Activity standardization of 134Cs and 137Cs

Jana Sochorová n, Pavel AuerbachCzech Metrology Institute, IIR, Radiová 1, 102 00 Praha 10, Czech Republic

H I G H L I G H T S

� 134Cs was primary standardised using 4πβ-γ coincidence, combined uncertainty o0.3%.� 137Cs was standardised using efficiency tracing, with 134Cs and 60Co as tracers.� Results and uncertainties of this method compared with results of TDCR measurement.

a r t i c l e i n f o

Available online 10 December 2013

Keywords:Coincidence methodEfficiency tracing methodTDCR methodCs-137 standardizationCs-134 standardization

a b s t r a c t

The paper presents the results from a primary standardization of 137Cs using two independent methods –efficiency tracing using PC-NaI coincidence and the TDCR method. The nuclides 60Co and 134Cs were usedas the tracers. Primary standardization of the 134Cs is also discussed. The efficiency extrapolation wascarried out by measuring samples of varying mass and using the wet extrapolation method. The resultsobtained are in good agreement; the differences did not exceed 0.5%. The advantages, pitfalls and alsopossibilities for improvement of the procedures are discussed.

& 2014 Published by Elsevier Ltd.

1. Introduction

The nuclide 137Cs disintegrates by β� emission to the groundstate of 137Ba (5.6%, Eβmax¼1175.63 keV, 2nd forbidden) and via a661.66 keV isomeric level of 137Ba (94.4%, Eβmax¼513.97 keV,unique 1st forbidden) which has a half-life of 2.55 min (Bé et al.,2004). The 661.66 keV transition is partly converted (αT¼0.1102).

The fact that γ-ray decay of the daughter is severely delayedmakes the classical β–γ coincidence method impossible to use.Therefore the nuclide 137Cs is primarily standardized as a purebeta nuclide. To determine the activity of the nuclide, a 4πβ–γcoincidence apparatus can be used, while the efficiency tracingmethod with a suitable tracer is used for determination ofdetection efficiency of β particles (Baerg et al., 1964). The tracingmethod is based on coincidence measurement of a mixture of apure β nuclide (mass Hβ) and a tracer (mass HT) with knownactivity AT. Assuming a polynomial relationship between theβ-efficiencies of β nuclide (εβ) and tracer (εβT)

εβ ¼ f ð1�εβT Þ; ð1Þthe activity of the pure beta nuclide can be calculated by extra-polation of 1�εβT to 0.

The nuclide used as the tracer must meet the followingconditions – it should be possible to measure it using the

coincidence method with sufficient accuracy, it should have asimilar β spectrum shape and end point energy as a pure β nuclide,the mixture of two nuclides must be homogenous, and sourcesshould have a low self-absorption.

Due to these conditions, it is possible to use the isotope 134Cs(Rytz, 1985). This nuclide fulfills the condition of a homogeneousmixture with 137Cs. A problem is posed by the presence of a 7.1%branch with relatively low beta energy 89 keV. This complicatesthe standardization of this nuclide as well as significantly affectingthe function f in Eq. (1). Another option is to use a widely usedtracer 60Co. It has a simple β spectrum, but its significantlydifferent atomic number affects the shape of the β spectrum.Moreover, there is a risk of non-homogeneous samples.

Based on the above, measurements with both nuclides wereperformed and the influence of various factors on the results wasobserved. The Triple to Double Coincidence Ratio (TDCR) (Brodaand Pochwalski, 1992) apparatus and calibrated ionization cham-ber were used for supplementary and control measurements.

2. Measurements

2.1. Apparatus and sources

The 4π(PC)-γ coincidence system consists of a stainless-steelcylindrical proportional counter (PC) with dimensions of 2�(18 mm�∅64 mm), using methane at atmospheric pressure in a

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0969-8043/$ - see front matter & 2014 Published by Elsevier Ltd.http://dx.doi.org/10.1016/j.apradiso.2013.11.127

n Corresponding author. Fax: þ420 26 602 0466.E-mail address: jsochorova2@cmi.cz (J. Sochorová).

Applied Radiation and Isotopes 87 (2014) 207–210

gas flow arrangement, and the γ-ray detection assembly (twoopposing NaI(Tl) detectors mounted close to the PC). The sourceswere prepared by deposition of 20–50 mg aliquots of activesolution (20 mg CsCl2/Lþ3 g HCl/L) onto conducting foil (goldcoated VYNS foils �40 mg g�1), treated with ludox and insulin.

The TDCR system at CMI described by Sochorova and Auerbach(2012) was used. The photomultiplier tubes (BURLE 8850), areplaced in a steel case with a custom developed rapid voltagedivider and preamplifier. High positive voltage is applied to theanode to reduce noise. For signal processing the MAC3 module isused (Bouchard and Cassette, 2000) which provides logic outputof 3 single channels, their logical sum, double and triple coin-cidences and the logical sum of double coincidences. A commonextended dead time of 40 ms is used. Changes in the verticalpositioning of the vial were used to vary efficiency. 10 sourcesfor LSC measurements were prepared using 5 plastic and 5 glass20 mL vials. Aliquots (weight around 25 mg) were added to 10 mLof scintillator (Ultima-Gold) in each vial. The vials were measuredrepeatedly – immediately after closing, then after 24 and 48 h.No significant decrease in calculated activity was observed.

