Journal of Nuclear and Radiochemical Sciences, Vol. 12, No.1, pp. 5-10, 2012

ArticlesEfficiency Calibration of Ge Detector for 131I and 134Cs in Soil Samples and a Simplified
Calculation of Cascade Summing Corrections for Volume Source
M. Asai,*, a Y. Kaneya,a,b T. K. Sato,a K. Tsukada,a K. Ooe,a N. Sato,a and A. ToyoshimaaabAdvanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan
Graduate School of Science and Engineering, Ibaraki University, 2-1-1 Bunkyo, Mito, Ibaraki 310-8512, Japan

Received: October 9, 2012; In Final Form: November 26, 2012
To measure radioactivities in soil contaminated by the accident of the Fukushima Daiichi Nuclear Power Plant,
efficiency calibration of Ge detectors for 131I, 134Cs, and 137Cs in volume sources was investigated. Gamma-ray
detection efficiencies for these nuclei were determined precisely using standard soil samples containing 134Cs,
137
Cs, 175Hf, and 88Zr. These standard sources were prepared by admixing radioactive solutions with soil, andpoint sources were made from the same solutions to determine their radioactivity concentrations. The efficiency
for the 364 keV γ ray of 131I was extracted from the experimental efficiencies of 137Cs and 175Hf. Cascade summing corrections for γ rays of 134Cs in soil samples were evaluated experimentally. To easily calculate the cascadesumming corrections for volume sources, we examined a simplified method using averaged efficiencies, andevaluated its validity through a comparison of the calculated correction factors with the experimental ones.

1. Introduction
The accident of the Fukushima Daiichi Nuclear Power Plant
dispersed a huge amount of radionuclides in the natural environment, and part of them were deposited on the ground surface in the extensive region of east Japan. Assessments of thedeposition densities of radionuclides and their geographicaldistributions provide important quantitative bases for estimations of radiation exposures of the residents, transfer of radionuclides into agricultural products, costs of decontaminations,etc. The Japanese government in collaboration with a few hundreds of researchers in universities and associations carried out
detailed measurements of radionuclides deposited on soil over
the whole area of Fukushima prefecture.1 Independent of thiswork, we carried out measurements of radionuclides in soil
samples collected in the north and east area of Ibaraki prefecture and in the east area of Tochigi prefecture. The soil samples were collected on May 21–22 and June 22 in 2011, and γ
rays originating from the β− decay of 131I, 134Cs, and 137Cs wereobserved with Ge detectors, whose details are described in a
separate paper.2
To measure radioactivities in soil with a Ge detector, wehave to know γ-ray detection efficiencies of the Ge detector forsoil samples. Typically soil samples have a large volume anddensity. Thus, to determine the efficiencies of Ge detectors, itis necessary to prepare the standard soil sample which contains
a known amount of radionuclides and whose shape, density,and elemental contents are approximately the same as those ofsoil samples.
At first, we used a standard soil sample distributed by IAEA
to measure the efficiencies. This soil sample contains 4.0–60
Bq kg−1 of 241Am, 109Cd, 134Cs, 137Cs, 54Mn, and 60Co. However,these radioactivity concentrations were too weak to determine
the detector efficiencies precisely. Moreover, this standard
source does not contain radionuclides which emit γ rays withenergies at the range of 90–600 keV. This makes it difficult todetermine the efficiency for the 364 keV γ ray of 131I.
A mixed γ-ray standard source which resembles soil samples
in shape, density, and elemental contents is commercially avail*Corresponding author. E-mail: asai.masato@jaea.go.jp. Fax:
+81-29-282-5927.

