MeV peaks gate) and 1010.3 70.7 Bq (1.17 þ1.33 MeV sum peak gate). These results are consistent with those obtained with the conventional electronics using a ladder type discriminator; 1007.671.0 Bq. In case of sum peak gating, an irregular bump is appreciable in the region around (1 eb)/eb ¼0.5, causing a slightly higher extrapolation. The cause of this anomaly is currently under investigation, but the effect of this bump was incorporated in the estimation of the uncertainty. Since two 1mm thick plastic scintillators were used for the b-ray detection, the slope is steep as compared with the results obtained with a proportional 4p counter. The slope will be decided mainly as a term of (ebg ec/eg), where ebg is the g-sensitivity of b-counter, and ec is the probability that a coincidence will be observed when the b-particle is undetected (Campion 1959). In our case,
Co
1.33 MeV Peak
6 (1.17+1.33) MeV Sum Peak
4 2 0 0
10
30
20
40
60x103
50
Channel Number Fig. 3. Pulse-height distribution of g-channel for this system.
60
Co acquired and analyzed by
1070 Apprent Radioactivity (Bq)
(3) Both b- and g-channels events are detected in coincidence, and each pulse-height information was recorded columns A and B, respectively (see rows 2–7).
2033
1060
60
Co
1050
(
) (1.17+1.33)MeV Sum Peak Gate
1040 (
1030 1020
) 1.17 & 1.33 MeV Peaks Gate
( ) 1.33 MeV Gate
1010 1000 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
(1−)/ Fig. 4. Efficiency functions obtained with this system for
60
Co.
1.6
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Y. Kawada et al. / Applied Radiation and Isotopes 70 (2012) 2031–2036
a high-geometry g-detector was used, Compton continua originated from 1.17 MeV g-rays and 1.33 MeV g-rays were summed, resulting an intense continuum extends to the higher energy region, and the second term ec/eg tends to increase. Even in the photo-peak region of 1.17 and 1.33 MeV, a considerable portion of Compton continuum lies under the photo-peaks. The slope is therefore very dependent on the g-window settings. In the case where the g-window was set on the sum peak, the slope term becomes ebg, resulting in an estimation of ebg ¼0.031. 4.2. Activity measurements of
134
Cs
The same procedures described in the above section were applied to the measurements of 134Cs. Fig. 5 represents the pulseheight spectrum in the g-channel. Due to the high efficiency of the g-detector, a dominant (0.605þ0.76) MeV sum peak and a
(0.605þ0.760 þ0.569) MeV triple sum peak are seen. The 4pb–g coincidence functions for three different g-windows are shown in Fig. 6. It should be noted that these coincidence functions are quite different from those obtained with ordinal 4pb–g coincidence counting system e.g., using 76 mm f 76 mm NaI(Tl) scintillation detectors for g-ray detection (for example: Baerg, 1973b; Kawada, 1972) as was already mentioned by Kawada et al. (2004). These differences might be due to the dominant sum effects. The extrapolations to (1 eb)/eb ¼0 with 2nd order polynomials are in good agreement with each other as shown in Fig. 6 and Table 1, and consistent with the results obtained by conventional electronics (see Table 1). 4.3. 4pb–g coincidence functions in the 152Eu activity measurements 152
Eu is typical complex decaying nuclide which involves
b-decay and EC decay. Several methods have been reported for 605 keV
10x103
134
Cs
(605+796) keV Sum Peak
14x103
796 keV
6 4 2
(605+796+569) keV Triple Sum Peak
Counts/200 Channel
Counts/200 channel
8
K-X Rays
152 Eu
12 10 8
122keV
344 keV
6 1085 keV & Sum
4
1408 keV & Sum
2 0 0
10
20
30
0
50x103
40
0
Channel Number Fig. 5. Pulse-height distribution of g-channel for 134Cs acquired and displayed by this system. As a result of the use of a big well type NaI(Tl) scintillator, dominant sum effects are seen.
C
B 10
20
30
40
50
60x103
Channel Number Fig. 7. Pulse-height distribution of g-channel for and C, see the text and the caption of Fig. 8.
152
Eu. For inverse triangles A, B
1060
900 880
152
Cs ( ) (605+796) keV Sum Peak Gate
860 840 820 ( ) 605 keV Peak Gate
Apparent Radioactivity (Bq)
134
Apparent Radioactivity (Bq)
A
800 ( ) 796 keV Peak Gate 0.1
0.2
0.3
0.4
0.5
0.6
Fig. 6. Efficiency functions for 134Cs for three different g-gate settings. Due to dominant sum effects the shape of the efficiency functions differs very much from those obtained with ordinary detector configuration.
605 keV peak gate 796 keV peak gate (605þ 796) keV sum peak gate
134
Gate 3
1020
Gate 2
1000
Gate 1
980 960
0.0
0.7
(1−)/
Table 1 Results of the extrapolations for also shown.
