Activity determination of 59Fe

Karsten Kossert n, Ole J. NählePhysikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116 Braunschweig, Germany

H I G H L I G H T S

� Iron-59 was measured by means of liquid scintillation counters.� CIEMAT/NIST efficiency tracing and the TDCR method were applied.� The models were extended for complex decay schemes.� The relative standard uncertainty was found to be 0.16%.

a r t i c l e i n f o

Keywords:59FeActivity standardizationTDCRCIEMAT/NIST efficiency tracingComplex beta–gamma decay

a b s t r a c t

Iron-59 was measured in three commercial and two custom-built liquid scintillation counters.The counting efficiencies were determined using CIEMAT/NIST efficiency tracing and the triple-to-double coincidence ratio (TDCR) method, respectively.

The efficiency computation for the TDCR method was realized by means of the MICELLE2 program,applying a stochastic model for the computation of electron emission spectra. The programwas extendedto make calculations of spectra originating from complex decay schemes possible. In addition, a newparameterization of electron stopping powers for 10 commercial liquid scintillation cocktails wasincluded in the software.

The activities determined with the two methods were in very good agreement; the relative standarduncertainty of the combined result was found to be 0.16%. It was used to calibrate a 4π ionizationchamber at PTB for future calibrations of this isotope which is used for investigations of iron metabolism.

A standardized solution was submitted to the Bureau International des Poids et Mesures (BIPM) to bemeasured in the ionization chambers of the International Reference System (SIR) for comparisonpurposes.

The liquid scintillation samples were also measured in a new portable TDCR system with threechannel photomultipliers. Although this system has a much lower counting efficiency, the activity was insatisfactory agreement with the conventional TDCR system. The usage of the portable TDCR system, thus,provides an important test of the free parameter model.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The isotope 59Fe (T1/2¼44.53(3) days; Schötzig and Schrader,2000) decays by several beta transitions to the ground state and tofour excited states of 59Co. High counting efficiencies can beexpected when using liquid scintillation counting. In this paper,we describe recent extensions of the method to calculate thecounting efficiency in a liquid scintillation (LS) system with twoand three photomultiplier tubes. The new computations makeapplications of the well-established CIEMAT/NIST efficiency tra-cing method and the triple-to-double coincidence ratio (TDCR)method possible. With the extended calculation method we can

compute the counting efficiency of a beta transition even if it isaccompanied by up to seven gamma transitions. For gammatransitions we also take the internal conversion (IC) into account.Simplifications of the decay scheme and/or the computationtechnique as carried out in the pioneering work by Günther(1994) are not required any more.

2. Experimental details

In March 2012, an ampoule containing a 59FeCl3 solution with anominal activity of 18.5 MBq was purchased from PerkinElmer.The solution was diluted with 0.5 mol L�1 HCl and a carrierconcentration of 97 μg inactive FeCl3 �6H2O per gram of solutionand then transferred into three glass ampoules of different types:

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n Corresponding author. Tel.: þ49 5315926110; fax: þ49 5315926305.E-mail address: karsten.kossert@ptb.de (K. Kossert).

Please cite this article as: Kossert, K., Nähle, O.J., Activity determination of 59Fe. Appl. Radiat. Isotopes (2014), http://dx.doi.org/10.1016/j.apradiso.2014.01.013i

Applied Radiation and Isotopes ∎ (∎∎∎∎) ∎∎∎–∎∎∎

one PTB-type AM05 ampoule which has been in use since 2005,one PTB-type ampoule AM which was mainly used before 2005,and one BIPM-type ampoule, which was sent to the BureauInternational des Poids et Mesures (BIPM) to be measured in anionization chamber of the International Reference System (SIR) forcomparison purposes (Rytz, 1983). All ampoules were flame-sealed and then measured by means of ionization chambers. Thesolution from AM05 ampoule was used to prepare point sourcesfor gamma ray spectrometry. No photon-emitting impurity wasdetected, confirming the outcome reported by the supplier of theraw material.

The remaining amount of the master solution was then used toprepare a diluted solution with the same carrier concentration asstated above and a dilution factor of 13.592(7). This solution wasused to prepare LS samples and to fill further three PTB-typeAM05 ampoules. These ampoules were also measured in theionization chamber and the dilution factor was confirmed. Themasses of all samples as well as the dilution factors weredetermined gravimetrically using two Mettler balances traceableto the German national mass standard.

All LS samples were prepared with a 15 mL Ultima Gold™scintillator. About 0.97 mL of distilled water and weighed portionsof about 30 mg of the active solution were added to each sample.One series with 7 samples was prepared with 20 mL low-potassium borosilicate glass vials; another series with 5 sampleswas made with 20 mL polyethylene vials. Each sample seriescomprised one sample without active solution in order to measurethe background counting rate, which was then subtracted. Nitro-methane (CH3NO2) was used to vary the counting efficiencies. Allsamples were shaken and centrifuged before beginning themeasurements.