able. However, typically it does not contain 131I and 134Cs. The
efficiency at 364 keV for 131I is extracted from the efficiency
calibration curve determined by using γ rays of, e.g., 203Hg (279keV), 51Cr (320 keV), 113Sn (392 keV), 85Sr (514 keV), and 137Cs(662 keV). However, these radionuclides except 137Cs are notalways available because of their short half-lives.
For 134 Cs, even if the efficiency calibration curve is determined precisely, one has to take account of the influence of thecascade summing effect which reduces or increases observed
γ-ray peak counts, especially when the sample is placed at a
close source-to-detector distance. For point sources, correction
factors for the cascade summing effect are easily calculatedusing total efficiencies and full-energy peak efficiencies of Ge
detectors determined experimentally.3-6 For volume sources,
however, the efficiencies are different at different parts of thesource, which leads to different summing corrections at eachpart. This forces us to confront a difficulty in obtaining thetotal and full-energy peak efficiencies at any parts of the volume source.
The correction factor for a certain γ ray depends only on the
decay scheme of the nuclide and on the geometry of the source
and the detector. Thus, if we can prepare the standard source
which contains the same radionuclide and has the same geometry (shape, density, and elemental contents) as those of soil
samples, we can determine the contents of radionuclides in soil
samples only through a comparison of observed γ-ray peakcounts between the standard source and a soil sample, because
the cascade summing corrections for both the standard source
and a soil sample are identical, and thus they are cancelled out.
The aim of the present study is to determine γ-ray detection
efficiencies of Ge detectors for 131I, 134Cs, and 137Cs in soil samples, and to evaluate the cascade summing corrections for 131I
and 134Cs in soil samples which has a large volume and density.
For this purpose, we make standard soil samples containing
134
Cs, 137Cs, 175Hf, and 88Zr. Contents of 134Cs and 137Cs radioactivities in soil samples are determined through a comparisonof observed γ-ray peak counts between the standard soil samples and other samples. For 131I, we propose a method to derive
the efficiency at 364 keV from the experimental efficiencies at
662 keV of 137Cs and at 343 keV of 175Hf. Comparing the efficiencies determined by using the standard soil sample of 134Cs
with those of 137Cs and 175Hf, we evaluate the cascade summing© 2012 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 12/27/2012

6

Asai

J. Nucl. Radiochem. Sci., Vol. 12, No. 1, 2012

corrections for the γ rays of Cs in soil samples experimentally. To easily calculate the cascade summing corrections forvolume sources, we examine a simplified method using averaged efficiencies, and evaluate its validity through a comparison of the calculated correction factors with the experimental
ones.
134

Efficiency / %2.1. Preparation of standard soil samples. The standard
soil samples were prepared as follows:
1) Hydrochloric or nitric acid solution containing 134Cs, 137Cs,
175
Hf, or 88Zr is prepared.
2) A small part of the solution is precisely pipetted andadmixed with soil. Then, the soil is packed into a standard
sample container.
3) Another small part of the solution is pipetted on a Ta disk
and evaporated to dryness to make a point source.
4) Radioactivity concentration in the solution is determined bymeasuring γ rays in the point source using a Ge detector
whose efficiency is determined precisely.
5) Radioactivity in the standard soil sample is calculated fromthe above concentration and the volume of the pippeted
solution.
To prepare the hydrochloric acid solution containing 134 Cs
and 137Cs, we used commercially available 134Cs and 137Cs solution. The 8 8 Zr and 175 Hf nuclei were produced in the89
Y(p,2n) 88Zr and 175 Lu(p,n)175 Hf reactions by bombarding a
metallic foil of Y (or Lu) with a 32 MeV (or 13 MeV) proton
beam using the 20 MV tandem accelerator at Japan Atomic
Energy Agency (JAEA). The irradiated target was dissolved
with conc. HCl solution, and 88Zr (or 175Hf) were chemicallyseparated from Y (or Lu) with anion-exchange chromatography.7 The effluent containing 88Zr (or 175Hf) from the column
was evaporated to dryness, and then it was dissolved in 4 M
HNO3 solution.
The soil was taken from a field at Tokai-mura in Ibaraki prefecture on April 2, 2011. Since the surface of the field wascontaminated, we used the soil taken from the underground at
more than 60 mm below the ground surface. The soil was
stuffed into a standard sample container (made of plastic, with
48 mm in diameter and 59 mm in height), and 134Cs and 137Cs
radioactivities in the soil were measured with a Ge detector
prior to the admixture of the radioactive solutions. Then, thesoil was moved into a glass dish with a 100 mm diameter, andthe radioactive solution was dropped on the surface of the soil
to be distributed as broad as possible, but not to touch the glass
wall. The volume of the solution admixed with the soil was
2000 µL for 134Cs, 300 µL for 137Cs, 2000 µL for 88Zr, and 500µL for 175Hf. To evaporate unwanted solution, the surface ofthe soil was heated under an infrared lamp for approximately
10 min. Then, the soil was moved into a plastic bag, andshaken in it to make a uniform distribution of the radionuclides.
After the soil was moved back into the standard container,
radioactivities remained in the plastic bag were measured witha Ge detector; they were less than 0.4% of the total radioactivities admixed with the soil. Finally, the container was sealedwith a container cap and with another plastic bag.
The point source of 175Hf was prepared by dropping 100 µLof the 175Hf solution on a Ta disk and evaporating it to dryness.
For 88Zr, 134Cs, and 137Cs, since the volume of the solution was
more than 100 µL, the solution was made absorbed into a small
piece of glass filter on a Ta disk, and gently evaporated on a hot
plate at 115 °C. This procedure was repeated several times.
Total volume of the solution dropped on the Ta disk was 200µL for 88Zr, 300 µL for 137Cs, and 300 µL and 1500 µL for 134Cs.
Each source was sealed with a plastic tape and in a small plastic bag.