Eu
940
780 0.0
1040
0.2
0.4
0.6 0.8 (1−)/
1.0
1.2
1.4
Fig. 8. Efficiency functions of 152Eu for three different g-window settings. The linear extrapolations were done using limited regions (see Table 2) of data points. Gate 1: 78 keV (markers A) 423 keV (B), Gate 2:78 keV(A) 1690 keV (C) and Gate 3:423 keV(B) 1690 keV (C).
Cs measurements using this system. Comparisons with the results by conventional counting are
Extrapolated result (Bq) (Software coincidence)
Extrapolated result (Bq) (Conventional counting)
869.157 0.36 (2nd order polynomial) 871.677 0.90 (2nd order polynomial) 871.177 2.02 (2nd order polynomial)
872.8 71.0 (2nd order polynomial) 873.9 71.2 (2nd order polynomial)
Y. Kawada et al. / Applied Radiation and Isotopes 70 (2012) 2031–2036
Table 2 Results of the extrapolations for Gate setting
152
2035
Eu measurements using this system. Extrapolated result (Bq) Remarks
Gate 1(A–B in Fig. 6) 78 keV–423 keV 966.00 7 2.0 Gate 2(A–C) 78 keV–1690 keV 968.727 1.3 Gate 3(B–C) 423 keV–1690 keV 968.157 0.7
the standardization of 152Eu (Ratel and Michotte, 2004). Among them, extrapolation techniques in the 4pb–g measurements are often used (Park et al., 2002; Johansson et al., 2003; Yamada et al., 2006; Hevelka and Sochorova, 2010). In these extrapolation techniques, however, the extrapolated points are somewhat dependent on the g-window setting and the adopted regions of the functions. In order to make more clear how the extrapolation point and the shape of the efficiency curve may change due to the g-window selection and/or the data range, 4pb–g efficiency functions for three different gate settings were observed. Fig. 7 shows the pulse-height spectrum and the imaginary gate positions. Due to a multiplicity of various energies of g-rays emitted, the peaks were overlapped and summed, resulting in a complex pulse-height spectrum. In the lower channels, we can see three ‘‘sister’’ peaks. It is considered that the middle is 122 keV photopeak, and the right a sum peak of 122 keV g-rays with Sm K-X rays and the left the escape peak. Following g-window settings are chosen; Gate 1; 78 keV–423 keV region (between inverse triangle markers A–B in Fig. 7). Gate 2; 78 keV–1690 keV region (between A–C) and Gate 3; 423 keV–1690 keV (region between B–C). The efficiency functions for these three g-window settings are shown in Fig. 8. As can be seen from the figure, the slope and shape of the efficiency functions are very dependent on the gate settings. With an increasing value of (1 eb)/eb, the apparent activity tends to saturate, and then turns to decrease, and a linear extrapolation is no longer applicable. Provided that only limited data regions are used for extrapolation, fairly good agreement will be obtained as shown in Fig. 7 and Table 2. These results suggest that the careful selection of g-gate and appropriate fitting using limited data-range are important in the measurements of such type of nuclides. In order to make more reliable measurements, other methods; e.g., 4pb–g coincidence spectrometry (Baba et al., 1982) or bi-dimensional extrapolation (Miyahara et al., 1990) are recommended. The resolution and stability of the present ADCs was suitable to use with a Gedetector, and hence 4pb–g software coincidence and/or 4pb–g coincidence spectrometry with a Ge detector can be carried out with this system. Detailed studies on such applications will be presented elsewhere.
4.4. Other possible applications When a full geometry arrangement such as 4pb 4pg detector configuration is used, we can also determine straightforwardly the source activity of complex decaying nuclides by 4pb þ4pg sum method (Winkler and Pavlik 1983; Kawada et al., 2004; Yamada et al., 2006; Neadjadi et al., 2010) from the total triggering number in this acquisition system, which corresponds to total OR numbers after some small corrections for the deadtime loss and intrinsic inefficiency. Since the total OR numbers can be determined as a function of b- and g-threshold in this system, the integral counts below the threshold levels can be also estimated by an extrapolation.
Linear extrapolation (1 eb)/eb o 0.75 Linear extrapolation (1 eb)/eb o 0.75 Linear extrapolation (1 eb)/eb o 1.0
As already mentioned, the sampling number after a trigger can be selected in a range from 1 to 1,048,576 in this system. Usually we select 1 in ordinal 4pb–g coincidence counting. If appropriate large sampling number after triggering are chosen, however, wave-forms of each pulse can be recorded. This mode of operation is useful for the studies of satellite spurious after-pulses and pileup phenomena and also for measurements of short half-life isomers.
