- Email: [email protected]
The Compton source efficiency tracing method in liquid scintillation counting: A new standardization method using a TDCR counter with a Compton spectrometer
ARTICLE IN PRESS
Applied Radiation and Isotopes 66 (2008) 1026–1032 www.elsevier.com/locate/apradiso
The Compton source efficiency tracing method in liquid scintillation counting: A new standardization method using a TDCR counter with a Compton spectrometer P. Cassette, Phuc Do LNE-Laboratoire National Henri Becquerel, CEA-Saclay, F91191 Gif-sur-Yvette Cedex, France
Abstract We describe a new standardization method in liquid scintillation counting based on the use of a temporary virtual tracer source created inside the scintillator by Compton interaction. The Compton tracer source is measured by the triple coincidence liquid scintillation counter after selection of the Compton events by a gamma-ray detector. The paper describes the principle of the method, the experimental setup and presents the results obtained by this method for the standardization of a 3H solution. These results are compared with those obtained using the classical triple to double coincidence ratio method. Possible application of this new method for international comparisons is addressed. r 2008 Elsevier Ltd. All rights reserved. Keywords: Liquid scintillation; Radionuclide standardization; Compton source efficiency tracing method; TDCR
1. Introduction Activity measurement techniques using a reference source are useful for comparative measurements or to maintain the standardization of radionuclides over a long period of time. An example is the use of an ionization chamber with a radium standard source. For pure-beta or low-energy emitting radionuclides, liquid scintillation counting (LSC) is generally used and this reference source can be provided through efficiency tracing methods. An example is the CIEMAT/NIST method using 3H as a tracer (Grau Malonda and Garcia-Toran˜o, 1982). If reproducible measurements are needed over several decades, for example in the frame of an international reference system, the use of 3 H as a tracer is not the proper choice because its half-life is only 12.32 a and its primary standardization is not trivial. For fundamental reasons related to the physical models used in the CIEMAT/NIST method, a low-energy tracer with a calculable spectrum is needed and up to now no alternative radionuclide with a longer half-life is found. On the other hand, primary standardization methods are Corresponding author.
E-mail address: [email protected] (P. Cassette). 0969-8043/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2008.02.062
preferred to tracer methods if the variability factors of the measurement are under control. In LSC, the primary standardization method is the triple to double coincidence ratio (TDCR) method (Broda et al., 1988). This method requires a correct description of the non-linearity of the scintillator depending on the composition of the LS source, which is not easily reproducible over a long period of time. To solve these problems we developed an LSC coupled to a Compton spectrometer, where a reference source is internally created in the LS cocktail to be measured by means of the Compton effect. This paper presents the concept and realization of this new measurement method and an example of its application to the standardization of 3H.
2. Measurement methods in LSC LSC techniques can be used for radionuclide activity measurement when the calculation of detection efficiency is possible or through comparison with a standard. The main advantages of these techniques are the possibility to measure low-energy-emitting radionuclides, the 4p detection geometry and the easy source preparation. Unlike
ARTICLE IN PRESS P. Cassette, P. Do / Applied Radiation and Isotopes 66 (2008) 1026–1032
most other radioactivity measurement methods, the source itself is a part of the detector, and if a precise measurement is needed (i.e. with a relative standard uncertainty lower than 1%) standards must have a similar composition as that of the sources to measure. If a standard is not available, the detection efficiency can be calculated in some cases. This is performed using a model of the physicochemical and statistical processes involved in light emission, detection and counting. This model is referred in the literature as the free parameter model (Grau Malonda, 1999), which quantifies the intrinsic light yield of the scintillator or, to be more specific, the mean value of photoelectrons created in each photomultiplier tube (PMT) after the absorption of a unit energy in the scintillator. This model can then be applied in two ways: by deducing the free parameter from the measurement of a tracer (the CIEMAT/NIST method) or by calculating this free parameter from the coincidence ratio in a specific three PMTs LS counter (the TDCR method). We describe here another way to apply the free parameter model in LSC with the help of a virtual tracer source created in situ by the Compton interaction. 3. The Compton virtual source concept A source of a radionuclide to measure is prepared following the usual procedure and a virtual tracer source is temporarily created inside it by a specially designed Compton spectrometer included in the LS counter. This virtual source is specifically measured to deduce the intrinsic light yield of the scintillator in these specific conditions (i.e. vial, volume, chemical composition and counter). This intrinsic light yield is expressed in terms of the mean number of photons emitted per keV of electronic energy absorbed by the scintillator. The virtual source is then ‘‘switched off’’, and the intrinsic light yield previously determined is used to calculate the detection efficiency of the radionuclide to measure in these specific conditions. The main advantage of this method is that the tracer is
1027
measured exactly in the same condition as that of the source and also that the detection efficiency is not dependent on the counting rate of this tracer but only on its spectrum, which is measured. The experimental system and elements of the theory used to analyze the experimental data are presented hereafter.
4. Creation of the virtual source The LSC source placed inside the LS counter is irradiated by an external 59.4 keV gamma-ray beam produced by a collimated 241Am source. A gamma-ray detector is placed under the optical chamber of the LS counter with its axis normal to the gamma-ray beam. The gamma-ray detector measures a part of the gamma photons scattered into the LS source by coherent scattering or by incoherent Compton scattering. For the incoherent photons, the spectrum is peaked around right scattering angles, which correspond to an average energy value of 53.2 keV. This Compton spectrum is easily separated from the coherent diffusion spectrum by using a gamma-ray detector with a decent resolution, such as a germanium or CdTe detector. The Compton scattered spectrum is selected by a single-channel analyzer (SCA) and this signal is used to validate the acquisition of photomultiplier detectors in the LS counter. All light pulses created by gamma-ray interactions in the LS source are seen by the LS counter, but only those in coincidence with the SCA signal are recorded. The light pulses emitted by the disintegration of the radionuclide present in the source are thus rejected by the coincidence system. This measurement method is made possible by the small duration of the LS light pulses, and the probability of false coincidences can be calculated from the non-coincident counting rate of the detector. It must be noted that the LS counter dead-time is triggered by any light pulse detected and thus the counting rate of useful events is quite low. The diagram of the system setup is presented in Fig. 1.