Point source at 77 mm

Total efficiency

100

Residual / %2. Experiments and Results(a)Full-energy
peak efficiency+4 (b)
+2
0
-2
-4

+1.5%
1.5%

102
103
Gamma-ray Energy / keV

Figure 1. (a) Total and full-energy peak efficiencies for point
sources placed at a source-to-detector distance of 77 mm. (b)Residuals of the measured full-energy peak efficiency values to thefitted curve.

2.2. Radioactivity measurement for point source.
Radioactivities in the point sources were measured with a 28%
n-type coaxial Ge detector (ORTEC GMX). The source wasplaced at the source-to-detector distance of 77 mm to reducethe influence of the cascade summing effect. Full-energy peakefficiencies of the detector were determined using a 152 Eu
source and a mixed γ-ray standard source containing 241Am,
109
Cd, 57Co, 137Cs, 60 Co, and 88Y. The disintegration rate of152
Eu in the source was guaranteed with an uncertainty of±1.3% (1σ). Those of the mixed γ-ray standard source were±1.5% (1σ). Gamma-ray peak counts observed in the decay of152
Eu, 60Co, and 88Y were influenced by the cascade summing
effect. The correction factors were calculated using total efficiencies and full-energy peak efficiencies determined in thiswork, and using information on the decay schemes. The
deduced full-energy peak efficiencies are plotted in Figure 1
together with a fitted curve. For γ rays with energies of 120–
1840 keV, a fitted curve was obtained through a least-squares
fitting of the following equation to the experimental efficiencies:3

εf (E) = a1 + ∑ a2n exp (–a2n+1E) ,

(1)

n=1

where ε f (E) is the full-energy peak efficiency at the γ-ray
energy E, and a n are the fitting parameters. The efficiency
curve in the <100 keV region was calculated using absorption
coefficients of γ rays in Ge and other materials existing
between Ge and the source, and was connected with the fitted
curve in the >120 keV region. Uncertainties of the fitted curve
were evaluated to be ±1.5% for 240–1500 keV γ rays from thedeviations between the fitted curve and the experimental values.
Total efficiencies of the Ge detector, which are used to calculate the cascade summing corrections, were determined
experimentally for the 343 and 662 keV γ rays using the 175Hf
and 137Cs point sources, respectively. For 175Hf, contributions