5. Concluding remarks By the use of two fast ADCs operated with a common clock pulse and triggered simultaneously, a powerful and versatile bi-dimensional data acquisition system was constructed. The data analyses of the acquired data were analyzed by the use of MS Excel. In order to demonstrate the usefulness and applicability of this system, 4pb(PS) 4pg measurements of 60Co, 134Cs and 152Eu were carried out as examples. The measurement and analyses procedures are very simple as if a conventional 4pb–g system were used. As one of general aspects of software coincidence measurements, 4pb–g coincidence functions for any g-window settings including separate regions can be easily constructed and analyzed within a short time from a vast volume of list-mode data pairs. The procedures with this system can be extended for most of all 4pb–g coincidence experiments including in the coincidence spectrometry with a Ge-detector, and also applicable to the analyses of spurious after-pulses and correlation counting (Lewis et al., 1973) etc. This data acquisition system can play an important role in the various stages of radioactivity standardization.
Acknowledgments The authors would like to express their appreciation to Mr. Hiroyasu Sato of Seikei University (at present the Japan Electrical Meters Inspection Corporation) for his contribution in the prototype experiments. References Baba, S., Ichikawa, S., Sekine, T., Ishikawa, I., Baba, H., 1982. A method for determination of the 152Eu activity. Nucl. Instrum. Methods 203, 273–280. Baerg, A.P., 1973a. Pressurized proportional counters for coincidence measurements. Nucl. Instrum. Methods 112, 95–99. Baerg, A.P., 1973b. The efficiency extrapolation method in coincidence counting. Nucl. Instrum. Methods 112, 143–150. Bobin, C., Bouchard, J., Censier, B., 2010. First results in the development of an online digital counting platform dedicated to the primary measurements. Appl. Radiat. Isot. 68, 1519–1522. Buckman, S.M., Ius, D., 1996. Digital coincidence counting. Nucl. Instrum. Methods A 369, 368–374. Butcher, K.S.A., et al., 2000. Digital coincidence counting – initial results. Nucl. Instrum. Methods A 450, 30–34. Campion, P.J., 1959. The standardization of radioisotopes by the beta-gamma coincidence method using high efficiency detectors. Int. J. Appl. Radiat. Isot. 4, 232–248. Chernyshev, V.I., Korostin, S.V., Martynyuk, Yu.N., Trofimov, A.S., Iordanskii, P.A., 2004. A digital coincidence method. Meas. Tech. 47, 1204–1210. Hevelka, M., Auerbach, P., Sochorova, J., 2002. Software coincidence counting. Appl. Radiat. Isot. 56, 265–268.
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Hevelka, M., Sochorova, J., 2010. Standardization of 124Sb and 152Eu using software coincidence. Appl. Radiat. Isot. 68, 1330–1334. Hwang, Y.H., Park, T.S., Oh, P.J., Lee, M.K., Lee, J.M., 1999. Standardization of 57Co by MCTS technique. Nucl. Instrum. Methods A438, 340–344. Johansson, L., Altzizogolou, T., Sibbens, G., Denecke, B., Reher, D.F.G., 2003. Six direct methods for standardization of 152Eu. Nucl. Instrum. Methods A508, 378–387. Kawada, Y., Ohtuka, M., Wang, Q., Hino, Y., 2004. Absolute radioactivity measurements by the use of a 4pb 4pg detector configuration. Appl. Radiat. Isot. 60, 357–362. Kawada, Y., 1972. Extended application and improvement of the 4pb–g coincidence method in the standardization of radionuclides. Res. Electrotechnical Laboratory. No.730. Keightley, J.D., Watt, G.C., 2002. Digital coincidence counting (DCC) and its use in the corrections for out-of-channel gamma events in 4pb–g coincidence counting. Appl. Radiat. Isot. 56, 205–210. Keightley, J.D., Park, T.S., 2007. Digital coincidence counting for radionuclide standardization. Metrologia 44, S32–S35. Lewis, V.E., Smith, D., Williams, D., 1973. Correlation counting applied to the determination of absolute determination rates for nuclides with delayed state. Metrologia 9, 14–20.
Miyahara, H., Kitaori, S., Watanabe, T., 1987. 4pb–g coincidence counting by using a live-timed bi-dimensional data-acquisition system. Appl. Radiat. Isot. 38, 793–797. Miyahara, H., Nozue, Y., Kitaori, S., Watanabe, T., 1990. Standardization of 152Eu by two-dimensional extrapolation. Nucl. Instrum. Methods A286, 497–501. Neadjadi, Y., Bailat, C., Caffari, Y., Bochud, F., 2010. Standardization of 18F by a coincidence method using full solid angle detectors. Appl. Radiat. Isot. 68, 1309–1313. Park, T.S., Hwang, H.Y., Lee, J.M., 1998. An improved coincidence counting techniques for standardization of radionuclides. Appl. Radiat. Isot. 49, 1147–1151. Park, T.S., Lee, J.M., Hwang, H.Y., 2002. Standardization of 152Eu and 88Y. Appl. Radiat. Isot. 56, 275–280. Ratel, G., Michotte, C., 2004. BIPM comparison BIPM, RI(II-K1.Eu152 of the activity measurements of radionuclide 152Eu and links for the international comparison CCRI(II) K2-Eu152, Metrologia, 41. Tech. Suppl. 06003. Winkler, G., Pavlik, A., 1983. Some aspects of activity measurements with NaI(Tl) well-type detectors. Int. J. Appl. Radiat. Isot. 34, 547–553. Yamada, T., Nakamura, Y., Kawada, Y., Sato, Y., Hino, Y., 2006. Standardization of 152 Eu and 154Eu by 4pb 4pg coincidence method and 4p(b þ g) integral counting. Appl. Radiat. Isot. 64, 1220–1224.