Fig. 1. Principle of the TDCR counter with a Compton spectrometer.
ARTICLE IN PRESS P. Cassette, P. Do / Applied Radiation and Isotopes 66 (2008) 1026–1032
1028
The spectrum of the virtual source can be directly deduced from the spectrum of the scattered Compton photons, measured in coincidence with the LS counter, using the energy balance in the Compton interaction. This system can also be used to simulate a monoenergetic electron source in the scintillator, if the SCA is adjusted to select a small-energy range of the gamma-ray detector. This allows screening the response of the LS cocktail to lowenergy electrons, and thus measuring the non-linearity of the scintillator in the low-energy range. 5. Measurement of the scintillator response The response of the scintillator to the virtual electron source can be analyzed from the amplitude spectrum of the PMT pulses. This method, used previously by Pe´ron and Cassette (1996) to analyze the non-linearity of a liquid scintillator, requires the deconvolution of the PMT spectrum on the basis of its eigenfunctions, calculated from the n-convolutions of the single-electron response (SER). This procedure was used for monoenergetic source, but its application to polyenergetic source is not straightforward, as the source spectrum must also be taken into account in the deconvolution process. Here, we took another approach based on the LSC free parameter model and on the TDCR ratio method. This approach is summarized hereafter. When using a triple PMT LS counter with detection thresholds adjusted to allow the detection of single photons in each channel, the detection probability of the light pulse emitted after the absorption of energy in the scintillator for one PMT can be derived from the calculation of the nondetection probability. If the absorbed energy, E, in a LS source produces a mean number m of photons, the detection probability in PMT X is n m X X ¼ 1 exp ; X ¼ A; B; C, (1) 3 where nX is the quantum efficiency of PMT X. The detection probabilities for three PMTs in double and triple coincidences are, respectively: n n X Y XY ¼ 1 exp m 1 exp m , 3 3 XY ¼ ðAB; BC; ACÞ (2) n n A B 1 exp m T ¼ 1 exp m 3 3 n C 1 exp m . (3) 3 And the detection efficiency in the logical sum of double coincidences is X D ¼ ðXY Þ T . (4) XY ¼AB; BC; AC
For a large number of observed events, the frequency ratio of triple to double coincidences converges towards the
probability ratio; thus: n T T Z ¼ m ; ZaX or Y . ¼ 1 exp XY XY 3
(5)
The value of the mean number of emitted photons multiplied by the quantum efficiency of PMT Z can be easily calculated by a logarithmic transformation of Eq. (5): T nZ ¼ 3 ln 1 ; XY ¼ ðAB; BC; ACÞ; ZaX or Y . XY (6) If the energy E varies from one event to another (i.e. if the scintillation pulses are produced by a polyenergetic source), Eqs. (1–5) must be weighted by the spectrum of the source with m(E) becoming a non-linear function of E to account for the ionization quenching phenomenon. Birks (1964) gives a semi-empirical relation between m(E) and E using the electron stopping power dE/dx and a parameter describing the non-linearity, the Birks factor kB: Z E dE , (7) mðEÞ ¼ a 1 þ kB dE=dx 0 where a is the mean number of photons emitted per unit of energy absorbed in the scintillator. This variable a can be considered as the intrinsic light yield of the specific LS source in a specific LS counter. In this case, Eq (5) becomes a system of three rational fractions with three unknowns— the three nX values multiplied by a: R E max Q SðEÞ 1 exp n3X mðEÞ dE 0 T X ¼A; B; C ¼ . (8) R E max Q XY SðEÞ 1 exp n3X m dE 0 XY
The system of Eq. (8) can be solved by minimizing D, which expresses the difference between the experimental coincidence ratios and the triple to double calculated detection efficiency ratios: X T T 2 D¼ . (9) XY XY XY ¼AB; BC; AC This can be done, for example, by multiparametric minimization using the Downhill Simplex algorithm (Press et al., 1992). In summary, if the spectrum of energy transferred to the scintillator is known, the mean number of photons emitted multiplied by the quantum efficiency of each PMT can be calculated from the experimental ratios of triple to double coincidences. These three values entirely characterize the response of the specific LS source used in the specific LS counter, allowing further calculation of the detection efficiency of any radionuclide present in the source, knowing the energy spectrum transferred to the scintillator by this radionuclide. It must be pointed out that this method only works if the system is not saturated, i.e. if the TDCRs are not close to one. This means that a useful virtual source must not cover
ARTICLE IN PRESS P. Cassette, P. Do / Applied Radiation and Isotopes 66 (2008) 1026–1032
a too high energy range. In practice, energy values in the 1–10 keV range are the most useful because they correspond to TDCR values lower than one and are in the region where the scintillator non-linearity is more pronounced.
6. Application to the TDCR method with a measured nonlinearity function In this application, a virtual source is created in the LS source to measure using an external 241Am source filtered to emit only 59.4 keV gamma photons. The SCA in the gamma channel is used to successively select monoenergetic gamma emission in the 59–49 keV range, corresponding to the release of Compton electrons of energies between 1 and 10 keV in the scintillator. Measurement of the source is done for each electron energy value with enough counting statistics. Then the intrinsic response of the scintillator is calculated, for each electron energy value, from the experimental TDCR values. These results give not only the relative quantum efficiency of each PMT but also the mean value of photons emitted as a function of the energy transferred. These latter data can be adjusted to any convenient function without physical meaning (for example a rational equation), and this function is then used in the replacement of Eq. (5) in the traditional TDCR method. The data set can also be adjusted to Eq. (5), giving the best estimate of the parameters kB and a which fully characterizes this specific LS source in the specific LS counter. In summary, this procedure allows the use of the TDCR method without the need to choose or adjust the kB parameter, which is really the weak point of the method especially for the measurement of low-energy radionuclides.
