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Applied Radiation and Isotopes 66 (2008) 937–940

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Liquid-scintillation-based anticoincidence counting ofCo-60 and Pb-210

R. Fitzgerald�, M.K. Schultz1

National Institute of Standards and Technology, 100 Bureau Dr., MS8462, Gaithersburg, MD 20899, USA

Abstract

The method of liquid-scintillation-based 4pb–g anticoincidence counting was employed to assay the radioactivity concentration of acid

solutions containing radionuclides 60Co and 210Pb (in equilibrium with its daughters). The limiting factors on the accuracy for such

activity measurements and suggestions for minimizing such factors are reported.

Published by Elsevier Ltd.

1. Introduction

The two similar methods of 4pb–g coincidence and4pb–g anticoincidence counting with efficiency extrapola-tion are powerful tools for radionuclidic metrology. Mostapplications of these methods use a proportional counterfor the beta channel (NCRP, 1985). A less common, yetoften applicable experimental design, is to use a liquid-scintillation (LS) detector for the beta channel, in whichcase the usual considerations of afterpulses and Comptonscattering inherent in LS counting have to be considered.For an anticoincidence measurement, the beta efficiency(eb) is monitored by the anticoincidence (NA) to singlegamma-ray (Ng) rates ratio

�b � 1�NA

Ng. (1)

To a first approximation, the activity (N0) is the interceptof an extrapolation of the beta count rate (Nb) to eb ¼ 1using the equation (Bryant, 1962)

Nb ¼ N0 1�NA

Ng

� �. (2)

e front matter Published by Elsevier Ltd.

radiso.2008.02.037

ing author. Tel.: +1301 975 5597; fax: +1 301 926 7416.

ess: ryan.fitzgerald@nist.gov (R. Fitzgerald).

ress: Department of Radiation Oncology, Department of

ne (Division of Cardiology), University of Iowa Hospitals

rver College of Medicine, Iowa City, IA, USA.

It is well known that in beta–gamma coincidencecounting, additional coincidences detected with efficiencyec, can be caused by Compton scattered gamma raysinteracting in both the beta and gamma detectors or,in more complicated decay schemes, a g–g coincidencebetween the two detectors. Various reference works onthe topic assert that such an effect does not occur inanticoincidence counting (ICRU, 1994; NCRP, 1985;Mann et al., 1988). Nonetheless, the effect is observedin an anticoincidence counting. This is to be expectedsince such coincidences are not random, and thereforethe anticoincidence rate will be duly affected. Thus, amodified extrapolation formula, similar to those used incoincidence counting (Campion, 1959; Baerg, 1973; Gri-gorescu, 1973; ICRU, 1994), must be employed. Thiscorrected extrapolation is of the form

Nb � N0 1� kNA

Ng

� �, (3)

where

k ¼1� �bg

1� ð�c=�gÞ. (4)

The correction factor (k) reflects the difference betweenthe LS efficiency for gamma rays (ebg) and the measure ofthat efficiency by the coincidence efficiency (ec) to gammas(efficiency eg) ratio. It can also be convenient to extrapolatethe apparent activity (N0*) versus an efficiency parameter

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Fig. 1. Measured and traced LS efficiency for a calibrated 60Co gamma-

ray source in modified geometry, versus the lower-level discriminator

(LLD) in volts. The solid diamonds represent true ebg (LS count rate/

photon emission rate), open circles and solid squares represent the

anticoincidence-monitored LS efficiency (1�NA/Ng) from gamma win-

dows G2 (photopeaks region) and G3 (sum peaks), respectively.

R. Fitzgerald, M.K. Schultz / Applied Radiation and Isotopes 66 (2008) 937–940938

[(1�eb)/eb)] (Campion, 1959). For anticoincidence count-ing, this becomes

Nn

0 ¼NbNg

Ng �NA

� N0 1þ1� �b�b

� ��bg �

�c

�g

� �� �. (5)

In the simple case of a radionuclide decaying by asingle beta–gamma cascade, and with the gamma-raydetector gated on the photopeak, ec ¼ 0, the true LSefficiency, which is sensitive to both eb and ebg, will behigher than the monitored efficiency, which is sensitive onlyto eb, and differ from it in a functional form over theextrapolation. On the other hand, if the gamma windowcontains a large enough portion of the Compton spectrum,the effect can be in the opposite direction, as theanticoincidence rate is overly sensitive to ec. Note that inboth extremes, the extrapolated activity approaches N0 asNA/Ng-0; only the functional form of the extrapolation isa problem.

Uncertainties due to counting statistics (k ¼ 1) are indicated. Notice that

for G2, this quantity is approximately proportional to ebg, yet for G3 it is

compatible with zero.