Contents lists available at SciVerse ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
A simple and versatile data acquisition system for software coincidence and pulse-height discrimination in 4pb–g coincidence experiments Y. Kawada a,n, T. Yamada a,b, Y. Unno a, A. Yunoki a, Y. Sato a, Y. Hino a a b
National Metrology Institute of Japan, National Institute of Advanced Industrial Sciences and Technology, Tsukuba Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan Japan Radioisotope Association, 2-28-45, Hon-komagome, Bunkyo, Tokyo 113-3941, Japan
a r t i c l e i n f o
abstract
Available online 1 March 2012
A simple but versatile data acquisition system for software coincidence experiments is described, in which any time stamping and live time controller are not provided. Signals from b- and g-channels are fed to separately two fast ADCs (16 bits, 25 MHz clock maximum) via variable delay circuits and pulse-height stretchers, and also to pulse-height discriminators. The discriminating level was set to just above the electronic noise. Two ADCs were controlled with a common clock signal, and triggered simultaneously by the logic OR pulses from both discriminators. Paired digital signals for each sampling were sent to buffer memories connected to main PC with a FIFO (First-In, First-Out) pipe via USB. After data acquisition in list mode, various processing including pulse-height analyses was performed using MS-Excel (version 2007 and later). The usefulness of this system was demonstrated for 4pb(PS)–4pg coincidence measurements of 60Co, 134Cs and 152Eu. Possibilities of other extended applications will be touched upon. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Software 4pb–g coincidence Efficiency function Excel 60 Co 134 Cs 152 Eu
1. Introduction For several decades, 4pb–g coincidence counting method (Campion, 1959) has been employed as the major technique for radionuclide standardization, in which extrapolation techniques are often used to determine most of efficiency dependent corrections. For the determination of the efficiency functions required in this procedure, it is necessary to perform many 4pb–g coincidence measurements for different b-efficiencies. To change b-efficiencies, adjustments of self-absorption and/or additions of absorber foils have historically been used. As an alternative, electronic discrimination techniques based upon pulse-height discrimination of signals from a pressurized 4pb–counter or a plastic/liquid scintillation detector has come into wide use (Baerg, 1973a). Pulse-height discrimination can be done manually by the adjustments of discrimination level or by the use of ladder type discriminators in a conventional 4pb–g coincidence counting system. In measuring complex decaying nuclides, the slope and shape of the efficiency functions are dependent on the g-window setting, and hence the 4pb–g extrapolation curve should be determined for each of different g-window settings. In order to avoid such tedious procedures, the use of a two dimensional list-mode-measurements (Miyahara et al., 1987) or software coincidence techniques has
n
Corresponding author. E-mail address: [email protected] (Y. Kawada).
0969-8043/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2012.02.060
become more popular instead of the use of a conventional 4pb–g coincidence counting. So far techniques and various applications of such digital coincidence systems were already reported by several authors (e.g.,: Buckman and Ius, 1996; Park et al., 1998; Hwang et al., 1999; Butcher et al., 2000; Hevelka et al., 2002, Chernyshev et al., 2004) and are currently used in some of standardizing institutes (Keightley and Park, 2007; Bobin et al., 2010). In this paper, we will describe a very simple but versatile data acquisition system developed in NMIJ for such purposes. In order to demonstrate the performance and usefulness of this system, 4pb(PS)–4pg coincidence measurements with a detector configuration of a sandwich type plastic scintillator(PS) and a well type NaI(Tl) scintillation detector were carried out for 60Co, 134Cs and 152Eu using this digital coincidence counting system. It should be emphasized that all data analyses including pulse-height analyses, bi-dimensional analyses for making efficiency functions and extrapolations can be performed by the conventional MS Excel from a huge number of list-mode data-pairs.
2. Data acquisition system The basic concept of our system succeeds to the first design described by Buckman and Ius (1996). However, since no time stamping system or live time controller are provided in our system, the system becomes simpler in both of hard- and softwares, and is very easy to operate.
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Fig. 1. Schematic diagram of our bi-dimensional data acquisition system with a 4pb 4pg detector configuration composed of a sandwich type 4p plastic scintillation detector and a well-type NaI(Tl) scintillation detector.