Efficiency Calibration of Ge Detector for 131I and 134Cs in Soil Samples

A = Ni /Ii /εf (Ei)/Ci,(2)

where Ni is the observed peak count rate of the γ ray i in unit ofcps (counts per second), Ii is the emission probability of the γ
ray i, Ei is the energy of the γ ray i, and Ci is the correction factor of cascade summing for the γ ray i. For 134 Cs, a decay
scheme containing 11 γ transitions9 depicted in Figure 2 wasused to calculate the cascade summing corrections, where all
the combinations of cascading γ rays including triple and quadruple cascades were taken into account. For 175Hf, a decay
scheme containing 8 γ transitions9 was employed. Summingwith characteristic X rays following internal conversion (IC)and electron capture (EC) is fully taken into account, whileangular correlations and summing with Bremsstrahlung X raysand β rays are not taken into account because their contributions are small under the present experimental condition. The
deduced correction factors for 134Cs are summarized in Table 1.
The correction factors for the 393 keV and 662 keV γ rays of88
Zr and 137Cs, respectively, were 1.0 because their initial levels
have long lifetimes.
From the deduced disintegration rates of the radionuclides in
the point sources, we have derived the radioactivity concentrations in the solution, and determined the disintegration rates of134
Cs, 137Cs, 175 Hf, 88Zr, and 88Y in the standard soil samples
with uncertainties of ±1.8–4.0%.
2.3. Efficiency determination for soil sample. Figure 3
shows a geometry for the measurement of soil samples in the

0

134

Cs

27.28%

4+

2.506%+

3

70.23%
0.045%

4
2+

0.008%

2++

1969.9604.7 (97.62%)

4+1365.2 (3.014%)
802.0 (8.69%)
569.3 (15.38%)
326.6 (0.0162%)1038.6 (0.988%)
475.4 (1.486%)242.7 (0.0272%)
795.9 (85.53%)
1168.0 (1.789%)
563.2 (8.35%)

of weak γ-ray lines other than the 343 keV one in the decay
scheme of 175Hf were subtracted from the total counts, whichwere estimated from the observed γ-ray peak counts and peakto-total ratios determined in this work. A total efficiency curve
was calculated by a method described in Reference 8 using
total absorption coefficients of γ rays. This calculation systematically underestimates the total efficiencies by a factor of 1.5–
2.0, because the contribution of scattered γ rays off the Pb
shield and other materials surrounding the detector are nottaken into account in this calculation. Thus, we scaled the calculated efficiency curve to fit the experimental efficiencies asshown in Figure 1.
Using these efficiency curves, disintegration rates A (in unitof Bq) of 134Cs, 137Cs, 175Hf, 88Zr, and 88Y (the daughter nuclideof 88Zr) in the point sources were determined with the following equation:

1643.3
1400.61168.0

134

Cs

131

I

Eγ / keV
475.4
563.2
569.3
604.7
795.9
802.0
1038.61168.01365.2
80.2
284.3
364.5
637.0

604.7

0+

0

134

Ba

Figure 2. Decay scheme of 134Cs,9 with which we calculated the cascade summing corrections for the γ rays of 134Cs.

Ge detector

Sample container

Pb

Cu

100 mmFigure 3. Schematic drawing of our detector setup for measurementsof soil samples.

TABLE 1: Correction factors of cascade summing for γ rays in the decay of 134Cs and 131I, calculated for the
point source placed at the source-to-detector distance of 77 mm and 4 mm, and for the volume source of soil
samples (48 mm in diameter and ~55 mm in height) placed at 4 mm from the detector window. For the volume source, the correction factors are calculated by the simplified method using averaged efficiencies
Nuclide7