2.1. CIEMAT/NIST measurements

The LS samples in glass vials were measured in a Wallac 1414Guardian™ and a TriCarbs 2800 TR liquid scintillation spectro-meter. Fig. 1 shows measured liquid scintillation spectra fromthese two counters. The calibration curve, i.e. the countingefficiency of 3H as a function of the quenching indicator SQP(E) or tSIE, respectively, was measured with the aid of a PTBstandard solution of 3H, standardized by internal gas counting(Günther, 1993). The LS samples containing 3H have the samesample composition and geometry as the 59Fe LS samples. Allsamples gave stable results during the whole observation timeof 45 days.

2.2. TDCR measurements

Three TDCR counters were used to measure both LS sampleseries. The samples were first measured in a custom-built TDCRsystem of PTB which was described by Nähle et al. (2010). For thiswork, the system was equipped with three Hamamatsu R331-05photomultiplier tubes (PMTs). The amplified and discriminatedsignals were fed into a MAC3 coincidence module (Bouchard andCassette, 2000). The LS samples were also measured in a newportable TDCR system. The system was equipped with threechannel PMTs. The optical chambers of both systems were madewith the material OP.DI.MA, which had a reflectivity of about 98%over a wide range of wavelengths. The portable system was placedin a light-tight suitcase. The coincidence module of the counter –referred to as the 4KAM module – is an FPGA-based systemdesigned at PTB (Weierganz, 2011).

Also a Hidex 300 SL commercial TDCR counter was tested inthis work. The systemwas modified by Hidex Oy and is referred toas the “METRO” version. Details about the modifications and the

adjustments made at PTB were recently described by Wanke et al.(2012).

2.3. Measurements with ionization chambers

The flame-sealed ampoules of the new PTB-type AM05 con-taining about 2 g of the 59Fe solution were measured by means of acalibrated 4π ionization chamber of type IG12/A20, Centronic 20thCentury Electronics Ltd. At PTB, the ionization chamber measure-ments of a radionuclide are always carried out together withmeasurements of a long-lived 226Ra standard so that possiblevariations in the response are largely compensated.

The chamber has an iron entrance window of approximately3 mm thickness and is filled with argon at a pressure of 2 MPa. Theionization current was measured by means of a commerciallyavailable Keithley electrometer model 6517A. The measurementswere used to establish a calibration factor for the new ampouletype which has slightly thinner walls than PTB-type ampoulesused before 2005. This small difference is negligible for radio-nuclides emitting photons with high energy (Nähle et al., 2008),but for low-energetic photons differences can be a few percent (e.g., 125I). In the case of 59Fe, no significant difference between thecalibration factors for the two ampoule types could be found.

0

5

10

15

20

25

0 200 400 600 800 1000 1200 1400 1600

channel

coun

ts in

1/s

0

2

4

6

8

10

12

14

16

0 100 200 300 400 500 600 700 800 900channel

coun

ts in

1/s

Fig. 1. Measured LS spectra of 59Fe. The measurements were carried out in a Wallac1414 (a) with logarithmic amplification and a TriCarb 2800TR (b) with linearamplification, respectively. Background spectra have been subtracted.

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3. Computation of the LS counting efficiencies and analysisof data

The required decay data for the efficiency computation weretaken from Bé et al. (2004). The decay scheme was taken intoaccount without any simplifications. It comprises five beta transitionsand seven gamma transitions as shown in Fig. 2 and Table 1. Ninedifferent cascades (pathways from ground state to ground state ofthe daughter nuclide) were taken into account. Four beta transitionswere of allowed nature, while the beta transition to the ground stateof 59Co was of non-unique second forbidden nature. Its maximumbeta energy was 1562.2(6) keV and, thus, a high LS countingefficiency was achieved. Consequently, also the shape factor functionof this transition was of minor importance. For all beta transitions,the shape factor function was assumed to be C(W)¼1. The overallbeta emission probability was normalized to 100%.

The CIEMAT/NIST efficiency computations were carried out withthe PTB program “beta” (version 2012, unpublished) which had beenused for several previous works (see, e.g., Kossert and Schrader,2004; Nähle et al., 2010). The program applied procedures tocalculate the counting efficiencies of beta transitions accompaniedby several gamma transitions. The procedures also required taking

into account that single transitions can cause a detection in only onePMT and corresponding probabilities of each component of a cascademust then be combined. Details on these procedures were presentedby Oropesa Verdecia and Kossert (2009). The ionization quenchingfunction Q(E) was calculated by means of the procedures describedin a previous article (Kossert and Schrader, 2004) and an ionizationquenching parameter kB¼0.0075 cm/MeV was used. For a 3Hefficiency of 50%, the counting efficiency of 59Fe was calculated tobe 97.03%. The results of the individual samples were in excellentagreement. The 59Fe counting efficiency ranged from about 93.6%to 96.6%.