The basic diagram of our data acquisition system is shown in Fig. 1. In order to demonstrate the performance of this system, we used a 4pb 4pg detector configuration composed of a 127 mmf 127 mm well type NaI(Tl) scintillation detector (well diameter: 30 mm) as the g-detector and a slender plastic scintillation detector as 4pb–detector (Kawada et al., 2004; Yamada et al., 2006). The source was sandwiched between two 1 mm thick plastic scintillators. In both of the b- and g-channels, the amplified pulses from an amplifier (Canberra 2024 for b-channel, ORTEC 572 for g-channel) are fed to separately to a fast ADC (16 bits, 25 MHz clock in maximum) via a pulse-peak-height stretcher (ORTEC 542) and an attenuator. To meet the requirement for the input voltage level of the ADC (2V maximum) and to accept the saturated pulses especially in the b-channel, use of a variable attenuator in the final stage of the analog electronics is important. In the output of the linear amplifier a conventional pulse-height discriminator (ORTEC 551 timing single channel analyzer as an integral mode) was connected whose discrimination level was set for slightly higher than the noise level. The output logic pulses from both discriminators were fed to a mixer circuit (logic OR) after passing a dead-time controller and a variable delay. Most of logic circuits including dead-time circuits, variable delay circuits etc. are laboratory made by the use of TTL ICs, and installed in a two span IEC module. These two ADCs (manufactured by Turtle Industries Co. Ltd. Japan together with the USB interface) in both channels are controlled with a common clock signal (25 MHz in maximum), and triggered simultaneously by the logic pulses from the mixer. In the use of this system, timing adjustments between the two analog pulses and two trigger signals are very important. Different time constant settings of the two linear amplifiers of b- and g-channels are therefore not recommended, and critical timing of the relative delay can be adjustable with ORTEC 542 pulse stretcher in a range within 5 ms. A variable delay circuit and dead-time controller were provided prior to digitization. The resolving time of the OR circuit was usually chosen as 1 ms. The width of stretched analog pulses can be also adjusted up to 5 ms in a case of ORTEC 542. The delay in the process of pulse-height stretching was somewhat dependent on the pulse-height especially for the saturated pulses, considerably large relative time jitter being observed. In order to avoid inadequate samplings, the pulse width of stretched analog pulse was chosen as 4 ms, but this pulse-width can be shortened
Fig. 2. Examples of data-pairs obtained in an Excel table. Only first and last parts are shown for illustration.
by the use of a strobe technique including clock pulses. In order to suppress the effect of after-pulses in the use of plastic scintillator, the dead-time of b- and g-channel were set equal to 10 ms or more in the present experiments. If a pressurized 4pb–counter is used, however, shorter dead times are permissible. Paired digitized signals obtained with both ADCs in each sampling are sent to a temporary buffer-memories (2 MB each) which are connected to the main PC with FIFO (First-In, First-Out) pipes via USB in a form of binary code. By the use of this system, the total acquisition number of the data-sets has no limits in practice. However, when MS Excel is used, the total triggering number is restricted below 220 ¼1,048,576 for one data acquisition. This will be solved by using multiple columns in the Excel spreadsheet, in which many more acquisition numbers can be treated. After finishing data acquisition, the binary code files are converted to CSV files for use with MS Excel, as shown in Fig. 2, where the column A is for b-channel, column B for g-channel, respectively. In this figure, only the first and last parts are shown for the illustration. The data pairs can be classified the following three categories; (1) Only a b-channel event is detected. In this case, a pulse-height information was recorded in the column A, and column B showed a small pulse-height near the noise level for the g-channel (see rows 8 in Fig. 2). (2) The converse of (case 1). (see rows 1 and 11).
Y. Kawada et al. / Applied Radiation and Isotopes 70 (2012) 2031–2036
3. Data processing In this system, the count-rates, nb, ng and nc, of b- and g- and coincidence channels, respectively, for various b-discrimination levels and any g-window settings are easily determined by a simple computer software as will be mentioned in the Section 3.2. The 4pb–g efficiency function is prepared from the relationship between apparent disintegration rate n¼ nbng/nc versus (1 eb)/eb, where eb ¼ nc/ng. Of course, these data processing and extrapolation procedures can be made by the use of FORTRAN or Cþþ etc., but in this work we will show that all these data processing can be easily performed by the use of an elementary MS Excel. 3.1. Display of pulse-height spectra Pulse-height distributions of the b- and g-channels can be obtained easily by using an Excel function ‘‘FREQUENCY’’ (after appropriate data binning) and the spectra are readily displayed in the spreadsheet to aid the setting of g-windows and b-channel discrimination levels. Examples of pulse-height spectra thus obtained can be seen in Figs. 3, 5 and 7. 3.2. Computer discrimination/window-setting and coincidence counting From the huge number of data, we can count promptly the number of events which satisfy the decided conditions by using a function ‘‘COUNTIFS’’. For example, the number of g-pulses whose pulse-height lies between channel 22,000 and 25,000 can be readily determined as ¼COUNTIFS(B:B,‘‘4 ¼22,000’’, B:B,‘‘o25,000’’). The same procedure can be extended for coincidence counting. The result of calculation by ¼ COUNTIFS(A:A,‘‘ 4 ¼2000’’, B:B,‘‘ 4=22,000’’, B:B,‘‘ o25,000’’) implies the total number of b-pulses having pulse-heights over 2000 channels which are coincident with g-pulses whose pulse-height lying in the pulseheight-window of 22,000–25,000 channels. From above three simple steps, we can determine instantly, from a huge number of raw list data, precise 4pb–g efficiency functions for any choice of g-window settings even for separate plural g-windows.