2.2. Standardization of 134Cs

The nuclide 134Cs disintegrates by β� emission to excited levelsof 137Ba (27.27%, Eβmax¼89.06 keV, allowed, 2.498%, Eβmax¼415.64 keV, allowed, 70.19%, Eβmax¼658.39 keV, allowed). Theγ-ray decay schema is quite complex with energies in the range(242–1365) keV (Bé et al., 2004). The 661.66 keV transition ispartly converted.

For a nuclide with a complex decay scheme, the coincidenceequation (Grigorescu, 1983) can be used. The linear extrapolationwith the slope kε can be performed only if the linearity conditionsare met.

NβNγ

NC¼N0ð1þskεÞ; ð2Þ

where

s¼ 1�ðNC=NγÞNC=Nγ

:

where Nβ, Nγ, NC are the count rates in PC, γ and coincidencechannel, corrected for background, dead time and accidentalcoincidences, respectively, N0 is the activity of the source, andkε is the slope of linear extrapolation when linearity conditionsare met.

To meet the linearity conditions, which require constantgamma efficiency for all decay branches, it seems convenient touse a wide window in the gamma channel. For the purpose of thetracing method, however, a gamma channel setting excludinggamma photons from the transition 661.66 keV 137Cs is necessary.With a gamma window setting with a lower level discriminator

(LLD) level of 720 keV, some gamma transitions from the betabranch of 415.64 keV are not registered. It is necessary to deter-mine how this will affect the resulting activity value. Measure-ments for LLDγ of 180, 470 and 720 keV were performed.

15 sources were prepared from a 134Cs solution (20 mg CsCl2/Lþ3 g HCl/L) using the described procedure. The extrapolation wascarried out by measuring samples of different masses, for which theefficiency range was 0.75–0.93, and using the wet extrapolationmethod which utilizes an absorption change during the drying of awater droplet added onto the source surface (Sochorova et al.,2008). The measurement results are shown in Table 1 and Fig. 1.

From Fig. 1 it is clear that the resulting activity is slightlyinfluenced by the choice of LLDγ. The kε value is in the range of(0.1146(24)–0.1538(30)) and increases with LLDγ value. The linear-ity of the fit was tested using different intervals of s¼(1�εβ)/εβvalue. The extrapolated activity changed by less than 0.15% forintervals (0.07–0.15), (0.07–0.2) and (0.07–0.25).

The most significant item in the list of uncertainties is theuncertainty of extrapolation, which includes the above mentionedfactors. It would be useful to have samples with higher efficiency.Preparation of samples with lower self-absorption will be thesubject of further research.

2.3. Efficiency tracing with 60Co and 134Cs.

The mixed solutions were prepared as follows:

1) 60Co solution (20 mg CoCl2/Lþ3 g HCl/L, approx. specific activ-ity of 150 kBq/g), preliminarily standardized using the coin-cidence method, and a 137Cs solution (20 mg CsCl2/Lþ3 g HCl/L), approx. specific activity of 150 kBq/g) with mixing ratio of1:1 and

2) 134Cs solution (20 mg CsCl2/Lþ3 g HCl/L) preliminarily tandar-dized using the coincidence method described previously andthe 137Cs solution with the same mixing ratio.

The sources were prepared by depositing 15–25 mg aliquots ofmix solution onto conducting foil (VYNS foil mentioned above).The beta efficiency was varied using the wet extrapolationmethod, and by using sources with different masses of solution.

The sources with 134Cs as the tracer were measured in thecoincidence system with LLDγ¼720 keV. The influence of theγ transition 661.66 keV was checked by γ spectra analysis; noinfluence higher than 0.03% was found. The coincidence spectrafor different gamma channel setting were analyzed using a digitalcoincidence system (Havelka, 2002).

The relation between εβ and (1�εβT) was determined usingdependence of Nβp on 1�εβT. For each point, Nβp was extracted

Table 1The results and uncertainty budget of 134Cs activitymeasurements.

Activity concentration (kBq/g) 149.24Counting statistics 0.1Dilution 0.05Weighing 0.01Background 0.06Dead time 0.01Extrapolation of efficiency curve 0.25

Combined uncertainty 0.28

Combined uncertainty (kBq) 1.02

y = 17.698x + 154.4 y = 20.949x + 154.45

y = 23.735x + 154.3

152

154

156

158

160

162

0.00 0.05 0.10 0.15 0.20 0.25

(1- )/

NNNC

LLD 180keVLLD 470keVLLD 720keV

Fig. 1. 134Cs efficiency extrapolations for different gamma window settings.

J. Sochorová, P. Auerbach / Applied Radiation and Isotopes 87 (2014) 207–210208

from count rate in β channel.

Nβp ¼ Aβεβð1�kT Þ ¼NβþβT �AT ð1þskεÞεβTkT ; ð3Þwhere Nβp is the part of β channel count rate belonging to the pureβ nuclide, kT is the dilution factor kT¼HT/(HTþHβ), NβþβT is thetotal count rate in the β channel, and kε is the extrapolation slopeof the tracer.