7. Application to efficiency tracing with a Compton virtual source In this application, a virtual source is also created in the LS source to measure using an external 241Am source filtered to emit only 59.4 keV gamma photons. The SCA in the gamma channel is adjusted to select an energy range corresponding to single Compton interactions in the LS cocktail. The spectrum is then recorded in the gamma channel in coincidence with the signal of the logical sum of double coincidences of the LS counter, and the Compton electron energy spectrum is calculated from the energy balance of the Compton effect. Then, the system of Eq. (8) is solved to get the intrinsic response of each PMT for this specific source. This step is the characterization of the experimental measuring conditions for this specific source. The external 241Am source is then removed and the source is measured by the normal triple coincidence LS counter. The detection efficiency in the logical sum of double coincidence is then calculated using Eq. (4),
1029
weighted by the energy spectrum of the source, to measure ! X ðXY Þ T . (10) D ¼ SðEÞ XY ¼AB;BC;AC
The terms eXY and eT are calculated using Eqs. (2) and (3) where m(E) is calculated from Eq. (7) by using the intrinsic response of each PMT obtained during the previous step. This method, called the Compton source efficiency tracing method (CSET), is in principle similar to the CIEMAT/NIST method where the detection efficiency of a radionuclide to measure is deduced from the intrinsic response of a LS source previously determined by the measurement of a standard tritium source. Nevertheless, the main advantages of the CSET method over the CIEMAT/NIST method are:
The characterization of the measurement system (i.e. specific source in the specific counter) is really made with the source to measure and not with a tracer source. The detection efficiency is derived from the experimental spectrum of the virtual tracer and not from its counting rate. Any change in the activity or geometry of the external gamma-ray source producing the virtual source has no effect on the result. There is no need for a radioactive standard and so no contribution of the uncertainty of this standard to the final uncertainty budget of the measurement. The detection efficiency can also be calculated using the classical TDCR method from the same experimental data set. This gives a possibility of control and coherence check of the results.
8. Experimental system The experimental system was realized by the association of a germanium detector with the LNHB RCTD1 LS counter. This counter, already described (Cassette and Vatin, 1992), uses standard 20 ml LS vials and 3 Burle 8850 PMTs placed 1201 apart in an optical chamber. A thin aluminium window is placed at the bottom of the chamber in front of the beryllium window of the germanium detector. The distance between the bottom of the vial and the germanium detector window is 2 cm. The germanium detector is shielded with a 2-mm-thick lead foil. A collimator, composed of a lead cylinder drilled with a central 0.8 mm diameter hole was inserted inside the optical chamber, between the two PMTs and in the plane formed by their longitudinal axis as shown in Fig. 2. A sealed 1.9 MBq 241Am source, placed in a lead cylinder, is adapted on this lead collimator. The low-energy part of the spectrum of 241Am is filtered by an iron foil. The shielding of the source and the collimator are sufficient to reduce the direct irradiation of the germanium detector by the incident 59.54 keV photon beam to a negligible level. The germanium detector signal is amplified by a spectroscopy
ARTICLE IN PRESS 1030
P. Cassette, P. Do / Applied Radiation and Isotopes 66 (2008) 1026–1032
amplifier (Intertechnique 7244) and the amplified signal is connected to a multichannel analyzer (MCA) and in parallel to a SCA (Tennelec TC450). The MCA signal can be recorded in coincidence with the LS double coincidence signal issued from the MAC3 unit (Bouchard
and Cassette, 2000), and properly delayed. The MAC3 unit was modified to delay and add a veto input to the output latches validation signal, as shown in Fig. 3. This veto is connected to the output of the SCA, and delays are adjusted to allow the validation of the MAC3 output signals only if the SCA signal is present during a 100 ns resolving time coincidence window. 9. Test of the method The method was tested by the measurement of a 3H LS source prepared in Ultima Golds liquid scintillator (PerkinElmer). The measurement using the virtual tracer technique was compared with the results given by the traditional TDCR measurement method using the same TDCR counter (LNHB RCTD1). The detection efficiencies calculated with the TDCR method and with the Compton tracer method are presented in Table. 1 as a function of the kB value used for the calculation of the Birks formula (Eq. (7)). The evolution of detection efficiency versus the kB value is plotted in Fig. 4 for both calculation models. The following conclusions can be drawn from Table 1 and Fig. 4:
Fig. 2. Optical chamber with a lead collimator for the external source.
241
Am
As expected, the detection efficiency of 3H derived from the TDCR method is very dependent on the kB value. The detection efficiency decreases by a factor of 4.7% if the kB value is changed from 0.007 to 0.015 cm/MeV.
Fig. 3. Diagram of the MAC3 unit modified for an external veto signal.