4. Example of applications 4.1. Activity measurements of
60
Co
First we will show radioactivity measurements of 60Co with 4pb(PS)–4pg coincidence counting by the use of this system. The detector part was already mentioned in full detail in our previous
10x103
1.17 MeV Peak
60
8
Counts/200 Channel
In this system, as the AD conversion time is less than submicro seconds and FIFO pipes are employed, the resolving time of the system is mostly decided by the dead-time circuit, and the small effects due to the dead-times and accidental coincidences can be corrected. The live-time controller was not therefore used in the present experiments, but such live-time mode can be usable if required. The sampling numbers after each trigger can be selected in the range of 1–1,048,576 in this system, but the sampling number for each trigger was usually chosen as 1 in most of our 4pb–g experiments.
reports (Kawada et al., 2004; Yamada et al., 2006). A 60Co source of activity approximately 1 kBq was dropped onto 1 mm thick plastic scintillator sheets, and a diluted solution of Ludox-SM30 was added. The source was covered with another plastic scintillator sheet after drying, making a 4p sandwich counter. The pulse-height spectrum of g-channel is shown in Fig. 3, where a dominant 1.17 þ1.33 MeV sum peak and Compton continuum at higher pulse-height region (Compton sum effect) were observed. Coincidence absorption functions obtained for three different g-window settings are shown in Fig. 4. In the determination of each data point, the effects due to the dead-times of individual channels, and accidental coincidences were corrected for using an approximate formula proposed by Keightley and Watt (2002) derived from Campion’s formula (Campion, 1959). The extrapolations of n ¼nbng/nc to (1 eb)/eb ¼0 agreed within 0.2% for three different g-window settings; 1007.4 70.4 Bq (1.33 MeV peak gate), 1006.3 70.5 Bq (1.17 and 1.33 MeV peaks gate) and 1010.3 70.7 Bq (1.17 þ1.33 MeV sum peak gate). These results are consistent with those obtained with the conventional electronics using a ladder type discriminator; 1007.671.0 Bq. In case of sum peak gating, an irregular bump is appreciable in the region around (1 eb)/eb ¼0.5, causing a slightly higher extrapolation. The cause of this anomaly is currently under investigation, but the effect of this bump was incorporated in the estimation of the uncertainty. Since two 1mm thick plastic scintillators were used for the b-ray detection, the slope is steep as compared with the results obtained with a proportional 4p counter. The slope will be decided mainly as a term of (ebg ec/eg), where ebg is the g-sensitivity of b-counter, and ec is the probability that a coincidence will be observed when the b-particle is undetected (Campion 1959). In our case,
Co
1.33 MeV Peak
6 (1.17+1.33) MeV Sum Peak
4 2 0 0
10
30
20
40
60x103
50
Channel Number Fig. 3. Pulse-height distribution of g-channel for this system.
60
Co acquired and analyzed by
1070 Apprent Radioactivity (Bq)
(3) Both b- and g-channels events are detected in coincidence, and each pulse-height information was recorded columns A and B, respectively (see rows 2–7).
2033
1060
60
Co
1050
(
) (1.17+1.33)MeV Sum Peak Gate
1040 (
1030 1020
) 1.17 & 1.33 MeV Peaks Gate
( ) 1.33 MeV Gate
1010 1000 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
(1−)/ Fig. 4. Efficiency functions obtained with this system for
60
Co.
