Radioanalytical Methods in Interdisciplinary Research - American

Downloaded by UNIV OF GUELPH LIBRARY on July 26, 2012 | http://pubs.acs.org Publication Date: November 4, 2003 | doi: 10.1021/bk-2004-0868.ch006

Chapter 6

Application of the Triple-to-Double Coincidence Ratio Method at National Institute of Standards and Technology for Absolute Standardization of Radionuclides by Liquid Scintillation Counting 1

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Β. E. Zimmerman , R. Collé , J. T. Cessna , R. Broda , and P. Cassette 3

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Ionizing Radiation Division, Physics Laboratory, National Institute of Standard and Technology, Gaithersburg, M D 20899-8462 Radioisotope Centre P O L A T O M , 05-400 Otwock-Swierk, Poland Labortoire National Henri Becquerel, 91191 Gif sur Yvette Cedex, France 2

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A new liquid scintillation spectrometer that uses the Triple-to-Double Coincidence Ratio (TDCR) method to experimentally determine counting efficiencies has been constructed at the NIST for the primary standardization o f β- emitting nuclides. This technique permits the efficiencies o f the detector to be determined without the need for standard efficiency tracing and is thus considered a quasi-absolute method. This paper describes the new T D C R system at NIST and presents results of tests aimed at assessing the its operating characteristics. The results indicate that the measured activites for previously calibrated solutions of 3H(tritiated water) and Ni agree with certified activity values to within 0.04 % and 0.2 %, respectively. 63

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© 2004 American Chemical Society In Radioanalytical Methods in Interdisciplinary Research; Laue, C., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2003.

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Introduction Because of the relatively high detection efficiency associated with liquid scintillation (LS) counting, it continues to be the preferred method used by most of the national metrology institutes (NMIs) around the world for the primary standardization and subsequent calibration of solutions for activity of radionuclides that undergo P- or a- decay. Acceptance of a particular technique by the metrology community requires that the methodology be accurate and reproducible, be based on a definable theoretical model, and have the ability to completely characterize the uncertainties associated with its application. Currently there are two such L S techniques in use by the various NMIs around the world: the CIEMAT/NIST* efficiency tracing method, and the Triple-toDouble Coincidence Ratio (TDCR) method. The application of the CIEMAT/NIST efficiency tracing method (/), (2) requires that L S cocktails containing a tracing standard, such as H or C , be prepared so as to be chemically identical (in terms of amount of added water, ion and acid concentration, and amount of added imposed quenching agent) to a set of cocktails containing the radionuclide being investigated. The efficiency of the detection system for the radionuclide of interest is calculated from the experimentally determined efficiency for the standard through a calculational program, such as E F F Y (5) or CIENIST 2001 (4) which calculates the counting efficiencies of both radionuclides as a function of a common, free variable. The degree to which the free variable has the same value for the matched cocktails of the standard and the nuclide of interest is monitored by a quenching variable (such as a quench indicating parameter determined by the spectrometer or composition variables such as total cocktail water fraction), through which corrections can be made to account for slight differences in composition that lead to differences in efficiency. The underlying assumption in the method is that the same mechanism for chemical quenching of the nuclide being studied is the same as that for the standard. While this assumption is often upheld, there are cases in which the chemistry of each cocktail is sufficiently different so as to result in incorrectable efficiency changes that result in erroneous values of the solution activity. 3

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The T D C R method (5, 6) avoids this problem by being able to experimentally determine the detection efficiency of the system without the need for an external standard. A s such, it is more of an "absolute" calibration The acronyms C I E M A T (Centro de Investigaciones Energ&icas Medioambientales y Tecnologicas) and NIST (National Institute of Standards and Technology) stand for the names of the national metrology laboratories of Spain and the United States, respectively, who jointly developed this efficiency tracing technique.

In Radioanalytical Methods in Interdisciplinary Research; Laue, C., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2003.

78 technique. B y observing the ratio of double and triple coincidences of photons that are produced in a liquid scintillator through the interaction with ionizing radiation in a three-photomultiplier tube (PMT) detector, the counting efficiency can be calculated from the assumed statistical distribution of photoelectrons and a theoretical quenching model. This paper describes the T D C R detection system currently in use at NIST and presents the first results of experiments aimed at characterizing its performance.