ARTICLE IN PRESS P. Cassette, P. Do / Applied Radiation and Isotopes 66 (2008) 1026–1032
1031
Table 1 Measurement of a 3H source prepared with Ultima Gold LS cocktail using the TDCR method and the Compton tracer method kB (cm/MeV)
0.007 0.008 0.009 0.01 0.011 0.012 0.013 0.014 0.015
TDCR method
Compton tracer method
Relative difference
TDCR
eD
eT
TDCR
eD
eT
TDCR
eD
eT
0.4925 0.4926 0.4926 0.4925 0.4925 0.4925 0.4925 0.4926 0.4926
0.5551 0.551 0.5471 0.5434 0.5401 0.537 0.5343 0.5317 0.5292
0.2734 0.2714 0.2695 0.2676 0.266 0.2645 0.2631 0.2619 0.2607
0.4849 0.4867 0.4883 0.4897 0.4912 0.4924 0.4936 0.4947 0.4959
0.5475 0.545 0.5428 0.5407 0.5389 0.5371 0.5355 0.5339 0.5326
0.2655 0.2652 0.265 0.2648 0.2647 0.2644 0.2643 0.2641 0.2641
1.54% 1.20% 0.87% 0.57% 0.26% 0.02% 0.22% 0.43% 0.67%
1.37% 1.09% 0.79% 0.50% 0.22% 0.02% 0.22% 0.41% 0.64%
2.89% 2.28% 1.67% 1.05% 0.49% 0.04% 0.46% 0.84% 1.30%
This is also why, with the CIEMAT/NIST method, the kB value has a dramatic influence on the calculation of the detection efficiency of pure electron capture radionuclides, like 55Fe, because in this case the energy released by the electron capture radionuclide is almost monoenergetic (about 6 keV for 55Fe), and the cancellation previously mentioned cannot happen. The dependence of the calculated detection efficiency using the CSET method can be solved by different means:
Fig. 4. Variation of detection efficiency in the logical sum of double coincidences of a 3H source for the TDCR and Compton tracer methods.
The dependence of the detection efficiency versus the kB value is somewhat lower for the detection efficiency calculated by the CSET method. Using the previous kB range, the detection efficiency variation is 2.7%. This can be observed in the slopes of the curves in Fig. 4. As the two curves of Fig. 4 cross, there is a kB value for which the detection efficiencies calculated from both the models are equal. This corresponds to a kB value of 0.012 cm/MeV, which is a value close to the one previously determined for Ultima Gold sources in our RCTD1 LS counter.
The lower dependence of the CSET method on the kB value can be explained by the fact that the Birks equation is calculated twice: once for the tracer and the second time for the radionuclide to measure. This causes cancellation of the inaccuracies of the model. This point was already observed in the CIEMAT/NIST method, where the influence of the kB value in the measurement of pure beta radionuclides was somewhat lower than it was in the TDCR method.
By comparison with the TDCR result, choosing the kB value for which the efficiency versus kB curves cross, as shown in Fig. 4. By variation of the detection efficiency and the adjustment of the kB value to get the same activity measurement. This is the traditional procedure used in the TDCR method. By measuring in situ the response of the scintillator as mentioned in Section 5 and using a fit of the experimental results.
10. Proposition to use the CSET method for international comparisons The need for an international comparison system similar to the Syste`me International de Re´fe´rence (SIR), which can be used for the comparison of sources of pure beta or electron capture radionuclides, has been identified for a long time and an ad hoc working group of CCRI(II) was formed for this purpose. It seems that there is a consensus to use the LSC techniques for this purpose but up to now no satisfactory method has been defined, mostly because the two traditional LSC standardization methods present some drawbacks and there is a need to use a reference scintillator cocktail. We think that the CSET method could be attractive for this purpose as it does not require any reference scintillator because the intrinsic characteristics of each LS sources can be measured in situ. One could object that the main drawback of the Compton tracer method is the necessity to use a specific LS counter with three PMTs and a gamma-ray detector.
ARTICLE IN PRESS 1032
P. Cassette, P. Do / Applied Radiation and Isotopes 66 (2008) 1026–1032
We proved in this paper that the construction of such a detector is possible after minor modification of a TDCR counter. Moreover, the use of a locally developed LS counter is, in our opinion, the best guarantee to have an instrument under full control. This is not the case for commercial LS counters, which are mostly designed for low-level measurement applications and which are essentially black boxes for the user. 11. Conclusion We showed that it is possible to temporarily add a controlled virtual electron source in a liquid scintillator using an external 241Am gamma source and a gamma-ray detector operating in coincidence with a triple PMT LS counter. This electron source can be used not only to study in situ the non-linear response of a liquid scintillator in the 1–10 keV energy range, but also as a tracer source for efficiency tracing activity measurements. This latter method, called CSET method, has been successfully tested in the measurement of a 3H source in comparison with the traditional TDCR method. Association of these two methods gives a simple way to optimize the Birks coefficient, kB, used for the calculation of detection efficiency in LSC by the free parameter method. As the CSET method includes in situ characterization of the LS
source to measure, we think that it could be used (without requiring a reference scintillator cocktail) in an international reference system for beta emitters or for maintaining the standardization of a pure beta radionuclide.
References Birks, J.B., 1964. The Theory and Practice of Scintillation Counting. Pergamon Press, Oxford, p. 187. Bouchard, J., Cassette, P., 2000. MAC3: an electronic module for the processing of pulses delivered by a three photomultiplier liquid scintillation counting system. Appl. Radiat. Isot. 52, 669–672. Broda, R., Pochwalski, K., Radoszewski, T., 1988. Calculation of liquidscintillation detector efficiency. Appl. Radiat. Isot. 39 (2), 159–164. Cassette, P., Vatin, R., 1992. Experimental evaluation of TDCR models for the 3PM liquid scintillation counter. Nucl. Instrum. Methods A 312, 95–99. Grau Malonda, A., 1999. Free Parameter Models in Liquid Scintillation Counting. CIEMAT, Madrid. Grau Malonda, A., Garcia-Toran˜o, E., 1982. Evaluation of counting efficiency in liquid scintillation counting of pure b-ray emitters. Int. J. Appl. Radiat. Isot. 33, 249–253. Pe´ron, M.N., Cassette, P., 1996. Study of liquid scintillator response to low-energy electrons with a Compton coincidence experiment. Nucl. Instrum. Methods Phys. Res. A 369, 344–347. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., 1992. Numerical Recipes in Fortran 77, second ed. Cambridge University Press, London, p. 402.
