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γ coincidence system based on the pulse-mixing method
Nuclear Instruments and Methods in Physics Research A 422 (1999) 395—399
A simple, powerful 4pb/c coincidence system based on the pulse-mixing method Jacques Bouchard*, Bruno Chauvenet BNM-LPRI (Laboratoire Primaire des Rayonnements Ionisants) CEA/Saclay, F 91191 Gif-Sur-Yvette Cedex, France
Abstract An improved version of a simple and powerful 4pb/c coincidence system based on the pulse-mixing method is described. It is based on the use of extendable dead-times measured by the live-time technique. The coincidence channel is replaced by a “virtual” common channel where pulses coming from both beta and gamma detectors are mixed and counted together. The basic property of this common channel is to register no more than one pulse per coincident pair of pulses. A single channel-analyzer or an analog-to-digital converter (ADC) can be incorporated in the gamma channel. If an ADC is used, coincident and non-coincident spectra can be deduced from the recording. All the major problems (dead-time, accidental coincidences corrections) encountered in conventional systems are eliminated. An important feature of this system is its insensitivity to the delay between beta and gamma pulses. This coincidence method has been tested successfully for several radionuclides (Co, Cs, Sr and Yb) presenting different measurement difficulties, including metastable states (Sr and Yb). It is now used routinely for activity measurements. 1999 Elsevier Science B.V. All rights reserved. PACS: 06.20.!f; 06.20.Fn Keywords: 4pb/c coincidence system; Live-time measurement; Dead-time corrections; Accidental coincidences; ADC
1. Introduction The coincidence technique is generally used when one has to measure very accurately the activity of a radionuclide emitting simultaneously two types of radiation per disintegration. If e is the b efficiency of the beta detector, e the efficiency of the c gamma detector, and A the activity of the source, one can write the following relations for each
* Corresponding author.
channel [1]: N "Ae , N "Ae , N "Ae e , b b c c bc where N , N , N are the count rates in the three b c channels. The activity of the source is then given by the basic formula A"N N /N . b c Most of the time, a conventional system is composed of two specialized channels (beta and
0168-9002/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 0 9 9 0 - 5
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J. Bouchard, B. Chauvenet/Nucl. Instr. and Meth. in Phys. Res. A 422 (1999) 395—399
gamma) having their own dead time (q , q ). Coinb c cidences between these two channels are obtained using a coincidence unit having a resolving time. The presence of two independent dead-times is a source of complications when deriving the deadtime corrections, especially in the coincidence channel [2,3]. This problem has already been solved by the “IMPECC” system described in Refs. [4,5]. The resolving time is another source of problems as its length, which is necessary to take into account the “time-jitter” between the two channels, allows the recording of accidental coincidences. This problem is even more serious when measuring the activity of radionuclides whose disintegration can lead to a daughter metastable state which has the same effect as wide “time-jitter”. In this case, alternative methods [6,7] having their own drawbacks have to be used. All these problems, adding to the “Gandy” effect [8], become more and more important and difficult to handle as the activity of the source being measured increases. In addition, there is, at high count rate, a mismatch between the formulae and the real behavior of the electronics; the so called “fixed dead-times” cannot be considered as strictly fixed anymore. All these problems lead us some years ago to develop a new coincidence method avoiding these problems. This was called the pulsemixing method [9] because the traditional coincidence unit is replaced by a common channel in which pulses coming from both beta and gamma detectors are simply mixed and counted together. This coincidence method has been tested for several radionuclides and is now used routinely for activity measurements. A new version of the common channel has been realized and is presented here. As will be seen, compared to the first version, it results into a simplification of the electronic setting which limits still more the risks of errors.