The TDCR Model The theoretical model used to develop the T D C R method has been fully developed elsewhere (J, d), but will be briefly summarized here to aid the reader. The counting efficiency, s , in a particular counting channel (singles, doubles, triples, sum of doubles) for detecting pulses produced in an L S detection system can be given by x

'Jste)P,(£,!fc)dtf o where S(£) is the normalized (3 particle spectrum (with energy, £ ) , and P* (2?, r\ ) is the energy-dependent detection probability for the particular counting channel given as as a function of E and the figure of merit, r\ (in units of photoelectrons per keV). The expressions for Pjc are (assuming a Poisson distribution of photons produced in the scintillator): 0

0

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Double coincidence: 1 -(2P -Po )» Triple coincidence: 1-(3P -3P +P ), and Sum of double coincidences: 1-(3P -2P ), 0

2

0

0

3

0

2

0

3

0

where P = exp(-r| EQ(E)). The quenching factor, Q(2s), is given by 0

0

dx 1

where kB is the Birks value (in cmkeV* , and which is treated as an adjustable parameter) and dE/dx is the energy loss function for the scintillator medium. Defining the ratio of double coincidences to triple coincidences (hereafter referred to as the T D C R ) as a parameter, K, either as a ratio of experimental


79 count rates in a doubles channel and triple coincidence channel or as a ratio of theoretical efficiencies in the doubles and triples coincidence channels, we seek in this application of the T D C R method a value of r) such that the difference between the theoretical K and experimental K is smaller than some arbitrary critical value, A: 0


toil.)

Once a value for r) is obtained, a system of equations is formed to allow for the calculation of the activity: 0

N =N % (B ,B ) N = N (p (s ,e ) N = N (f>Js B ) Ah

hc

ac

0

h

A

0

h

hc

h

0

c

Z9

c

A^r = iVbcpT(B ,6 ,6 ) a

b

c

where N is the counting rate in the coincidence channel between PMTs x and y, N is the counting rate in the triples coincidence channel, N is the activity, cp is the efficiency for the appropriate coincidence channel, and e is the detection efficiency for each individual P M T . The four variables (N , s , e , and e ) can be then solved for analytically using the system of equations. The advantage of this particular approach is that unlike previous versions, it is no longer assumed that the efficiencies of the three phototubes are equal. Instead, the efficiencies of each P M T are directly determined. As will be discussed below, this improvement is very important for the system that has been installed at NIST. xy

T

0

xy

z

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a

b

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The NIST TDCR System The design of the NIST T D C R system is based on the systems currently in use in the laboratories at the Laboratoire National Henri Becquerel (LNHB) and P O L A T O M and is depicted schematically in Figure 1. The three PMTs were modified by reversing the high voltage polarity and applying it on the anode instead of die photocathode (thereby reducing thermal noise), by adding a high voltage input to the first dynode ^permitting higher gain), and by adding an


80 additional high voltage lead to the focusing electrode (allowing variable focusing voltage, thereby changing detection efficiency). The respective high voltage inputs for the anode, first dynode, and focusing electrode are connected at a common point for each of the three P M T s so that the voltage on each input can be simultaneously changed for each P M T using a single supply for each input. A l l of the data acquisition, as well as the high voltage on the focusing electrodes, is controlled through a LabView program that was developed inhouse specifically for this application. The heart of the system is the M A C - 3 unit (7) , which was designed and built at L N H B and which contains all of the coincidence logic and extending deadtime correction circuitry in a single N I M module. The three phototubes are arranged in a sample chamber at an angle of 120° apart and approximately 1 cm from the L S sample vial. A l l surfaces of the inside of the sample chamber have been painted with reflective paint to increase the light collection efficiency. The P M T s and sample chamber are enclosed in a light-tight aluminum box that has an upper chamber to allow for dark storage of counting sources and for manual changing of the sources. One important difference between the design of the instrument in use at L N H B and at NIST and the one at P O L A T O M is the ability of the systems at the former two laboratries to add a gamma-ray detector under the sample chamber that will allow the entire detector system to be used additionally as a p-y coincidence or anticoincidence detector or as a traditional T D C R detector with gamma-ray gating capability. To date, the additions for the gamma-ray channel have been implemented only at LNHB.