1.6
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a high-geometry g-detector was used, Compton continua originated from 1.17 MeV g-rays and 1.33 MeV g-rays were summed, resulting an intense continuum extends to the higher energy region, and the second term ec/eg tends to increase. Even in the photo-peak region of 1.17 and 1.33 MeV, a considerable portion of Compton continuum lies under the photo-peaks. The slope is therefore very dependent on the g-window settings. In the case where the g-window was set on the sum peak, the slope term becomes ebg, resulting in an estimation of ebg ¼0.031. 4.2. Activity measurements of
134
Cs
The same procedures described in the above section were applied to the measurements of 134Cs. Fig. 5 represents the pulseheight spectrum in the g-channel. Due to the high efficiency of the g-detector, a dominant (0.605þ0.76) MeV sum peak and a
(0.605þ0.760 þ0.569) MeV triple sum peak are seen. The 4pb–g coincidence functions for three different g-windows are shown in Fig. 6. It should be noted that these coincidence functions are quite different from those obtained with ordinal 4pb–g coincidence counting system e.g., using 76 mm f 76 mm NaI(Tl) scintillation detectors for g-ray detection (for example: Baerg, 1973b; Kawada, 1972) as was already mentioned by Kawada et al. (2004). These differences might be due to the dominant sum effects. The extrapolations to (1 eb)/eb ¼0 with 2nd order polynomials are in good agreement with each other as shown in Fig. 6 and Table 1, and consistent with the results obtained by conventional electronics (see Table 1). 4.3. 4pb–g coincidence functions in the 152Eu activity measurements 152
Eu is typical complex decaying nuclide which involves
b-decay and EC decay. Several methods have been reported for 605 keV
10x103
134
Cs
(605+796) keV Sum Peak
14x103
796 keV
6 4 2
(605+796+569) keV Triple Sum Peak
Counts/200 Channel
Counts/200 channel
8
K-X Rays
152 Eu
12 10 8
122keV
344 keV
6 1085 keV & Sum
4
1408 keV & Sum
2 0 0
10
20
30
0
50x103
40
0
Channel Number Fig. 5. Pulse-height distribution of g-channel for 134Cs acquired and displayed by this system. As a result of the use of a big well type NaI(Tl) scintillator, dominant sum effects are seen.
C
B 10
20
30
40
50
60x103
Channel Number Fig. 7. Pulse-height distribution of g-channel for and C, see the text and the caption of Fig. 8.
152
Eu. For inverse triangles A, B
1060
900 880
152
Cs ( ) (605+796) keV Sum Peak Gate
860 840 820 ( ) 605 keV Peak Gate
Apparent Radioactivity (Bq)
134
Apparent Radioactivity (Bq)
A
800 ( ) 796 keV Peak Gate 0.1
0.2
0.3
0.4
0.5
0.6
Fig. 6. Efficiency functions for 134Cs for three different g-gate settings. Due to dominant sum effects the shape of the efficiency functions differs very much from those obtained with ordinary detector configuration.
605 keV peak gate 796 keV peak gate (605þ 796) keV sum peak gate
134
Gate 3
1020
Gate 2
1000
Gate 1
980 960
0.0
0.7
(1−)/
Table 1 Results of the extrapolations for also shown.
Eu
940
780 0.0
1040
0.2
0.4
0.6 0.8 (1−)/
1.0
1.2
1.4
Fig. 8. Efficiency functions of 152Eu for three different g-window settings. The linear extrapolations were done using limited regions (see Table 2) of data points. Gate 1: 78 keV (markers A) 423 keV (B), Gate 2:78 keV(A) 1690 keV (C) and Gate 3:423 keV(B) 1690 keV (C).
Cs measurements using this system. Comparisons with the results by conventional counting are
Extrapolated result (Bq) (Software coincidence)
Extrapolated result (Bq) (Conventional counting)
869.157 0.36 (2nd order polynomial) 871.677 0.90 (2nd order polynomial) 871.177 2.02 (2nd order polynomial)
872.8 71.0 (2nd order polynomial) 873.9 71.2 (2nd order polynomial)
Y. Kawada et al. / Applied Radiation and Isotopes 70 (2012) 2031–2036
Table 2 Results of the extrapolations for Gate setting
152
2035
Eu measurements using this system. Extrapolated result (Bq) Remarks
Gate 1(A–B in Fig. 6) 78 keV–423 keV 966.00 7 2.0 Gate 2(A–C) 78 keV–1690 keV 968.727 1.3 Gate 3(B–C) 423 keV–1690 keV 968.157 0.7
the standardization of 152Eu (Ratel and Michotte, 2004). Among them, extrapolation techniques in the 4pb–g measurements are often used (Park et al., 2002; Johansson et al., 2003; Yamada et al., 2006; Hevelka and Sochorova, 2010). In these extrapolation techniques, however, the extrapolated points are somewhat dependent on the g-window setting and the adopted regions of the functions. In order to make more clear how the extrapolation point and the shape of the efficiency curve may change due to the g-window selection and/or the data range, 4pb–g efficiency functions for three different gate settings were observed. Fig. 7 shows the pulse-height spectrum and the imaginary gate positions. Due to a multiplicity of various energies of g-rays emitted, the peaks were overlapped and summed, resulting in a complex pulse-height spectrum. In the lower channels, we can see three ‘‘sister’’ peaks. It is considered that the middle is 122 keV photopeak, and the right a sum peak of 122 keV g-rays with Sm K-X rays and the left the escape peak. Following g-window settings are chosen; Gate 1; 78 keV–423 keV region (between inverse triangle markers A–B in Fig. 7). Gate 2; 78 keV–1690 keV region (between A–C) and Gate 3; 423 keV–1690 keV (region between B–C). The efficiency functions for these three g-window settings are shown in Fig. 8. As can be seen from the figure, the slope and shape of the efficiency functions are very dependent on the gate settings. With an increasing value of (1 eb)/eb, the apparent activity tends to saturate, and then turns to decrease, and a linear extrapolation is no longer applicable. Provided that only limited data regions are used for extrapolation, fairly good agreement will be obtained as shown in Fig. 7 and Table 2. These results suggest that the careful selection of g-gate and appropriate fitting using limited data-range are important in the measurements of such type of nuclides. In order to make more reliable measurements, other methods; e.g., 4pb–g coincidence spectrometry (Baba et al., 1982) or bi-dimensional extrapolation (Miyahara et al., 1990) are recommended. The resolution and stability of the present ADCs was suitable to use with a Gedetector, and hence 4pb–g software coincidence and/or 4pb–g coincidence spectrometry with a Ge detector can be carried out with this system. Detailed studies on such applications will be presented elsewhere.