2. Instruments and methods

The National Institute of Standards and Technology(NIST) 4pb–g live-timed anticoincidence system comprisesa single close-geometry photomultiplier tube (PMT)/LSdetector for the beta channel, and a 9-cm inner-diameterthallium-doped, sodium iodide [NaI(Tl)] well-type detectorfor the gamma channel (Lucas, 1998). The LS-betaefficiency (eb) is varied by application of a lower-leveldiscriminator (LLD) acting on the amplified detectoroutput. Up to three anticoincidence gamma-ray gates(G1, G2, G3) can be set on the NaI spectrum. The sharedlive-time and anticoincidence logic are carried out by an in-house custom-designed logic unit (Lucas, 1998). For thepresent work, a 100 ms extending dead-time was employedand a modest minimum lower-level discriminator was used.The suppression of afterpulses was confirmed by observingthat the LS count rate did not vary over a large range ofextending dead-times (50–400 ms).

The LS sources consist of 3 cm diameter, glass pseudo-hemispheres sealed with epoxy and coupled with opticalgrease to the PMT. For the 60Co measurements, thehemispheres were filled with 4mL of HiSafe-32 LS cocktail(Perkin Elmer, Waltham, MA, USA) between (1 and5) kBq of 1.1-M HCl 60Co solution and additional carriersolution for an overall aqueous fraction of 0.02. For the210Pb measurements, the hemispheres were filled with 4mLof PCS LS cocktail (Amersham Biosciences, Sweden)between (1 and 3) kBq of 0.6-M NHO3

210Pb solutionand additional carrier solution for an overall aqueous massfraction of 0.06 (Fig. 1).

2Certain commercial equipment, instruments, and materials are

identified in this paper to foster understanding. Such identification does

not imply recommendation or endorsement by NIST, nor does it imply

that the materials and/or equipment are the best available for the purpose.

3. Results and discussion

3.1. Cobalt-60

The efficiency extrapolation method was explored in thecourse of a primary calibration of 60Co. Gamma-ray gateG1 encompassed only Compton-scattered events, G2encompassed both photopeaks and G3 encompassed onlythe sum peak. Linear extrapolations based on G1, G2 andG3 gave relative results for N0 of 0.993, 1, and 1.004,respectively, illustrating the sensitivity of ec to the choice ofgate. A quadratic fit did not significantly change theseresults, nor did the results change by extrapolating theapparent activity versus (1�eb)/eb using Eq. (5), as shownin Fig. 2. To explore the details of this effect, the correctionfor k was measured using a 60Co gamma-ray point source.The source was sealed in a 2-mm-thick black plastic andmounted above the hemisphere position in the apparatus.The source activity was measured with and without thepresence of an LS-cocktail filled hemisphere. The resultsreveal that ebg increases significantly for low-energygamma-ray gates, as shown in Fig. 3. The presence of thiseffect even in the absence of LS cocktail suggests that itinvolves the interaction of gamma rays with the PMT itself,as has been reported previously (BIPM, 1980). To testwhether bremsstrahlung, or other beta-induced events werepresent, we measured the LS efficiency using the b–ganticoincidence method and the same three gates men-tioned above. The ec values for gate G3, which isexclusively sensitive to events in which both gamma raysdeposit all their energy in the NaI detector, were consistentwith zero. Therefore, the measured ebg values were not betainduced. If these low-energy events differ in origin from the

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Fig. 2. Apparent activity (N0*) extrapolation using Eq. 5. The diamonds,

open circles and squares represent gamma gates G1 (Compton region), G2

(photopeaks) and G3 (sum peak), respectively. Uncertainties due to

counting statistics (k ¼ 1) are indicated for N0* only. Uncertainties the

abscissae are not shown.

Fig. 3. LS-spectra of an LS cocktail-filled glass hemisphere (dash-dotted

line), 60Co point source (dashed line) and the same 60Co point source

mounted above the LS cocktail-filled hemisphere (solid line). The

approximate energy scale is based on 60Co and 3H endpoint energies.

Table 160Co activity values equal to the intercept from efficiency extrapolations

using 3 gamma windows: G1, G2 and G3, corresponding to the Compton

region, photopeaks region and sum peak, respectively

G1 G2 G3

Uncorrected 0.9937.001 1.00017.0001 1.0047.002

Corrected 1.0017.002 1 1.0017.001

The values in the bottom row have been corrected for ebg and ec, as

determined using a point source. All values are relative to the corrected G2

value. Uncertainties (k ¼ 1) are from standard deviations of sample set

(top row) and geometrical scaling (bottom row).

R. Fitzgerald, M.K. Schultz / Applied Radiation and Isotopes 66 (2008) 937–940 939

Compton-scattering LS events, then their factor k will alsodiffer. Also note that Baerg’s justification for usingquadratic extrapolations in some cases, for example whena beta-decay branch to the ground state exists, was that thedetection inefficiencies for two beta-decay branches tend tobe smooth, low-order functions of each other (Baerg,1973). Such justification is not necessarily applicable to thepresent discussion.

The measured values of ebg and ec were scaled for themodified geometry of the point-source experiment versusthe 60Co massic-activity measurements and used in anextrapolation based on Eq. (3) to determine the sourceactivity. The dispersion in the activity determinations usingthe three gates was significantly reduced by applying thiscorrection, as summarized in Table 1. The averagecorrection to the results from using gates G1 and G3 werein the order of 0.5% and for G2 was only 0.013%. For the

sum peak (G3) ec ¼ 0, so ebg can be determined fromEq. (5) (Campion, 1959; Williams and Campion, 1963). Inthis way, the mean value of ebg ¼ 0.06470.003 (coveragefactor of 1) was determined, where the uncertainty is thestandard deviation of the linear fit over the range of theextrapolation. These results suggest that a gamma-ray gatecovering both photopeaks from 60Co yields a linearextrapolation with less than about 0.05% systematic errorin the intercept due to ebg and ec.