To check if the linear fit can be used, calculations of linearfunctions in 1�εβT intervals of (0.095–0.15) and (0.095–0.25) wereperformed for the set of dry sources and wet extrapolations.

A typical result of the measurement of a set of 10 dry sourcesand wet extrapolation of two sources is in Fig. 2. The quadraticfunction was calculated for interval 0.095–0.25. The difference ofthe resulting value did not exceed 0.4%. For efficiency calculation,the linear function was used and the variance of results wasincluded in the uncertainty calculations. The influence of conver-sion electrons from the 661.66 keV transition was calculatedseparately as

k¼ 1þ αTεCE1þαT

:

The correction was found as 1.0915.The sources with 60Co tracer were measured in the coincidence

system with LLDγ¼1050 keV. The results of extrapolation are inFig. 3. The influence of possible non-linearity of the fit was testedby comparing results of linear fit in the range of 0.052–0.20 andquadratic fit in the range 0.052–0.42. The difference did not exceed0.5%; the linear function was used for εβ calculation and thedifference was included in the uncertainty calculations.

2.4. TDCR measurement

A set of 10 vials (5 plastic and 5 glass) with 6 counting pointswith different efficiencies for each vial was measured. The count-ing threshold was set just below the single electron peak. Theefficiency was varied by changes in vertical positioning(0–10 mm). The maximum achieved T/D ratio was 0.982; theminimum was 0.75. Efficiency calculations were performed usingthe software TRIDAB (Sochorova and Auerbach, 2012)with β shapefactors of p2þq2 and 1 for Eβmax of 513.97 keV and 1175.63 keVrespectively (Cassette, 2012). Calculations for different β shapefactors (1, p2þq2, 0.004 p2þq2) were performed. The difference inthe resulting activity did not exceed 0.15% and decreases withincreasing T/D ratio. The inputs for calculation of contribution ofXK, gamma and conversion electrons to the total efficiency werecalculated using the MCNPX code. After assessment of activitydependence on TDCR values for different kB, the kB value of 0.012was used. For values of kB in the range (0.007–0.015) thedifference in resulting activity was 0.2% for maximum achievedT/D ratio and increases with decreased T/D.

y = -17.497x + 81.801

y = -12.119x2 - 13.178x + 81.445y = -16.586x + 81.675

76

77

78

79

80

81

82

83

0 0.05 0.1 0.15 0.2 0.25 0.3

1-

N wetdry

Fig. 2. Efficiency extrapolation results for 134Cs as a tracer. Calculations wereperformed for intervals (0.095–0.25) (linear), (0.095–0.15) (linear, dashed line) and(0.095–0.25) (quadratic).

y = 56.358x2 - 65.894x + 79.47

y = -54.094x + 79.12

60

65

70

75

80

85

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

1-

N

Fig. 3. Efficiency extrapolation results for 60Co as a tracer. Calculations wereperformed for intervals (0.052–0.20) (linear) and (0.052–0.42) (quadratic).

Table 2The results and uncertainty budget of 137Cs activity measurements.

TDCR Efficiency tracer 60Co Efficiency tracer 134Cs

Activity concentration (kBq/g) 149.14 149.69 149.46

Uncertainty budget (%)Counting statistics 0.1 0.10 0.10Dilution 0.05 0.05 0.05Weighing 0.01 0.01 0.01Background 0.08 0.10 0.10Dead time 0.01 0.03Source stability 0.1Source homogeneity 0.30 0.20Tracer 0.20 0.28Input parameters and statistical model, quenching 0.45Extrapolation of efficiency curve 0.60 0.35Half life 0.01 0.01 0.01Correction for decay scheme 0.50 0.05 0.05

Combined uncertainty 0.69 0.72 0.58

Combined uncertainty (kBq) 1.02 1.07 0.77

Difference from the value determined using calibrated IC (%) �0.24 0.13 �0.03

J. Sochorová, P. Auerbach / Applied Radiation and Isotopes 87 (2014) 207–210 209

3. Conclusions

The nuclide 137Cs was measured with 3 methods. As supple-mentary measurement the measurement in a calibrated ionizationchamber was performed. The results summarized in Table 2 are ingood agreement, but their uncertainties differ. For the TDCRmethod, the most important contributions to the uncertaintybudget as specified in Table 2 are items “ correction for decayscheme” and “input parameters and statistical model, quenching”which cover the difference in resulting efficiency for different kBvalues and β spectrum shape and the uncertainty of input para-meters for XK and γ. These items are supposed to be lowered withmore precise MCNP calculations and by further research focusingon input parameters of TDCR calculation (kB, β shape). The mostproblematic method is efficiency tracing with 60Co. Although theefficiency of the tracer is close to 1, the difference in results fordifferent intervals of 1�εβT indicates a possible problem withthe expression of efficiency function or with homogeneity of thesource. Efficiency tracing with 134Cs has a slightly lower uncer-tainty. This method can be significantly refined by reducing self-absorption in the sample. This will be the subject of furtherresearch.

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