J. Nucl. Radiochem. Sci., Vol. 12, No. 1, 2012

Calculated correction factors of cascade summing: C
Point source at 77 mm
Soil sample
Point source at 4 mm
0.955
0.898
0.684
0.952
0.891
0.662
0.952
0.891
0.664
0.971
0.933
0.782
0.971
0.932
0.781
0.956
0.899
0.686
0.986
0.970
0.912
1.013
1.037
1.149
1.028
1.075
1.284
0.972
0.933
0.775
0.970
0.941
0.810
1.00071.00171.009
1.00011.00031.0016Asai

J. Nucl. Radiochem. Sci., Vol. 12, No. 1, 2012

rays emitted following EC and IC; it is estimated that 97% of
the summing events results from the sum with Lu K X rays.
Fortunately, the events arising from the sum of the 343 keV γray peak with the Lu K X rays (including full-energy peaks andscattered components) are clearly visible in the spectrum asshown in Figure 6. By adding these summing events with the
343 keV peak counts, we can obtain the corrected efficiency
for the 343 keV γ ray. The efficiency curve was obtained
through a fitting of a linear function in a log-log plot to theexperimental efficiencies at 343 and 662 keV, which is drawn
by a dashed line in Figure 5(a). As shown in Figure 5(a), thisstraight line well reproduces the full-energy peak efficiency
curve within the energy range of 300–660 keV, leading to theprecise determination of the full-energy peak efficiency for the
364 keV γ ray of 131I.
The comparison of this fitted line (dashed one) with theexperimental efficiencies allows us to estimate the correction
factors of cascade summing for the γ rays of 134Cs in soil samples. The efficiency for the 605 keV γ ray of 134Cs is found to
be 6.7% lower than the fitted line, which corresponds to the

Hf 343(a) Without cascadesumming correction
Hf 89

796
Y 898

Cs 605

175

88

200

300

100
270°

Ge

95

90°

0

Container
180°0°(b) With cascadesumming correction

Residual / %100(b) 137Cs 662 keV

100
200
Angle / Degree

300

Figure 4. Relative γ-ray count rates observed at 8 different directionsof the sample container for (a) 134Cs and (b) 137Cs in the standard soil
samples. The geometry of the detector and the sample container isalso drawn in the figure.

+8
+4
0
-4
-8

Cs 662

Cs 605 keV

137

134

(a)

88

100

90
0
105

Relative -ray Count Rate

Full-energy
peak efficiency

134
Cs
88

Hf 343
Zr 393

175

Total efficiency

134

10

1

Efficiency / %Relative -ray Count Rate95

90

Cs 662
137

100

105
100

Soil sample

175

Full-energy
peak efficiency

Efficiency / %present work. We used a horizontal-type Ge detector with arelative efficiency of 28% (ORTEC GMX). The sample container was placed so that its radial side should face the front
window of the Ge detector. The distance between the window
and the sample container was 4 mm.
To verify the homogeneity of radioactivity distributions inthe standard soil samples, the direction of the sample container
facing the detector was changed several times by axially rotating the container at 45° (or 90°) steps. Figure 4 shows relative
γ-ray count rates for 134Cs and 137Cs observed at the 8 different
directions. It was found that the observed γ-ray count rates
fluctuated within ±2%, indicating that the good homogeneity
was achieved for the standard soil samples. To minimize theinfluence of this fluctuation, we adopted the average countrates to deduce detector efficiencies.
Full-energy peak efficiencies determined by measuring theγ rays of 134 Cs, 137Cs, 175Hf, 88Zr, and 88Y in the standard soil
samples are shown in Figure 5. Open circles plotted in Figure5(a) denote the efficiencies without cascade summing corrections, while closed circles in Figure 5(b) denote the efficiencies
with cascade summing corrections whose details are describedin the next section. A solid curve in Figure 5(a) shows a fullenergy peak efficiency curve obtained by fitting eq 1 to thecorrected efficiencies, which is also drawn in Figure 5(b).
Although the efficiencies plotted in Figure 5(a) are largely
scattered because of the cascade summing effect, we have to
use these non-corrected efficiencies in the analysis of each γ
ray to deduce the 134Cs radioactivity, because the cascade summing corrections are compensated between the measurementsof soil samples and the 134 Cs standard. Using these standard
soil samples and resultant efficiencies, we can deduce theradioactivities of 134Cs and 137Cs in soil samples precisely.
The full-energy peak efficiency for the 364 keV γ ray of 131I
was extracted from the experimental efficiencies at 343 and662 keV measured with the 175Hf and 137Cs standard soil samples, respectively. For this purpose, the cascade summing correction for the 343 keV γ ray have to be done properly. The 343
keV γ ray of 175Hf is summed with the 89 keV γ ray and Lu K X