4.4. Other possible applications When a full geometry arrangement such as 4pb 4pg detector configuration is used, we can also determine straightforwardly the source activity of complex decaying nuclides by 4pb þ4pg sum method (Winkler and Pavlik 1983; Kawada et al., 2004; Yamada et al., 2006; Neadjadi et al., 2010) from the total triggering number in this acquisition system, which corresponds to total OR numbers after some small corrections for the deadtime loss and intrinsic inefficiency. Since the total OR numbers can be determined as a function of b- and g-threshold in this system, the integral counts below the threshold levels can be also estimated by an extrapolation.
Linear extrapolation (1 eb)/eb o 0.75 Linear extrapolation (1 eb)/eb o 0.75 Linear extrapolation (1 eb)/eb o 1.0
As already mentioned, the sampling number after a trigger can be selected in a range from 1 to 1,048,576 in this system. Usually we select 1 in ordinal 4pb–g coincidence counting. If appropriate large sampling number after triggering are chosen, however, wave-forms of each pulse can be recorded. This mode of operation is useful for the studies of satellite spurious after-pulses and pileup phenomena and also for measurements of short half-life isomers.
5. Concluding remarks By the use of two fast ADCs operated with a common clock pulse and triggered simultaneously, a powerful and versatile bi-dimensional data acquisition system was constructed. The data analyses of the acquired data were analyzed by the use of MS Excel. In order to demonstrate the usefulness and applicability of this system, 4pb(PS) 4pg measurements of 60Co, 134Cs and 152Eu were carried out as examples. The measurement and analyses procedures are very simple as if a conventional 4pb–g system were used. As one of general aspects of software coincidence measurements, 4pb–g coincidence functions for any g-window settings including separate regions can be easily constructed and analyzed within a short time from a vast volume of list-mode data pairs. The procedures with this system can be extended for most of all 4pb–g coincidence experiments including in the coincidence spectrometry with a Ge-detector, and also applicable to the analyses of spurious after-pulses and correlation counting (Lewis et al., 1973) etc. This data acquisition system can play an important role in the various stages of radioactivity standardization.
Acknowledgments The authors would like to express their appreciation to Mr. Hiroyasu Sato of Seikei University (at present the Japan Electrical Meters Inspection Corporation) for his contribution in the prototype experiments. References Baba, S., Ichikawa, S., Sekine, T., Ishikawa, I., Baba, H., 1982. A method for determination of the 152Eu activity. Nucl. Instrum. Methods 203, 273–280. Baerg, A.P., 1973a. Pressurized proportional counters for coincidence measurements. Nucl. Instrum. Methods 112, 95–99. Baerg, A.P., 1973b. The efficiency extrapolation method in coincidence counting. Nucl. Instrum. Methods 112, 143–150. Bobin, C., Bouchard, J., Censier, B., 2010. First results in the development of an online digital counting platform dedicated to the primary measurements. Appl. Radiat. Isot. 68, 1519–1522. Buckman, S.M., Ius, D., 1996. Digital coincidence counting. Nucl. Instrum. Methods A 369, 368–374. Butcher, K.S.A., et al., 2000. Digital coincidence counting – initial results. Nucl. Instrum. Methods A 450, 30–34. Campion, P.J., 1959. The standardization of radioisotopes by the beta-gamma coincidence method using high efficiency detectors. Int. J. Appl. Radiat. Isot. 4, 232–248. Chernyshev, V.I., Korostin, S.V., Martynyuk, Yu.N., Trofimov, A.S., Iordanskii, P.A., 2004. A digital coincidence method. Meas. Tech. 47, 1204–1210. Hevelka, M., Auerbach, P., Sochorova, J., 2002. Software coincidence counting. Appl. Radiat. Isot. 56, 265–268.
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