A comparable analytical approach is not yet available for theanalysis of TDCR data when measuring radionuclides with suchcomplex decay schemes. Thus, the analytical free parameter model(Grau Malonda, 1999; Broda et al., 2007) was replaced by astochastic approach (Grau Carles, 2007) which has been extendedto compute the triple and double counting efficiencies for a systemwith three photomultiplier tubes as described by Kossert and GrauCarles (2010). The method was already applied to standardize177Lu (Kossert et al., 2012) showing excellent agreement betweenthe stochastic and the analytical approach for the CIEMAT/NISTmethod. In addition, the results of the TDCR method were in goodagreement with other methods, including CIEMAT/NIST. Thecomputations were made using the MICELLE2 code which is apowerful tool to compute the counting efficiency of many radio-nuclides. However, so far the code could not be used forbeta branches when they are accompanied by more than twocoincident gamma/IC transitions. Thus, the code was extended tomake computations of beta branches in coincidence with upto 7 gamma/IC transitions possible. Also electron-capture branchescan now be computed with up to 7 coincident gamma/ICtransitions.

The counting efficiencies are computed in the following way.The number of electrons Mi and their energies Eil are computedand stored for all simulated decay events. The triple countingefficiency εT as a function of the free parameter λ is then given by

εΤ ðλÞ ¼ ∑Ν

i ¼ 11�exp

� ∑Μι

l ¼ 1EilQ ðΕilÞ

3λ

26664

37775

8>>><>>>:

9>>>=>>>;

3

=Ν : ð1Þ

The counting efficiency for double coincidences can be com-puted in a similar manner. The number of simulated decay eventsN was selected to be 2�105.

A benefit of the method is that emissions of more than oneelectron per decay event are treated in a natural way. Thus, thecounting efficiency of electron capture and beta branches can beeasily computed, even when they are in coincidence with severalgamma transitions (including internal conversion).

The accuracy of the Monte-Carlo-based procedure depends to agreat extent on the number of simulated events, in particularwhen studying beta emitters. For the calculation of the 59Fecounting efficiency, all nine cascades were calculated separatelyusing 2�105 decay events per simulation. The results of thecoincidence counting efficiencies of interest versus the free para-meter were stored in files and later combined using the decayprobabilities as weighting factors. The procedure was time-consuming and must be repeated to study the influence of inputparameters like the ionization quenching parameter kB.

The ionization quenching function was first computed with thesame method as recently described by Kossert and Grau Carles(2010) using an ionization quenching constant kB¼0.0075 cm/MeV. In addition, the ionization quenching function was calculatedwith a new procedure which makes use of theoretical electronstopping powers for 10 commercial liquid scintillation cocktails in

β1

β2

β3

β4

β5

γ 1

γ 2

γ 3

γ 4

γ 5γ 6

γ 7

59 Fe

Co59

−Q

= 1

565.

2 ke

V

Fig. 2. Decay scheme of 59Fe (see also Table 1).

Table 1Nine cascades are taken into account. Each cascade comprises one beta transitionand up to three gamma/IC transitions (see also Fig. 2). The overall beta emissionprobability is normalized to 100%.

Cascadeno.

Probabilityin %

Components with their energies in parentheses

1 0.0604 β1 (83.6 keV), γ2 (1481.58 keV)2 0.0215 β1 (83.6 keV), γ1 (382.32 keV), γ7 (1099.262 keV)3 0.9217 β2 (130.9 keV), γ3 (142.652 keV), γ6 (1291.611 keV)4 0.2640 β2 (130.9 keV), γ4 (335.00 keV), γ7 (1099.262 keV)5 0.0628 β2 (130.9 keV), γ3 (142.652 keV), γ5 (192.349 keV), γ7

(1099.262 keV)6 42.2753 β3 (273.6 keV), γ6 (1291.611 keV)7 2.8796 β3 (273.6 keV), γ5 (192.349 keV), γ7 (1099.262 keV)8 53.2650 β4 (465.9 keV), γ7 (1099.262 keV)9 0.2497 β5 (1565.2 keV)

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the energy range from 20 eV to 20 keV as published by Tan and Xia(2012). These values were now included in the MICELLE programusing linear interpolation and linear extrapolation to (0, 0). Thisnew parameterization is of minor importance when studying 59Feor other radionuclides with high counting efficiency, but it isexpected that it has significant influence for low-energy emitters.A detailed description and further studies of the extended modelwill be presented elsewhere (Kossert et al., 2014).