Y 1836

8

+2%

(c)

2%

102
103
Gamma-ray Energy / keV

Figure 5. Total and full-energy peak efficiencies for soil samples.
Open circles plotted in (a) denote the efficiencies without cascadesumming corrections, while closed circles in (b) denote the efficiencies with cascade summing corrections. A full-energy peak efficiency curve in (a) and (b) is obtained by fitting eq 1 to the corrected
efficiencies. A dashed line in (a) is obtained by fitting a linear function in a log-log plot to the experimental efficiencies at 343 and 662
keV, where the efficiency at 343 keV is corrected for the cascadesumming effect. Residuals of the corrected full-energy peak efficiency values to the fitted curve are given in (c).

102

1
V

C1

100
200
300
400
Gamma-ray Energy / keV

Figure 6. Gamma-ray spectrum observed with the 175Hf standard
soil sample.

correction factor of 0.933 for the 605 keV γ ray. Those for the
563 and 569 keV γ rays are deduced to be 0.914 and 0.891,
respectively. These correction factors are compared with thecalculated ones in the next section.
To determine the full-energy peak efficiency at 364 keV, it
should be better to use the 393 keV γ ray of 88Zr because no
cascade summing correction is needed for this γ ray. However,
because of the weak radioactivity of the 88Zr point source, we
could not obtain the accurate values of the 88Zr and 88Y radioactivities in this work. Thus, we did not use the 88Zr and 88Y
data to determine the efficiency at 364 keV in this work. Only
relative values were used to obtain a fitted curve in the next
section.
3. Discussions
3.1. Cascade summing corrections for 134Cs in soil sample.
If one can prepare a standard soil sample of 134 Cs like thiswork, no cascade summing correction is needed to determine
134
Cs radioactivities in soil samples. On the other hand, if one
cannot prepare a standard soil sample of 134Cs, one has to calculate the correction factors of cascade summing for 134Cs. As
already mentioned in Section 1, the exact calculation of cascade summing corrections for a volume source is very difficult
because it is hard to experimentally obtain total and full-energy
peak efficiencies at any parts of the volume source. Thus, it isworthwhile proposing an easier method to estimate the correction factors as an alternative to the exact calculation.
Here, we examine the method to calculate correction factors
for a volume source using averaged efficiencies.10 Consider the
decay scheme consisting of two γ transitions (γ1 and γ2 ) in a
one-to-one cascade like 60Co. The correction factor for γ1 for apoint source is calculated as
C1 = 1 − εT (E2),(3)

where εT (E2) is the total efficiency for a point source at the γray energy E 2 . For a volume source, the correction factor is
calculated with the following equation: 6
C1 = 1 −

1
V

=1−

1
V

ʃ ε (E , r)ε (E , r)dV ⁄ V1 ʃ ε (E , r)dV
f

1

T

2

f

ʃ ε (E , r)ε (E , r)dV ⁄ ε (E ),
f

1

T

2

f

1

9

ʃ ε (E , r)ε (E , r)dV
f

1

T

2

ε f (E1)ε T (E2),(5)

and convert eq 4 into

101

0

J. Nucl. Radiochem. Sci., Vol. 12, No. 1, 2012

dard soil sample. In the present simplified calculation, we
replace ʃ εf (E1, r)εT (E2, r)dV/V into ε f (E1)ε T (E2), that is,