2. Principle of the system The system makes use of extendable dead-times and of the live-time technique. This technique, which enables the correction of count rates for dead-time using live-time integrators, was firstly described and used for 4pb/c coincidence counting systems by Gandy in 1963 [10]. The great advan-
Fig. 1. Dead times in channels 1, 2 and common. A: event detected in channels 1 and 2; B: event detected in channel 1 only; C: event detected in channel 2 only.
tages of this technique applied to Poisson processes lie in its validity for any type of dead-time and the simplicity of corrections. At the output of each detector, the signals are sampled through two different dead-time circuits, one proper to each detector and one which is common to both of them. The purpose of the common channel is to systematically eliminate from the counting the last pulse of correlated pairs (see Fig. 1). This is realized under the condition that dead-times in the common channel are larger than the longest delay between coincident pulses. If this condition holds, the relations presented hereafter can be obtained. As a first step, let us suppose that there is no window selector or ADC in either channel but only a low-level threshold [11]. If a radioactive source of activity A is measured, the true count rates are respectively B#C and G#C in the beta and gamma channels, B representing the uncorrelated beta pulses, G the uncorrelated gamma pulses, and C the correlated pulses. ¹ is the measuring time, P , P , P the live-to-total time ratios in the beta, gamma, and common counting channels, respectively. If N , N , N are the numbers of pulses counted in the beta, gamma and common channels, P ¹"t , P ¹"t , and P ¹"t , the live times in the three channels, one gets the following relations: N /t "B#C, N /t "G#C, N /t "B#G#C
J. Bouchard, B. Chauvenet/Nucl. Instr. and Meth. in Phys. Res. A 422 (1999) 395—399
397
and the activity of the source is given by A"N /t N /t /(N /t #N /t !N /t ). A single-channel analyzer or an ADC can be incorporated in one channel. The use of an ADC allows the recording of two spectra (generally gamma-ray spectra) from which coincident and non-coincident spectra can be deduced in order to select energy windows with computer. If we incorporate a single-channel analyzer or an ADC in the gamma channel, and if there exist coincident pairs with the beta pulse counted first [11], then the coincidence count rate for the gamma pulses in the window w is equal to C "C(N /t !N /t )/(N /t !N /t ) U U U and the activity of the source is given by A"N /t N /t /C U U with G and C defined as above, N the number of U pulses in the window w counted in the gamma channel, N the number of gamma pulses selected U in the gamma window and counted in the common channel, and C the true count rates of coincident U gamma pulses in the gamma window. The expression of the activity A is very simple. Only the count rates corrected for dead-times in the three channels are needed. The suppression of the resolving-time eliminates problems like the determination of accidental coincidences and corrections due to the time jitter between beta and gamma pulses, electronic settings for time-delay cancellation between the two channels, and measurements of resolving times.
3. Description of the system A simplified scheme of the system can be seen in Fig. 2. To measure live-times properly, it is very important to have a pulse representing exactly the real paralysis of the channel. This pulse can then be used to sample a clock-pulse train which allows live-time measurements. An important feature of this system is the absence of shaping which could lead to a loss of dead-time information. This is the case, when the pulses at the output of preamplifiers are shortened (problem of hidden dead-times). The
Fig. 2. Simplified scheme of the system presented.
extendable dead-time module (patented) used in this system has been developed at LPRI. The new common channel is very simple as there is no associated dead-time module. It becomes a “virtual” channel which is composed of: (1) An ‘‘OR” gate whose inputs are connected to the output of the dead-times of the beta and gamma channels. The output of this ‘‘OR” gate is connected to a shaper which detects the low-to-high transition of the signal and delivers a pulse which can be counted (N ). It can be seen that in the case of a coincidence, only one pulse will be counted (Fig. 1). (2) An ‘‘AND” gate whose inputs are connected to the outputs of the live-time counting of each channel. The sampled clock-pulse at the output of this ‘‘AND” gate can also be counted and gives the live-time information of the common channel as the main clock generator is common to both beta and gamma channels (Fig. 1). In the first version of this system [11], a deadtime was connected, through an “OR” gate, to the output of the beta and gamma discriminators to constitute the common channel. One drawback of
IV. INFORMATION PROCESSING
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J. Bouchard, B. Chauvenet/Nucl. Instr. and Meth. in Phys. Res. A 422 (1999) 395—399
this design was the necessity to have a third deadtime module with all its surrounding (threshold and dead-time settings, etc.). The dead time generated had to be set longer than the longest of the two other dead-times and the thresholds had to be set carefully as, in this method, it is very important that the common channel processes the same pulses which have been processed by the other channels. In the new version, all these requirements are conceptually fulfilled. The gamma channel can be equipped with a single-channel analyzer or an ADC. At LPRI, we use an ADC, (8K channels) connected to a memory having a capacity of 16K channels. A very simple circuit has been inserted between the ADC and the memory to shift the gamma spectrum from the lower part of the memory (first 8K channels) to the higher part according to the time of detection of the gamma pulse. If the detected gamma pulse is preceded by a beta pulse (the common channel is also triggered by this beta pulse), then this gamma pulse is stored in the upper part of the memory. In the other cases, the gamma pulse is stored in the lower part of the memory. At the end of a measurement, we get two spectra. The sum of these two spectra gives the complete gamma spectrum and the common spectrum which is recorded in the upper part of the memory enables us to derive a coincident spectrum.