Applied Radiation and Isotopes 66 (2008) 1026–1032 www.elsevier.com/locate/apradiso
The Compton source efficiency tracing method in liquid scintillation counting: A new standardization method using a TDCR counter with a Compton spectrometer P. Cassette, Phuc Do LNE-Laboratoire National Henri Becquerel, CEA-Saclay, F91191 Gif-sur-Yvette Cedex, France
Abstract We describe a new standardization method in liquid scintillation counting based on the use of a temporary virtual tracer source created inside the scintillator by Compton interaction. The Compton tracer source is measured by the triple coincidence liquid scintillation counter after selection of the Compton events by a gamma-ray detector. The paper describes the principle of the method, the experimental setup and presents the results obtained by this method for the standardization of a 3H solution. These results are compared with those obtained using the classical triple to double coincidence ratio method. Possible application of this new method for international comparisons is addressed. r 2008 Elsevier Ltd. All rights reserved. Keywords: Liquid scintillation; Radionuclide standardization; Compton source efficiency tracing method; TDCR
1. Introduction Activity measurement techniques using a reference source are useful for comparative measurements or to maintain the standardization of radionuclides over a long period of time. An example is the use of an ionization chamber with a radium standard source. For pure-beta or low-energy emitting radionuclides, liquid scintillation counting (LSC) is generally used and this reference source can be provided through efficiency tracing methods. An example is the CIEMAT/NIST method using 3H as a tracer (Grau Malonda and Garcia-Toran˜o, 1982). If reproducible measurements are needed over several decades, for example in the frame of an international reference system, the use of 3 H as a tracer is not the proper choice because its half-life is only 12.32 a and its primary standardization is not trivial. For fundamental reasons related to the physical models used in the CIEMAT/NIST method, a low-energy tracer with a calculable spectrum is needed and up to now no alternative radionuclide with a longer half-life is found. On the other hand, primary standardization methods are Corresponding author.
E-mail address: [email protected] (P. Cassette). 0969-8043/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2008.02.062
preferred to tracer methods if the variability factors of the measurement are under control. In LSC, the primary standardization method is the triple to double coincidence ratio (TDCR) method (Broda et al., 1988). This method requires a correct description of the non-linearity of the scintillator depending on the composition of the LS source, which is not easily reproducible over a long period of time. To solve these problems we developed an LSC coupled to a Compton spectrometer, where a reference source is internally created in the LS cocktail to be measured by means of the Compton effect. This paper presents the concept and realization of this new measurement method and an example of its application to the standardization of 3H.
2. Measurement methods in LSC LSC techniques can be used for radionuclide activity measurement when the calculation of detection efficiency is possible or through comparison with a standard. The main advantages of these techniques are the possibility to measure low-energy-emitting radionuclides, the 4p detection geometry and the easy source preparation. Unlike
ARTICLE IN PRESS P. Cassette, P. Do / Applied Radiation and Isotopes 66 (2008) 1026–1032
most other radioactivity measurement methods, the source itself is a part of the detector, and if a precise measurement is needed (i.e. with a relative standard uncertainty lower than 1%) standards must have a similar composition as that of the sources to measure. If a standard is not available, the detection efficiency can be calculated in some cases. This is performed using a model of the physicochemical and statistical processes involved in light emission, detection and counting. This model is referred in the literature as the free parameter model (Grau Malonda, 1999), which quantifies the intrinsic light yield of the scintillator or, to be more specific, the mean value of photoelectrons created in each photomultiplier tube (PMT) after the absorption of a unit energy in the scintillator. This model can then be applied in two ways: by deducing the free parameter from the measurement of a tracer (the CIEMAT/NIST method) or by calculating this free parameter from the coincidence ratio in a specific three PMTs LS counter (the TDCR method). We describe here another way to apply the free parameter model in LSC with the help of a virtual tracer source created in situ by the Compton interaction. 3. The Compton virtual source concept A source of a radionuclide to measure is prepared following the usual procedure and a virtual tracer source is temporarily created inside it by a specially designed Compton spectrometer included in the LS counter. This virtual source is specifically measured to deduce the intrinsic light yield of the scintillator in these specific conditions (i.e. vial, volume, chemical composition and counter). This intrinsic light yield is expressed in terms of the mean number of photons emitted per keV of electronic energy absorbed by the scintillator. The virtual source is then ‘‘switched off’’, and the intrinsic light yield previously determined is used to calculate the detection efficiency of the radionuclide to measure in these specific conditions. The main advantage of this method is that the tracer is
1027
measured exactly in the same condition as that of the source and also that the detection efficiency is not dependent on the counting rate of this tracer but only on its spectrum, which is measured. The experimental system and elements of the theory used to analyze the experimental data are presented hereafter.
4. Creation of the virtual source The LSC source placed inside the LS counter is irradiated by an external 59.4 keV gamma-ray beam produced by a collimated 241Am source. A gamma-ray detector is placed under the optical chamber of the LS counter with its axis normal to the gamma-ray beam. The gamma-ray detector measures a part of the gamma photons scattered into the LS source by coherent scattering or by incoherent Compton scattering. For the incoherent photons, the spectrum is peaked around right scattering angles, which correspond to an average energy value of 53.2 keV. This Compton spectrum is easily separated from the coherent diffusion spectrum by using a gamma-ray detector with a decent resolution, such as a germanium or CdTe detector. The Compton scattered spectrum is selected by a single-channel analyzer (SCA) and this signal is used to validate the acquisition of photomultiplier detectors in the LS counter. All light pulses created by gamma-ray interactions in the LS source are seen by the LS counter, but only those in coincidence with the SCA signal are recorded. The light pulses emitted by the disintegration of the radionuclide present in the source are thus rejected by the coincidence system. This measurement method is made possible by the small duration of the LS light pulses, and the probability of false coincidences can be calculated from the non-coincident counting rate of the detector. It must be noted that the LS counter dead-time is triggered by any light pulse detected and thus the counting rate of useful events is quite low. The diagram of the system setup is presented in Fig. 1.
