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Activity measurement of phosphorus-32 in the presence of pure beta-emitting impurities The CSIR Research and Innovation Conference National Metrology Laboratory Dr Bruce Simpson and Freda van Wyngaardt R&D Metrologists: Radioactivity 27 February 2006

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Slide 2 © CSIR Introduction Phosphorus-32 is an important radionuclide in nuclear medicine. Required dose is achieved by delivering known amounts of activity. Activity measurements are traceable to national radioactivity measurement standards. The CIPM MRA requires National Metrology Institutes to regularly check measurements for uniformity and equivalence. In 2005 the BIPM organised an international key comparison of 32 P activity measurements. Method: followed the decay, with the following variations collected double- and triple-coincidence data fresh counting sources weekly rates per unit mass analysed established the counting efficiency by two independent methods

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Slide 3 © CSIR Beta decay is the process whereby the nucleus of an atom transforms spontaneously into a stable nuclide. An electron (called a beta particle) is emitted directly from the nucleus. The energy ranges from 0 to E max. So the beta particle has a continuous energy distribution. An antineutrino is also emitted to conserve energy. Background Information

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Slide 4 © CSIR The activity A is the rate of decay of a radioactive source. The number of nuclei that disintegrate per second is given the unit becquerel (Bq). The decay is a random process, with all nuclei of a given nuclide having identical decay probability. The decay law (based on experimental evidence) is: A(t) = N(t), where N(t) is the number of nuclei present at an instant of time t. Solving, A(t) = A(0) exp (- t). The decay is exponential with a decay constant.

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Slide 5 © CSIR Phosphorus-32 ( 32 P) is a pure beta emitter with high energy (E max = 1711 keV). Each disintegration produces one beta particle. So we need to count the number of -particles in a time interval t to obtain the activity A. If the count rate is given by B c/s, then, where is the counting efficiency. 32 P has a high 4 detection efficiency, but < 100 %.

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Slide 6 © CSIR APPARATUS Three phototubes viewing a LS source are connected in coincidence: S ources comprise an aliquot of the P-32 solution mixed in liquid scintillator. Data are corrected for: - Background events - Counting deadtime (1 s) - Coincidence resolving time (0.47 s) PM 2 3 Double and triple coincidence unit PM 1 Source activity = N o MEASURE: DOUBLE-TUBE RATE, N d = N o d TRIPLE-TUBE RATE, N t = N o t

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Slide 7 © CSIR Detector housing Liquid scintillation counting source

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Slide 8 © CSIR COUNTING SYSTEM Electronic modules for pulse processing and the data acquisition system (CAMAC interval timer and scaler modules under computer control).

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Slide 9 © CSIR P-33 and S-35 were possible impurities in the P-32 solution. All are pure beta emitters. Cannot independently determine the Phosphorus-33 and Sulphur-35 activities. For a given source comprising mass m of the master solution: 32 P count rate at time t : N 1 (t) = N 1 exp(- 1 t) 33 P count rate at time t : N 2 (t) = N 2 exp(- 2 t) 35 S count rate at time t : N 3 (t) = N 3 exp(- 3 t) All we can do is measure the total count rate N(t) : N(t) = N 1 (t) + N 2 (t) + N 3 (t) …………………………………….(1) Therefore must follow the decay over time and determine the best fit to the data using expression (1). This extracts the count rates N 1, N 2 and N 3 at the reference date chosen.

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Slide 10 © CSIR Sum of three exponential functions Weighted least-squares fitting: Take difference (squared) between measured value N i at time t i and the mathematical expression, i.e. Q = ∑ (N i – N 1 exp(- 1 t i ) – N 2 exp(- 2 t i ) – N 3 exp(- 3 t i ) ) 2 Q is minimised by differentiating with respect to the coefficients N 1, N 2 and N 3 and equating to zero. This gives rise to a set of linear algebraic equations that can be expressed in matrix form. The solution is given by a matrix inversion technique. This gives the values and uncertainties for the three coefficients N 1, N 2 and N 3.

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Slide 11 © CSIR Example The decay constant = / T ½, T ½ is the h alf-life. 32 P: T ½ = days, = , N 1 = c/s at time t = 0 33 P: T ½ = days, = , N 2 = 1800 c/s at time t = 0 35 S: T ½ = days, = , N 3 = 555 c/s at time t = 0 Days 32 P 33 P 35 STotal Program gives: 32 P = ± 152 c/s 33 P = 1710 ± 118 c/s 35 S = 574 ± 23 c/s

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Slide 12 © CSIR This plot shows the cluster of data points collected on day one. Expressed as count rate given by the master solution. These are double-tube coincidence rates. EXPERIMENTAL DATA

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Slide 13 © CSIR Extracted count rate concentrations (s -1 g -1 ) : N 1 = N 2 = 2355 N 3 = 134 A plot of the 106 data points collected over six weeks. Red line: 32 P Blue line: 33 P Black line: 32 P + 33 P + 35 S LOCAL ref. date:

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Slide 14 © CSIR Double rate (s -1 g -1 ) Activity conc. (Bq/g) Triple rate (s -1 g -1 ) Activity conc. (Bq/g) Impurity as fraction of P-32 (%) P ± ± P ± ± – 2.9 S ± ± – 0.5 A quench-matched 63 Ni source was used to characterize the system in terms of the figure-of-merit P. Using P, the efficiencies d (and t ) were determined: 32 P = % (99.26), 33 P = 84.6 % (81.6), 35 S = 75.2 % (70.6)

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Slide 15 © CSIR Alternative 32 P efficiency determination by the TDCR technique Triple and double rates corrected for 33 P and 35 S contributions. Then is solved for P. Mean efficiency = Mean activity conc. = ± 44 Bq/g

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Slide 16 © CSIR weighing0.02 dead time0.01 background0.01 resolving time0.005 adsorption to vial0.10 tracer0.006 half life0.18 fit to decay data sets0.18 satellite pulses0.015 COMBINED0.28 UNCERTAINTY COMPONENTS FOR 32 P % of activity conc. (1 )

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Slide 17 © CSIR Conclusions Application of the decay method successfully extracted the 32 P activity content in the presence of pure beta-emitting impurities. The two schemes adopted to convert count rates into activities produced consistent results. Participation in the key comparison has furthered the NML’s capabilities, will establish degrees of equivalence with the other participants and offer traceability to the local user community.

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