4. Activity measurement This coincidence system has been tested successfully for several radionuclides (Sr, Co, Cs, and Yb) presenting different measurement difficulties, including metastable states (Sr and Yb). It is now used routinely for activity measurements. The measurement of Co sources is rather simple as there is no metastable state in the decay scheme and no strong internal conversions in the gamma transitions. The results were in agreement with those obtained with the “IMPECC” coincidence system described in [4,5]. The difficulty of measuring the activity of Sr sources results from a metastable state of 1 ls in its decay scheme. The result was in agreement with the activity given by
Fig. 3. Comparison of activity measurements by different systems.
a 4p ionization chamber already calibrated by an older anti-coincidence measurement [11]. The decay schemes of Cs and Yb are complex [12], and in the case of Yb, a metastable state of 0.66 ls adds to the complexity of measurements. An extrapolation procedure is necessary [13] to get the activity by the 4pb/c coincidence method. In these cases, computer discrimination to select gamma windows was tested and used. The results were compared to those obtained with a well-type crystal (4pc method) and again, there was a good agreement. All these results are presented in Fig. 3. It can be seen in this figure that the uncertainty obtained with the pulse-mixing method is quite good. Type-A uncertainties are equivalent to those obtained with conventional systems. They can be calculated using a simple general formula [9]. The advantage of this method, especially with the new version of its electronics over conventional systems is that there adds almost no type-B uncertainties when in conventional systems type-B uncertainty components must be added for the problems previously mentioned like “time-jitter”.
5. Conclusion This system has proved its ability to measure the activity of radionuclides in a simple way, even those
J. Bouchard, B. Chauvenet/Nucl. Instr. and Meth. in Phys. Res. A 422 (1999) 395—399
having a complex decay-scheme or a metastable state. This confirms the many advantages of this instrument over conventional systems. It takes full advantage of the use of extendable dead times, and the associated live-time measurement. The formulae are general and quite simple compared to those used in the classical coincidence method. The new version of the common channel still increases this simplicity of operation. With this new implementation of the common channel, the third dead-time is not needed anymore. The incorporation in one channel of a single-channel analyzer or even better an ADC (which allows computer discrimination), provides a useful instrument to measure the activity of radionuclides whatever the complexity of their decay schemes.
399
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
P.J. Campion, Nucl. Instr. and Meth. 4 (1959) 232. D. Smith, Nucl. Instr. and Meth. 152 (1978) 505. D. Smith, Appl. Radiat. Isotopes A 38 (1987) 813. J. Bouchard, IEEE Trans. Nucl. Sci. NS-41 (4) (1994) 957. J. Bouchard, B. Chauvenet, R. Vatin, Rapport CEA R-5431, 1988. J. Bryant, Nucl. Instr. and Meth. 13 (1962) 273. A.P. Baerg, K. Munzenmayer, G.C. Bowes, Metrologia 12 (1976) 77. A. Gandy, Int. J. Appl. Radiat. Isotopes 11 (1961) 75. B. Chauvenet, J. Bouchard, Nucl. Instr. and Meth. A 312 (1992) 53. A. Gandy, Int. J. Appl. Radiat. Isotopes 13 (1963) 385. J. Bouchard, B. Chauvenet, IEEE Trans. Nucl. Sci. NS-43 (1996) 1381. N. Coursol, Table Radionucleides, 1992. A.P. Baerg, Metrologia 2 (1966) 23.