4. Results

The activity concentrations determined with the various coun-ters are listed in Table 2. All results are in good agreement. Thelowest relative standard uncertainty of 0.16% is achieved with thestandard TDCR system of PTB. The relative standard uncertainty ofthe CIEMAT/NIST method was found to be 0.19%. Uncertaintybudgets for both methods are shown in Table 3. When changingkB from 0.0075 cm/MeV to 0.0110 cm/MeV, the determined activ-ity concentration would only decrease by less than 0.07% for theCIEMAT/NIST method, whereas it would increase by less than0.09% for the TDCR method. A similar anti-correlation with respectto the kB value has been observed for other beta emitters (Nähleand Kossert, 2011). The influence of the decay data was evaluatedby changing some parameters, like the shape factor function of thesecond forbidden transitions or the branching ratios. The overallrelative uncertainty assigned to decay data was estimated to be0.05% for both methods. The uncertainty of the decay correctionwas estimated using a half-life of 44.53(3) days (Schötzig andSchrader, 2000) and assuming the maximum time difference of 45days between the individual measurements and the reference

date. This can be considered as very conservative since most of themeasurements were carried out close to the reference date. In thisway, the outcome was also in agreement with the result whichwas obtained when using a half-life of T1/2¼44.495(8) d, as statedin the evaluation from Bé et al. (2004).

The uncertainty budget in Table 3 includes an uncertaintycomponent assigned to the dilution. Thus, the overall relativeuncertainties are valid for the solution which was sent to the BIPM.Until now, comparison results have not yet been provided byBIPM. The value reported by PTB is the weighted mean of the tworesults obtained with the standard TDCR system and the CIEMAT/NIST method. The relative standard uncertainty of 0.16% of theTDCR result is adopted for the final result, which is larger than theinternal (0.13%) and external (0.12%) relative uncertainties of theweighted mean. The stochastic model was checked by replacingthe analytical approach for the CIEMAT/NIST method by thecounting efficiencies computed with the new MICELLE code. Therelative deviation was found to be lower than 0.01%.

Despite the considerably lower counting efficiency of theportable TDCR system, its result is in good agreement with thefinal result. The lowest counting efficiency for 59Fe in the portablesystem is only 82.6%. Thus, the application of the portable systemcorresponds to an extreme extension of the free-parameter regionand the good agreement with other results can be regarded as animportant test of the model.

The result from the Hidex counter is also in good agreementwith other results and, thus, the counter seems to be suitable for59Fe measurements, too.

The coincidence counting rates of any pair of PMTs were verysimilar in all measurements reported on here. Thus, a potentialasymmetry of PMT response is of minor importance and thesame free parameter may be assumed for the three PMTs of therespective counter.

5. Summary and conclusions

In this work, it was shown that liquid scintillation counting is anadequate tool for the activity standardization of 59Fe. The model forthe computation of the efficiencies was extended and, for the firsttime, the TDCR method was applied to measure this isotope. Themodel could also be validated by means of a new portable TDCRsystem which achieves considerably lower counting efficiencies.

Table 3Uncertainty budgets for the activity concentration of the 59Fe solution measured by means of two LS methods.

Component u(a)/a (%)

CIEMAT/NIST TDCR

Counting statistics 0.02 0.03Weighing 0.06 0.06Dead time 0.10 0.03Background 0.05 0.03Counting time 0.01 0.01Adsorption 0.05 0.05Decay correction (half-life T1/2¼44.53(3) days) 0.05 0.05Dilution(s) (weighing) 0.05 0.05Impurities (no radioactive impurity detected) 0.03 0.033H tracer activity and interpolation of efficiency curve 0.05 –

TDCR value and interpolation of efficiency curve – 0.01Nuclear and atomic data, model excluding ionization quenching 0.05 0.05Ionization quenching and kB value 0.07 0.09PMT asymmetry o0.03 0.02Square root of the sum of quadratic components(correlation coefficients are taken into account in the summation)

0.19 0.16

Table 2Results for the determined activity concentration of the 59Fe solution which wassent to the SIR at BIPM (reference date: March 15th 2012, 0:00 UTC). The final resultcorresponds to the weighted mean of the TDCR system with Hamamatsu PMTs andthe CIEMAT/NIST result.

Method a (kBq/g) Relative deviationfrom final result

TDCR (Hamamatsu PMTs) 2027.7(33) �0.14%CIEMAT/NIST 2032.6(39) þ0.10%Mini-TDCR 2027.1(61) �0.17%Hidex-TDCR (“Metro” version) 2032.5(51) þ0.09%Final result 2030.6(33) –

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The final result was combined with ionization chamber measure-ments to determine calibration factors of the new ampoule typeAM05. Thereby, PTB will also in future be able to carry out activitydeterminations by means of calibrated ionization chambers and, inthis way, guarantee the dissemination of the unit of activity for 59Fe.

Acknowledgments

We wish to thank R. Dersch for gamma ray spectrometrymeasurements to check for potential photon-emitting impurities.

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