Fig. 1. Principle of the TDCR counter with a Compton spectrometer.
ARTICLE IN PRESS P. Cassette, P. Do / Applied Radiation and Isotopes 66 (2008) 1026–1032
1028
The spectrum of the virtual source can be directly deduced from the spectrum of the scattered Compton photons, measured in coincidence with the LS counter, using the energy balance in the Compton interaction. This system can also be used to simulate a monoenergetic electron source in the scintillator, if the SCA is adjusted to select a small-energy range of the gamma-ray detector. This allows screening the response of the LS cocktail to lowenergy electrons, and thus measuring the non-linearity of the scintillator in the low-energy range. 5. Measurement of the scintillator response The response of the scintillator to the virtual electron source can be analyzed from the amplitude spectrum of the PMT pulses. This method, used previously by Pe´ron and Cassette (1996) to analyze the non-linearity of a liquid scintillator, requires the deconvolution of the PMT spectrum on the basis of its eigenfunctions, calculated from the n-convolutions of the single-electron response (SER). This procedure was used for monoenergetic source, but its application to polyenergetic source is not straightforward, as the source spectrum must also be taken into account in the deconvolution process. Here, we took another approach based on the LSC free parameter model and on the TDCR ratio method. This approach is summarized hereafter. When using a triple PMT LS counter with detection thresholds adjusted to allow the detection of single photons in each channel, the detection probability of the light pulse emitted after the absorption of energy in the scintillator for one PMT can be derived from the calculation of the nondetection probability. If the absorbed energy, E, in a LS source produces a mean number m of photons, the detection probability in PMT X is n m X X ¼ 1 exp ; X ¼ A; B; C, (1) 3 where nX is the quantum efficiency of PMT X. The detection probabilities for three PMTs in double and triple coincidences are, respectively: n n X Y XY ¼ 1 exp m 1 exp m , 3 3 XY ¼ ðAB; BC; ACÞ (2) n n A B 1 exp m T ¼ 1 exp m 3 3 n C 1 exp m . (3) 3 And the detection efficiency in the logical sum of double coincidences is X D ¼ ðXY Þ T . (4) XY ¼AB; BC; AC
For a large number of observed events, the frequency ratio of triple to double coincidences converges towards the
probability ratio; thus: n T T Z ¼ m ; ZaX or Y . ¼ 1 exp XY XY 3
(5)
The value of the mean number of emitted photons multiplied by the quantum efficiency of PMT Z can be easily calculated by a logarithmic transformation of Eq. (5): T nZ ¼ 3 ln 1 ; XY ¼ ðAB; BC; ACÞ; ZaX or Y . XY (6) If the energy E varies from one event to another (i.e. if the scintillation pulses are produced by a polyenergetic source), Eqs. (1–5) must be weighted by the spectrum of the source with m(E) becoming a non-linear function of E to account for the ionization quenching phenomenon. Birks (1964) gives a semi-empirical relation between m(E) and E using the electron stopping power dE/dx and a parameter describing the non-linearity, the Birks factor kB: Z E dE , (7) mðEÞ ¼ a 1 þ kB dE=dx 0 where a is the mean number of photons emitted per unit of energy absorbed in the scintillator. This variable a can be considered as the intrinsic light yield of the specific LS source in a specific LS counter. In this case, Eq (5) becomes a system of three rational fractions with three unknowns— the three nX values multiplied by a: R E max Q SðEÞ 1 exp n3X mðEÞ dE 0 T X ¼A; B; C ¼ . (8) R E max Q XY SðEÞ 1 exp n3X m dE 0 XY
The system of Eq. (8) can be solved by minimizing D, which expresses the difference between the experimental coincidence ratios and the triple to double calculated detection efficiency ratios: X T T 2 D¼ . (9) XY XY XY ¼AB; BC; AC This can be done, for example, by multiparametric minimization using the Downhill Simplex algorithm (Press et al., 1992). In summary, if the spectrum of energy transferred to the scintillator is known, the mean number of photons emitted multiplied by the quantum efficiency of each PMT can be calculated from the experimental ratios of triple to double coincidences. These three values entirely characterize the response of the specific LS source used in the specific LS counter, allowing further calculation of the detection efficiency of any radionuclide present in the source, knowing the energy spectrum transferred to the scintillator by this radionuclide. It must be pointed out that this method only works if the system is not saturated, i.e. if the TDCRs are not close to one. This means that a useful virtual source must not cover
ARTICLE IN PRESS P. Cassette, P. Do / Applied Radiation and Isotopes 66 (2008) 1026–1032
a too high energy range. In practice, energy values in the 1–10 keV range are the most useful because they correspond to TDCR values lower than one and are in the region where the scintillator non-linearity is more pronounced.
6. Application to the TDCR method with a measured nonlinearity function In this application, a virtual source is created in the LS source to measure using an external 241Am source filtered to emit only 59.4 keV gamma photons. The SCA in the gamma channel is used to successively select monoenergetic gamma emission in the 59–49 keV range, corresponding to the release of Compton electrons of energies between 1 and 10 keV in the scintillator. Measurement of the source is done for each electron energy value with enough counting statistics. Then the intrinsic response of the scintillator is calculated, for each electron energy value, from the experimental TDCR values. These results give not only the relative quantum efficiency of each PMT but also the mean value of photons emitted as a function of the energy transferred. These latter data can be adjusted to any convenient function without physical meaning (for example a rational equation), and this function is then used in the replacement of Eq. (5) in the traditional TDCR method. The data set can also be adjusted to Eq. (5), giving the best estimate of the parameters kB and a which fully characterizes this specific LS source in the specific LS counter. In summary, this procedure allows the use of the TDCR method without the need to choose or adjust the kB parameter, which is really the weak point of the method especially for the measurement of low-energy radionuclides.