IV. INFORMATION PROCESSING
A simple, powerful 4pb/c coincidence system based on the pulse-mixing method Jacques Bouchard*, Bruno Chauvenet BNM-LPRI (Laboratoire Primaire des Rayonnements Ionisants) CEA/Saclay, F 91191 Gif-Sur-Yvette Cedex, France
Abstract An improved version of a simple and powerful 4pb/c coincidence system based on the pulse-mixing method is described. It is based on the use of extendable dead-times measured by the live-time technique. The coincidence channel is replaced by a “virtual” common channel where pulses coming from both beta and gamma detectors are mixed and counted together. The basic property of this common channel is to register no more than one pulse per coincident pair of pulses. A single channel-analyzer or an analog-to-digital converter (ADC) can be incorporated in the gamma channel. If an ADC is used, coincident and non-coincident spectra can be deduced from the recording. All the major problems (dead-time, accidental coincidences corrections) encountered in conventional systems are eliminated. An important feature of this system is its insensitivity to the delay between beta and gamma pulses. This coincidence method has been tested successfully for several radionuclides (Co, Cs, Sr and Yb) presenting different measurement difficulties, including metastable states (Sr and Yb). It is now used routinely for activity measurements. 1999 Elsevier Science B.V. All rights reserved. PACS: 06.20.!f; 06.20.Fn Keywords: 4pb/c coincidence system; Live-time measurement; Dead-time corrections; Accidental coincidences; ADC
1. Introduction The coincidence technique is generally used when one has to measure very accurately the activity of a radionuclide emitting simultaneously two types of radiation per disintegration. If e is the b efficiency of the beta detector, e the efficiency of the c gamma detector, and A the activity of the source, one can write the following relations for each
* Corresponding author.
channel [1]: N "Ae , N "Ae , N "Ae e , b b c c bc where N , N , N are the count rates in the three b c channels. The activity of the source is then given by the basic formula A"N N /N . b c Most of the time, a conventional system is composed of two specialized channels (beta and
0168-9002/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 0 9 9 0 - 5
IV. INFORMATION PROCESSING
396
J. Bouchard, B. Chauvenet/Nucl. Instr. and Meth. in Phys. Res. A 422 (1999) 395—399
gamma) having their own dead time (q , q ). Coinb c cidences between these two channels are obtained using a coincidence unit having a resolving time. The presence of two independent dead-times is a source of complications when deriving the deadtime corrections, especially in the coincidence channel [2,3]. This problem has already been solved by the “IMPECC” system described in Refs. [4,5]. The resolving time is another source of problems as its length, which is necessary to take into account the “time-jitter” between the two channels, allows the recording of accidental coincidences. This problem is even more serious when measuring the activity of radionuclides whose disintegration can lead to a daughter metastable state which has the same effect as wide “time-jitter”. In this case, alternative methods [6,7] having their own drawbacks have to be used. All these problems, adding to the “Gandy” effect [8], become more and more important and difficult to handle as the activity of the source being measured increases. In addition, there is, at high count rate, a mismatch between the formulae and the real behavior of the electronics; the so called “fixed dead-times” cannot be considered as strictly fixed anymore. All these problems lead us some years ago to develop a new coincidence method avoiding these problems. This was called the pulsemixing method [9] because the traditional coincidence unit is replaced by a common channel in which pulses coming from both beta and gamma detectors are simply mixed and counted together. This coincidence method has been tested for several radionuclides and is now used routinely for activity measurements. A new version of the common channel has been realized and is presented here. As will be seen, compared to the first version, it results into a simplification of the electronic setting which limits still more the risks of errors.