3.2. Lead-210

A massic activity determination of 210Pb solution, inequilibrium with its daughters, by 4pb–g anticoincidencewas recently undertaken as a confirmation of a primarycalibration performed by NIST (Laureano-Perez et al.,2007). The measurements were carried out over a 24-dayperiod and no indication of disequilibrium was observed.In this case, the LS efficiency for detecting the decay of thedaughters 210Bi (1.1MeV beta) and 210Po (5.3MeV alpha)is near unity, and the efficiency variation is mainly over thebeta decay of the 210Pb. The 210Pb beta endpoint energiesand probabilities are (Browne, 2003): Eb1 ¼ 17 keV,Pb1 ¼ 0.84 and Eb2 ¼ 63.5 keV, Pb2 ¼ 0.16. The onlygamma ray from the decay chain is associated with b1:Eg ¼ 46.5 keV, Pg ¼ 0.0425. Therefore, this gamma ray wascounted in the NaI detector and used to monitor the LSefficiency for the 17 keV betas, eb1. The intercept of theextrapolation of the total LS count rate to eb1 ¼ 1, wasmultiplied by a factor f ¼ 0.331 2870.000 02 (calculatedfrom the various decay constants) to determine the 210Pbactivity. A similar measurement was undertaken by Woodset al. (2000) using their 4pb(LS)�g coincidence system.Unlike the present work, they separated the 210Pb from itsdaughters chemically before counting. The advantageof the present method is that the contribution ofthe uncertainty in the 210Pb efficiency extrapolation tothe combined uncertainty in the activity is mitigated byroughly the factor f. However, as was the case for Woodset al. (2000), the range of eb1 was limited top0.3 due to thepresence of noise and afterpulses in the one-photon peak.Yet although the extrapolation covered a large domain,0.3peb1p1, the extrapolated LS efficiency range was only0.98peLSp1. This pleasantry is due to the presence of the

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Fig. 4. Anticoincidence data from a single 210Pb experiment (1000 s per

point). The total LS count rate (NLS) is plotted against the inefficiency of

the LS detector to the 17 keV 210Pb beta decay [NA/NgE(1�eb1)].

Uncertainties only from counting statistics are displayed. The line is a

quadratic extrapolation following Eq. (6).

R. Fitzgerald, M.K. Schultz / Applied Radiation and Isotopes 66 (2008) 937–940940

high-energy daughter decays and the strong conversion ofthe 46.5 keV gamma ray (a ¼ 18.7).

The functional form of the extrapolation is complicateddue to the presence of the conversion electron as well as thevariation of eb2 and to a lesser extent, the variation of theefficiencies for the 210Bi beta (eBi) and

210Po alpha decays.Based on calculations of the relevant Fermi functions, thebeta inefficiencies, (1�eb2) and (1�eBi), were found to bequadratic functions of (1�eb1) and therefore the extrapola-tion function, Eq. (2), becomes

NLS � N0 1� aNA

Ng� b

NA

Ng

� �2" #

, (6)

where a and b are fitting parameters. A typical data set andquadratic extrapolation are displayed in Fig. 4. Theaccuracy of the activity value was limited by theuncertainty in the extrapolation and therefore only aplausible activity range of73% (k ¼ 2) was established fora confirmation of the NIST standardization [see furtheruncertainty discussion in Laureano-Perez et al. (2007)]. Togain confidence in the extrapolated value and assumptionsimplicit in Eq. (6), a higher LS efficiency would be useful.

4. Conclusions

In the case of 60Co, the presence of two gamma rays ofsimilar energy allows the effect of k to be minimized bysetting a gamma-ray window around both photopeaks.

Thus, if one of the gamma rays is detected by the LSdetector, the other can still be detected in the gamma-raydetector, and thus the actual LS efficiency is measured. Inthis way, the uncertainty in the extrapolation of the massicactivity can be reduced to about 0.05%. For a single-photon decay on the other hand, the width of the gateshould be determined experimentally to encompass boththe photopeak and enough of the Compton spectrum suchthat the correction for ebg and ec is minimized. This can bepractically accomplished by adjusting the gate to minimizethe absolute value of the slope in an extrapolation based onEq. (5). This is the type of experimental design suggestedby various authors to reduce the order of the extrapolation(Baerg, 1973; Williams and Campion, 1963; Grigorescu,1973). For low-energy beta emitters, such as 210Pb, the lowLS efficiency is the limiting factor on the accuracy of themethod. To this end, modifications to the hemispherical LSvial are underway to maximize the light transfer to thephototube. It is hypothesized that these modifications,along with attempts to minimize quenching in the solution,will lead to an increased LS efficiency.

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