7. Application to efficiency tracing with a Compton virtual source In this application, a virtual source is also created in the LS source to measure using an external 241Am source filtered to emit only 59.4 keV gamma photons. The SCA in the gamma channel is adjusted to select an energy range corresponding to single Compton interactions in the LS cocktail. The spectrum is then recorded in the gamma channel in coincidence with the signal of the logical sum of double coincidences of the LS counter, and the Compton electron energy spectrum is calculated from the energy balance of the Compton effect. Then, the system of Eq. (8) is solved to get the intrinsic response of each PMT for this specific source. This step is the characterization of the experimental measuring conditions for this specific source. The external 241Am source is then removed and the source is measured by the normal triple coincidence LS counter. The detection efficiency in the logical sum of double coincidence is then calculated using Eq. (4),
1029
weighted by the energy spectrum of the source, to measure ! X ðXY Þ T . (10) D ¼ SðEÞ XY ¼AB;BC;AC
The terms eXY and eT are calculated using Eqs. (2) and (3) where m(E) is calculated from Eq. (7) by using the intrinsic response of each PMT obtained during the previous step. This method, called the Compton source efficiency tracing method (CSET), is in principle similar to the CIEMAT/NIST method where the detection efficiency of a radionuclide to measure is deduced from the intrinsic response of a LS source previously determined by the measurement of a standard tritium source. Nevertheless, the main advantages of the CSET method over the CIEMAT/NIST method are:
The characterization of the measurement system (i.e. specific source in the specific counter) is really made with the source to measure and not with a tracer source. The detection efficiency is derived from the experimental spectrum of the virtual tracer and not from its counting rate. Any change in the activity or geometry of the external gamma-ray source producing the virtual source has no effect on the result. There is no need for a radioactive standard and so no contribution of the uncertainty of this standard to the final uncertainty budget of the measurement. The detection efficiency can also be calculated using the classical TDCR method from the same experimental data set. This gives a possibility of control and coherence check of the results.
8. Experimental system The experimental system was realized by the association of a germanium detector with the LNHB RCTD1 LS counter. This counter, already described (Cassette and Vatin, 1992), uses standard 20 ml LS vials and 3 Burle 8850 PMTs placed 1201 apart in an optical chamber. A thin aluminium window is placed at the bottom of the chamber in front of the beryllium window of the germanium detector. The distance between the bottom of the vial and the germanium detector window is 2 cm. The germanium detector is shielded with a 2-mm-thick lead foil. A collimator, composed of a lead cylinder drilled with a central 0.8 mm diameter hole was inserted inside the optical chamber, between the two PMTs and in the plane formed by their longitudinal axis as shown in Fig. 2. A sealed 1.9 MBq 241Am source, placed in a lead cylinder, is adapted on this lead collimator. The low-energy part of the spectrum of 241Am is filtered by an iron foil. The shielding of the source and the collimator are sufficient to reduce the direct irradiation of the germanium detector by the incident 59.54 keV photon beam to a negligible level. The germanium detector signal is amplified by a spectroscopy
ARTICLE IN PRESS 1030
P. Cassette, P. Do / Applied Radiation and Isotopes 66 (2008) 1026–1032
amplifier (Intertechnique 7244) and the amplified signal is connected to a multichannel analyzer (MCA) and in parallel to a SCA (Tennelec TC450). The MCA signal can be recorded in coincidence with the LS double coincidence signal issued from the MAC3 unit (Bouchard
and Cassette, 2000), and properly delayed. The MAC3 unit was modified to delay and add a veto input to the output latches validation signal, as shown in Fig. 3. This veto is connected to the output of the SCA, and delays are adjusted to allow the validation of the MAC3 output signals only if the SCA signal is present during a 100 ns resolving time coincidence window. 9. Test of the method The method was tested by the measurement of a 3H LS source prepared in Ultima Golds liquid scintillator (PerkinElmer). The measurement using the virtual tracer technique was compared with the results given by the traditional TDCR measurement method using the same TDCR counter (LNHB RCTD1). The detection efficiencies calculated with the TDCR method and with the Compton tracer method are presented in Table. 1 as a function of the kB value used for the calculation of the Birks formula (Eq. (7)). The evolution of detection efficiency versus the kB value is plotted in Fig. 4 for both calculation models. The following conclusions can be drawn from Table 1 and Fig. 4:
Fig. 2. Optical chamber with a lead collimator for the external source.
241
Am
As expected, the detection efficiency of 3H derived from the TDCR method is very dependent on the kB value. The detection efficiency decreases by a factor of 4.7% if the kB value is changed from 0.007 to 0.015 cm/MeV.
Fig. 3. Diagram of the MAC3 unit modified for an external veto signal.