2. Principle of the system The system makes use of extendable dead-times and of the live-time technique. This technique, which enables the correction of count rates for dead-time using live-time integrators, was firstly described and used for 4pb/c coincidence counting systems by Gandy in 1963 [10]. The great advan-
Fig. 1. Dead times in channels 1, 2 and common. A: event detected in channels 1 and 2; B: event detected in channel 1 only; C: event detected in channel 2 only.
tages of this technique applied to Poisson processes lie in its validity for any type of dead-time and the simplicity of corrections. At the output of each detector, the signals are sampled through two different dead-time circuits, one proper to each detector and one which is common to both of them. The purpose of the common channel is to systematically eliminate from the counting the last pulse of correlated pairs (see Fig. 1). This is realized under the condition that dead-times in the common channel are larger than the longest delay between coincident pulses. If this condition holds, the relations presented hereafter can be obtained. As a first step, let us suppose that there is no window selector or ADC in either channel but only a low-level threshold [11]. If a radioactive source of activity A is measured, the true count rates are respectively B#C and G#C in the beta and gamma channels, B representing the uncorrelated beta pulses, G the uncorrelated gamma pulses, and C the correlated pulses. ¹ is the measuring time, P , P , P the live-to-total time ratios in the beta, gamma, and common counting channels, respectively. If N , N , N are the numbers of pulses counted in the beta, gamma and common channels, P ¹"t , P ¹"t , and P ¹"t , the live times in the three channels, one gets the following relations: N /t "B#C, N /t "G#C, N /t "B#G#C
J. Bouchard, B. Chauvenet/Nucl. Instr. and Meth. in Phys. Res. A 422 (1999) 395—399
397
and the activity of the source is given by A"N /t N /t /(N /t #N /t !N /t ). A single-channel analyzer or an ADC can be incorporated in one channel. The use of an ADC allows the recording of two spectra (generally gamma-ray spectra) from which coincident and non-coincident spectra can be deduced in order to select energy windows with computer. If we incorporate a single-channel analyzer or an ADC in the gamma channel, and if there exist coincident pairs with the beta pulse counted first [11], then the coincidence count rate for the gamma pulses in the window w is equal to C "C(N /t !N /t )/(N /t !N /t ) U U U and the activity of the source is given by A"N /t N /t /C U U with G and C defined as above, N the number of U pulses in the window w counted in the gamma channel, N the number of gamma pulses selected U in the gamma window and counted in the common channel, and C the true count rates of coincident U gamma pulses in the gamma window. The expression of the activity A is very simple. Only the count rates corrected for dead-times in the three channels are needed. The suppression of the resolving-time eliminates problems like the determination of accidental coincidences and corrections due to the time jitter between beta and gamma pulses, electronic settings for time-delay cancellation between the two channels, and measurements of resolving times.
3. Description of the system A simplified scheme of the system can be seen in Fig. 2. To measure live-times properly, it is very important to have a pulse representing exactly the real paralysis of the channel. This pulse can then be used to sample a clock-pulse train which allows live-time measurements. An important feature of this system is the absence of shaping which could lead to a loss of dead-time information. This is the case, when the pulses at the output of preamplifiers are shortened (problem of hidden dead-times). The
Fig. 2. Simplified scheme of the system presented.
extendable dead-time module (patented) used in this system has been developed at LPRI. The new common channel is very simple as there is no associated dead-time module. It becomes a “virtual” channel which is composed of: (1) An ‘‘OR” gate whose inputs are connected to the output of the dead-times of the beta and gamma channels. The output of this ‘‘OR” gate is connected to a shaper which detects the low-to-high transition of the signal and delivers a pulse which can be counted (N ). It can be seen that in the case of a coincidence, only one pulse will be counted (Fig. 1). (2) An ‘‘AND” gate whose inputs are connected to the outputs of the live-time counting of each channel. The sampled clock-pulse at the output of this ‘‘AND” gate can also be counted and gives the live-time information of the common channel as the main clock generator is common to both beta and gamma channels (Fig. 1). In the first version of this system [11], a deadtime was connected, through an “OR” gate, to the output of the beta and gamma discriminators to constitute the common channel. One drawback of
IV. INFORMATION PROCESSING
398
J. Bouchard, B. Chauvenet/Nucl. Instr. and Meth. in Phys. Res. A 422 (1999) 395—399
this design was the necessity to have a third deadtime module with all its surrounding (threshold and dead-time settings, etc.). The dead time generated had to be set longer than the longest of the two other dead-times and the thresholds had to be set carefully as, in this method, it is very important that the common channel processes the same pulses which have been processed by the other channels. In the new version, all these requirements are conceptually fulfilled. The gamma channel can be equipped with a single-channel analyzer or an ADC. At LPRI, we use an ADC, (8K channels) connected to a memory having a capacity of 16K channels. A very simple circuit has been inserted between the ADC and the memory to shift the gamma spectrum from the lower part of the memory (first 8K channels) to the higher part according to the time of detection of the gamma pulse. If the detected gamma pulse is preceded by a beta pulse (the common channel is also triggered by this beta pulse), then this gamma pulse is stored in the upper part of the memory. In the other cases, the gamma pulse is stored in the lower part of the memory. At the end of a measurement, we get two spectra. The sum of these two spectra gives the complete gamma spectrum and the common spectrum which is recorded in the upper part of the memory enables us to derive a coincident spectrum.