433.0

343.4 + K X

103

229.6

89.4

104

353.3

Counts / Channel

Lu K X

105

343.4

Efficiency Calibration of Ge Detector for 131I and 134Cs in Soil Samples

1(4)

where ʃ ε(r)dV/V means the integration of the efficiency ε(r) at
the position r over the whole volume of the source, dV is thevolume element at each position, and V is the total volume ofthe source. ε denotes the efficiency averaged over the wholevolume of the source, which is equal to ʃ ε (r)dV/V, and isequivalent to the experimental efficiency measured with a stan-1 − ε T (E2),(6)

which is equivalent to eq 3 for a point source.
This approximation (eq 5) systematically underestimates ʃ εf
(E1, r)εT (E2, r)dV/V by ~15% in the present experimental condition. However, if the correction factor C1 is 0.9, the ~15%
deviation induces only 1.5% error to the final result, which isaccurate enough for most of purposes of environmental radioactivity measurements. The accuracy of this approximation
was investigated by several authors11-13 through Monte Carlosimulations or numerical calculations for various nuclides andgeometries. Although the difference between the exact calculation and the simplified one was found to be significant for
cascades involving low-energy X/γ rays, the differences forhigh-energy γ-ray cascades are estimated to be typically of theorder of a few per cent for geometries with averaged total efficiencies of <10%.
There are several sophisticated codes available to calculatecascade summing corrections for volume sources, which are
based on full Monte Carlo simulations or numerical calculations using calculated efficiencies (References 11, 12, and 14
and references therein). However, the recent intercomparison
exercise14 revealed that the calculated correction factors for a
volume source were largely scattered between laboratories bymore than ±10%. This large scattering is probably due toincorrect total efficiencies used in the calculations. On theother hand, the present simplified method utilizes experimental
averaged efficiencies ε f and ε T . This is another advantage ofthis simplified method, because the ε f and ε T can be obtainedwith good accuracies using standard sources, which ensures
the reliability and the accuracy of the deduced correction factors.
To confirm the validity and accuracies of this simplified
method, we calculate the correction factors for the γ rays of
134
Cs, 175 Hf, and 88Y. The total efficiencies ε T (E) are determined using the experimental efficiencies measured with the175
Hf and 137Cs standard soil samples at 343 and 662 keV, and at
Lu K X-ray energy which is extracted from the events originating from the sum of the 343 keV γ-ray peak with the Lu K X
rays observed in the 175Hf spectrum. The total efficiency curve
fitted to the experimental data is shown in Figure 5(b). The
deduced correction factors for 134Cs are summarized in Table 1,
and the corrected full-energy peak efficiencies for 134Cs, 175Hf,
and 88Y are plotted in Figure 5(b) by closed circles.
The full-energy peak efficiencies which seemed to be largely
scattered without corrections turn out to be in line with asmooth fitted curve. This fitted curve also coincides with thedashed line in Figure 5(a) at the energy range of 300–660 keV.
The calculated correction factors for the 569 and 604 keV γ
rays of 134 Cs agree very well with the experimental ones.
Although the correction factors calculated for the 796, 802,
1039, 1168, and 1365 keV γ rays of 134Cs are very different eachother, the corrected full-energy peak efficiencies all come close
to the fitted line within a few % deviations. These results demonstrate that this simplified calculation is accurate enough toestimate correction factors of cascade summing for volume
sources if required uncertainty level is not lower than a few per
cent.
3.2. Cascade summing corrections for 131I in soil samples.
This simplified calculation is also applied to the cascade summing corrections for 131I in soil samples. The decay scheme of131
I contains 19 γ transitions, among which the 364 keV γ ray