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Performance Tests In order to test the behavior of the new T D C R system and determine the optimum operating characteristics, a series of L S samples was prepared with NIST standard solutions of H (as tritiated water) and N i . Nominally 10 m L of OptiPhase HiSafe III L S scintillant (Wallac Oy, Turku, Finland) was added to glass vials, followed by the addition of nominally 100 mg of solution from either NIST Standard Reference Material 4226C ( Ni) (8) or a gravimetric dilution of NIST Standard Reference Material 4927F (tritiated water) (0). Background blanks were prepared by the addition of 100 mg of distilled water to nominally 10 m L of HiSafe III scintillant in glass vials. 3

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Certain commercial equipment, instruments, or materials are identified in this paper to foster understanding. Such identification does not imply recommendation by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.



Figure 1. Schematic of acquistion hardware comprising the TDCR detection system installed at NIST.


82 Since the primary purpose of these experiments was to investigate the performance of the T D C R system and not to perform a full calibration of the solutions, mere was no intentional experimental design. Instead, the intent was to merely count the L S sources several times under various conditions and check the resulting activities to see i f changes to either the apparatus or analysis and acquisition codes were required. Therefore, the vials were counted in the NIST T D C R system at between 4 and 8 focusing voltages for between 1 and 3 minutes at each voltage. Each source was counted at least once, but the first source prepared for both the H and N i (denoted " T - l " and " N - l " , respectively) were counted at least 4 times each. The data were analyzed using the computer codes TDCR-02B and T D C R 02P, which are modified versions of the TDCR-02 code (70). The TDCR-02B program contained only minor changes to the original, but the version T D C R 02P added the ability to calculate the detection efficiencies as a function o f the T D C R using the Polya, or negative binomial, distribution in place of the Poisson distribution. This modification was made because of the fact that the Poisson distribution is not valid for extremely small numbers of photoelectrons, such as the case with low-energy P-emitters. The results of such a counting experiment can be seen in Figure 2. The first striking characteristic of this instrument is the relatively large inequality of the counting efficiencies between the double coincidence channels despite modest attempts to match the PMTs. This inequality is most likely due to small differences remaining in nominal values of the resistors in the PMTs. Despite this, the program TDCR-02B is able, to compensate for this effect. Because of the low energies involved in the decay of both the H and N i , the choice of statistical distribution used to describe the photoelectrons is critical. In most cases, the Poisson distribution is valid because the average number of photoelectrons produced is fairly large. In the case of very low energy decays, however, the average number of photoelectrons can very small, even less than 1. Under these conditions, the Poisson model is no longer valid, requiring another distribution such as the negative binomial, or Polya. For the N i data depicted in Figure 2, the average number o f photoelectrons per P M T is calculated to be between 4 and 8. However, in the H cocktails that were counted, the average number of photoelectrons per P M T is between 1 and 2, precluding the use of a Poisson distribution. Figure 3 shows the experimental efficiencies for the three double coincidence channels as a function of T D C R , along with the theoretical efficiencies calculated using the Poisson distribution and a k B value of 0.012 cm-keV" . It can be clearly seen that the calculated efficiencies are consistently higher than the experimental value. In comparison, Figure 4 shows the same experimental data with the theoretical efficiencies calculated using a Polya distribution and the same value for k B . In this case, much better agreement is obtained due to the fact that a much more appropriate distribution has been used to perform the calculations.


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Figure 2. Experimental and theoretical counting efficiencies, £„ for double coincidence channels AB, BC, and AC as a function of the ratio of triple-photon to double-photon coincidences (TDCR) for NiLS source N-L Each point represents two repeated counts at each focusing voltage (efficiency value), with the standard deviation of each measurement lying within the respective symbol for each point The theoretical efficiencies were calculated with the program TDCR-02B using a Poisson distribution and a kB value of 0.012 cmkeV . 63

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Figure 3. Experimental and theoretical counting efficiencies, e» for double coincidence channels AB, BC, and AC as a function of TDCR for HLS source T-l, which contained an aliquant of a gravimetrically diluted NIST standard solution oftritiated water. Each point represents three repeated counts at each focusing voltage (efficiency value), with the standard deviation of each measurement lying within the respective symbolfor each point. The theoretical efficiencies were calculated with the program TDCR-02B using a Poisson distribution and a kB value of 0.012 cmkeV . 3

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£

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Figure 4. Experimental and theoretical counting efficiencies, for double coincidence channels AB, BC, and AC as a function of TDCR for HLS source T-l, which contained an aliquant of a gravimetrically diluted NIST standard solution of tritiated water. Each point represents three repeated counts at each focusing voltage (efficiency value), with the standard deviation of each measurement lying within the respective symbolfor each point The theoretical efficiencies were calculated with the program TDCR-02P using a Polya distribution and a kB value of 0.012 cmkeV . 3