4. Activity measurement This coincidence system has been tested successfully for several radionuclides (Sr, Co, Cs, and Yb) presenting different measurement difficulties, including metastable states (Sr and Yb). It is now used routinely for activity measurements. The measurement of Co sources is rather simple as there is no metastable state in the decay scheme and no strong internal conversions in the gamma transitions. The results were in agreement with those obtained with the “IMPECC” coincidence system described in [4,5]. The difficulty of measuring the activity of Sr sources results from a metastable state of 1 ls in its decay scheme. The result was in agreement with the activity given by
Fig. 3. Comparison of activity measurements by different systems.
a 4p ionization chamber already calibrated by an older anti-coincidence measurement [11]. The decay schemes of Cs and Yb are complex [12], and in the case of Yb, a metastable state of 0.66 ls adds to the complexity of measurements. An extrapolation procedure is necessary [13] to get the activity by the 4pb/c coincidence method. In these cases, computer discrimination to select gamma windows was tested and used. The results were compared to those obtained with a well-type crystal (4pc method) and again, there was a good agreement. All these results are presented in Fig. 3. It can be seen in this figure that the uncertainty obtained with the pulse-mixing method is quite good. Type-A uncertainties are equivalent to those obtained with conventional systems. They can be calculated using a simple general formula [9]. The advantage of this method, especially with the new version of its electronics over conventional systems is that there adds almost no type-B uncertainties when in conventional systems type-B uncertainty components must be added for the problems previously mentioned like “time-jitter”.
5. Conclusion This system has proved its ability to measure the activity of radionuclides in a simple way, even those
J. Bouchard, B. Chauvenet/Nucl. Instr. and Meth. in Phys. Res. A 422 (1999) 395—399
having a complex decay-scheme or a metastable state. This confirms the many advantages of this instrument over conventional systems. It takes full advantage of the use of extendable dead times, and the associated live-time measurement. The formulae are general and quite simple compared to those used in the classical coincidence method. The new version of the common channel still increases this simplicity of operation. With this new implementation of the common channel, the third dead-time is not needed anymore. The incorporation in one channel of a single-channel analyzer or even better an ADC (which allows computer discrimination), provides a useful instrument to measure the activity of radionuclides whatever the complexity of their decay schemes.
399
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
P.J. Campion, Nucl. Instr. and Meth. 4 (1959) 232. D. Smith, Nucl. Instr. and Meth. 152 (1978) 505. D. Smith, Appl. Radiat. Isotopes A 38 (1987) 813. J. Bouchard, IEEE Trans. Nucl. Sci. NS-41 (4) (1994) 957. J. Bouchard, B. Chauvenet, R. Vatin, Rapport CEA R-5431, 1988. J. Bryant, Nucl. Instr. and Meth. 13 (1962) 273. A.P. Baerg, K. Munzenmayer, G.C. Bowes, Metrologia 12 (1976) 77. A. Gandy, Int. J. Appl. Radiat. Isotopes 11 (1961) 75. B. Chauvenet, J. Bouchard, Nucl. Instr. and Meth. A 312 (1992) 53. A. Gandy, Int. J. Appl. Radiat. Isotopes 13 (1963) 385. J. Bouchard, B. Chauvenet, IEEE Trans. Nucl. Sci. NS-43 (1996) 1381. N. Coursol, Table Radionucleides, 1992. A.P. Baerg, Metrologia 2 (1966) 23.
IV. INFORMATION PROCESSING