ARTICLE IN PRESS P. Cassette, P. Do / Applied Radiation and Isotopes 66 (2008) 1026–1032
1031
Table 1 Measurement of a 3H source prepared with Ultima Gold LS cocktail using the TDCR method and the Compton tracer method kB (cm/MeV)
0.007 0.008 0.009 0.01 0.011 0.012 0.013 0.014 0.015
TDCR method
Compton tracer method
Relative difference
TDCR
eD
eT
TDCR
eD
eT
TDCR
eD
eT
0.4925 0.4926 0.4926 0.4925 0.4925 0.4925 0.4925 0.4926 0.4926
0.5551 0.551 0.5471 0.5434 0.5401 0.537 0.5343 0.5317 0.5292
0.2734 0.2714 0.2695 0.2676 0.266 0.2645 0.2631 0.2619 0.2607
0.4849 0.4867 0.4883 0.4897 0.4912 0.4924 0.4936 0.4947 0.4959
0.5475 0.545 0.5428 0.5407 0.5389 0.5371 0.5355 0.5339 0.5326
0.2655 0.2652 0.265 0.2648 0.2647 0.2644 0.2643 0.2641 0.2641
1.54% 1.20% 0.87% 0.57% 0.26% 0.02% 0.22% 0.43% 0.67%
1.37% 1.09% 0.79% 0.50% 0.22% 0.02% 0.22% 0.41% 0.64%
2.89% 2.28% 1.67% 1.05% 0.49% 0.04% 0.46% 0.84% 1.30%
This is also why, with the CIEMAT/NIST method, the kB value has a dramatic influence on the calculation of the detection efficiency of pure electron capture radionuclides, like 55Fe, because in this case the energy released by the electron capture radionuclide is almost monoenergetic (about 6 keV for 55Fe), and the cancellation previously mentioned cannot happen. The dependence of the calculated detection efficiency using the CSET method can be solved by different means:
Fig. 4. Variation of detection efficiency in the logical sum of double coincidences of a 3H source for the TDCR and Compton tracer methods.
The dependence of the detection efficiency versus the kB value is somewhat lower for the detection efficiency calculated by the CSET method. Using the previous kB range, the detection efficiency variation is 2.7%. This can be observed in the slopes of the curves in Fig. 4. As the two curves of Fig. 4 cross, there is a kB value for which the detection efficiencies calculated from both the models are equal. This corresponds to a kB value of 0.012 cm/MeV, which is a value close to the one previously determined for Ultima Gold sources in our RCTD1 LS counter.
The lower dependence of the CSET method on the kB value can be explained by the fact that the Birks equation is calculated twice: once for the tracer and the second time for the radionuclide to measure. This causes cancellation of the inaccuracies of the model. This point was already observed in the CIEMAT/NIST method, where the influence of the kB value in the measurement of pure beta radionuclides was somewhat lower than it was in the TDCR method.
By comparison with the TDCR result, choosing the kB value for which the efficiency versus kB curves cross, as shown in Fig. 4. By variation of the detection efficiency and the adjustment of the kB value to get the same activity measurement. This is the traditional procedure used in the TDCR method. By measuring in situ the response of the scintillator as mentioned in Section 5 and using a fit of the experimental results.
10. Proposition to use the CSET method for international comparisons The need for an international comparison system similar to the Syste`me International de Re´fe´rence (SIR), which can be used for the comparison of sources of pure beta or electron capture radionuclides, has been identified for a long time and an ad hoc working group of CCRI(II) was formed for this purpose. It seems that there is a consensus to use the LSC techniques for this purpose but up to now no satisfactory method has been defined, mostly because the two traditional LSC standardization methods present some drawbacks and there is a need to use a reference scintillator cocktail. We think that the CSET method could be attractive for this purpose as it does not require any reference scintillator because the intrinsic characteristics of each LS sources can be measured in situ. One could object that the main drawback of the Compton tracer method is the necessity to use a specific LS counter with three PMTs and a gamma-ray detector.
ARTICLE IN PRESS 1032
P. Cassette, P. Do / Applied Radiation and Isotopes 66 (2008) 1026–1032
We proved in this paper that the construction of such a detector is possible after minor modification of a TDCR counter. Moreover, the use of a locally developed LS counter is, in our opinion, the best guarantee to have an instrument under full control. This is not the case for commercial LS counters, which are mostly designed for low-level measurement applications and which are essentially black boxes for the user. 11. Conclusion We showed that it is possible to temporarily add a controlled virtual electron source in a liquid scintillator using an external 241Am gamma source and a gamma-ray detector operating in coincidence with a triple PMT LS counter. This electron source can be used not only to study in situ the non-linear response of a liquid scintillator in the 1–10 keV energy range, but also as a tracer source for efficiency tracing activity measurements. This latter method, called CSET method, has been successfully tested in the measurement of a 3H source in comparison with the traditional TDCR method. Association of these two methods gives a simple way to optimize the Birks coefficient, kB, used for the calculation of detection efficiency in LSC by the free parameter method. As the CSET method includes in situ characterization of the LS
source to measure, we think that it could be used (without requiring a reference scintillator cocktail) in an international reference system for beta emitters or for maintaining the standardization of a pure beta radionuclide.
References Birks, J.B., 1964. The Theory and Practice of Scintillation Counting. Pergamon Press, Oxford, p. 187. Bouchard, J., Cassette, P., 2000. MAC3: an electronic module for the processing of pulses delivered by a three photomultiplier liquid scintillation counting system. Appl. Radiat. Isot. 52, 669–672. Broda, R., Pochwalski, K., Radoszewski, T., 1988. Calculation of liquidscintillation detector efficiency. Appl. Radiat. Isot. 39 (2), 159–164. Cassette, P., Vatin, R., 1992. Experimental evaluation of TDCR models for the 3PM liquid scintillation counter. Nucl. Instrum. Methods A 312, 95–99. Grau Malonda, A., 1999. Free Parameter Models in Liquid Scintillation Counting. CIEMAT, Madrid. Grau Malonda, A., Garcia-Toran˜o, E., 1982. Evaluation of counting efficiency in liquid scintillation counting of pure b-ray emitters. Int. J. Appl. Radiat. Isot. 33, 249–253. Pe´ron, M.N., Cassette, P., 1996. Study of liquid scintillator response to low-energy electrons with a Compton coincidence experiment. Nucl. Instrum. Methods Phys. Res. A 369, 344–347. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., 1992. Numerical Recipes in Fortran 77, second ed. Cambridge University Press, London, p. 402.