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The ultimate test of the detection system and analysis software, of course, is the ability to correctly determine the activity of the solutions being measured. Through all of the testing and adjusting of the apparatus, a total of five activity measurements, with repeated measurements on two different sources, were able to be analyzed as independent determinations of the massic activity (in terms of B q g ' ) for the L S cocktails containing the H standard. Likewise, four independent determinations of the massic activity of the N i standard solution were able to be analyzed, with three measurements on one source and a single measurement on a second. The results of the measurements are presented in Table I. For the H using the Polya-fitted results, the average massic activity, C , was 28.10±0.29 kBq-g" , where the uncertainty is an expanded (k=2) uncertainty calculated from the quadratic addition of the standard deviation on the activity determinations for typically 8 points in a counting series having different 1

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86 efficiency values (average of 0.09 %) and the standard deviation on the 5 independent determinations of C with three sources (0.5 %). This result is in excellent agreement with the previously certified value of 28.11 ±0.20 k B q g ' , where the uncertainty is also an expanded (k=2) uncertainty. A

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Table I. TDCR counting results of NIST standard reference material solutions of H and N i . Experimental massic activities C (in units of kBq-g" ) are given, along with the NIST-certified value. All uncertainties are expanded (k=2) uncertainties. 3

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Nuclide 6 3

Exp.

Certified

C /kBq-g' A

A

28.11 ±0.20 48.26 ±0.44

28.10 ±0.29 48.18 ±0.32

Ni

C /kBqg'

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The average value of C for the N i solution was measured to be 48.18 ±0.32 kBqg" , where, as in the case of the H solution, the uncertainty is an expanded (k=2) uncertainty calculated from the quadratic addition of the standard deviation on the activity determinations for typically 8 points in a counting series having different efficiency values (average of 0.11 %) and the standard deviation on the 4 independent determinations of C with two sources (0.33 %). Again, this result is in excellent agreement with the previously certified massic activity value of 48.26±0.44 kBqg" , where the uncertainty is an expanded (k=2) uncertainty. A

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Conclusion A new T D C R spectrometry system, based on the design of systems currently in use at the French and Polish standards laboratories ( L N H B and P O L A T O M , respectively), has been constructed at NIST. Tests of the apparatus indicate that despite attempts to match the PMTs, an asymmetry exists in the efficiencies of the three phototubes that make up the detector, meaning that older T D C R models that assume equality among the PMTs are invalid in this case. Activity determinations on previously calibrated solutions of H (as tritiated water) and N i gave excellent results when compared to the certified values. For the H solution, the agreement was 0.04 % and for the N i , the agreement was 0.2 %, and were within the measurement uncertainties. In the case of the H measurements, the best agreement was obtained when the Polya distribution was used to describe the photoelectrons in place of the Poisson. This is not entirely surprising, since the Poisson distribution is invalid when the number of 3

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87 photoelectrons approaches unity, as was found for most of the measurements of the H sources in these experiments. With the addition of this new spectrometry system, NIST adds another technique to those already available for the standardization of β-emitting radionuclides. The ease of sample preparation and the ability to internally determine the detection efficiency give the T D C R method a distinct advantage over other techniques such as efficiency tracing. Future plans include its application not only to β- emitters, but also electron capture emitters.


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References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Coursey, B. M. et al. Nucl. Iustrum. Methods Phys. Res., Sect. A 1986, 279, 603-610. Zimmerman, B. E.Collé, R. J. Res. Natl. Inst. Stand. Technol. 1997, 102, 455-477. Garcia-Toraño, E.Grau Malonda, A. Comput. Phys. Commun. 1985, 36, 307-312. Ε. Günther, CIENIST 2001, private communication, 2001. Pochwalski, K. et al. Appl. Radiat. Isot. 1988, 39, 165-172. Broda, R; Pochwalski, Κ. Nucl. Instrum. Methods Phys. Res., Sect. A 1992, A312, 85-89. Bouchard, J.; Cassette, P. Appl. Radiat. Isot. 2000, 52, 669-672. National Institute of Standards and Technology Standard Reference Material 4226C, Radioactivity Standard, Nickel-63, 1995. National Institute of Standards and Technology Standard Reference Material 4927F, Radioactivity Standard, Hydrogen-3, 2000. Broda, R. et al. Appl. Radiat. Isot. 2000, 52, 673-678.


Radioanalytical Methods in Interdisciplinary Research - American

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