10

Asai

J. Nucl. Radiochem. Sci., Vol. 12, No. 1, 20129

has the largest intensity of 81.7%. Using this decay scheme,
we calculate the correction factors for the four intense γ rays of
80, 284, 364, and 637 keV of 131I as summarized in Table 1.
The correction factor for the 364 keV γ ray is 1.0017, indicatingthat the cascade summing correction for the 364 keV γ ray isnegligible.
3.3. Cascade summing corrections for other geometry.
The correction factors summarized in Table 1 are valid only
for the specific geometry of the sources and the detector in thepresent work. However, we can imagine that the correction
factors would resemble if total efficiencies are similar between
one geometry and another. Thus, it is very useful to summarize the correction factors for various geometries, because
using those values other researchers can also obtain a roughestimate of the correction factors for their own geometry. For
this purpose, we present another result of the efficiency calibration and cascade summing corrections for the geometry of ashort source-to-detector distance.
Here, we measured efficiencies of the Ge detector for a point
source placed at a source-to-detector distance of 4 mm. Thiscondition is supposed to be the ones to measure weak radioactivities in environmental samples such as filter paper at theclosest geometry. A 4-mm thick plastic plate was inserted
between the source and the detector to absorb β particles. Fullenergy peak efficiencies were measured by using a mixed γ-ray
standard source containing 109Cd, 57Co, 137Cs, and 60Co, and thepoint sources of 134Cs, 137Cs, and 175Hf prepared in Section 2.1.
A total efficiency curve was calculated with the method
described in Section 2.2 to reproduce the experimental efficiencies measured with the 175Hf and 137Cs sources. The total
efficiency and the full-energy peak efficiencies with and without cascade summing corrections are shown in Figure 7
together with fitted curves. Although the efficiencies withoutcascade summing corrections are largely scattered, the corrected efficiencies are all in line with a smooth fitted curve,(a)Efficiency / %101

Full-energy
peak efficiency

100+8 (b)+4
0-4-8

Residual / %Point source at 4 mm

Total efficiency

+2%
2%

102
103
Gamma-ray Energy / keV

Figure 7. (a) Total and full-energy peak efficiencies for point sources
placed at a source-to-detector distance of 4 mm. Open circles denotethe efficiencies without cascade summing corrections, and closed circles denote the efficiencies with cascade summing corrections. A
full-energy peak efficiency curve is obtained by fitting eq 1 to thecorrected efficiencies. (b) Residuals of the corrected full-energy
peak efficiency values to the fitted curve.

indicating that the cascade summing corrections are appropriate. The correction factors calculated for the γ rays of 134 Cs
and 131I are summarized in Table 1.
4. Conclusion
To measure radioactivities in soil contaminated by the accident of the Fukushima Daiichi Nuclear Power Plant, γ-ray
detection efficiencies of Ge detectors for 131I, 134Cs, and 137Cs insoil samples were determined precisely using standard soil
samples of 134Cs, 137Cs, 175Hf, and 88Zr. The standard soil samples were prepared by ourselves by admixing solutions containing 134Cs, 137Cs, 175Hf, and 88Zr with soil. Contents of 134Cs and137
Cs radioactivities in soil samples were determined through a
comparison of observed γ-ray peak counts between the standard soil samples and other samples, which eliminates theinfluence of the cascade summing effect for 134Cs. For 131I, we
proposed a method to derive the efficiency at 364 keV from theexperimental efficiencies at 343 keV of 175Hf and at 662 keV of
137
Cs. Uncertainties of the deduced efficiency values for 131I,
134
Cs, and 137Cs were evaluated to be ±2.7–3.5%.
The cascade summing corrections for the γ rays of 134Cs insoil samples were evaluated experimentally from the deviations
among the experimental efficiencies of 134Cs, 137Cs, and 175Hf.
To easily calculate the cascade summing corrections for volume sources, we examined a simplified method using averaged
efficiencies, and evaluated its validity through a comparison of
the calculated correction factors with the experimental ones.
The calculated correction factors agreed very well with theexperimental ones, demonstrating the validity of this method.
References(1) http://radioactivity.mext.go.jp/old/ja/distribution_map_
around_FukushimaNPP/ (in Japanese).
(2) T. K. Sato, Y. Kaneya, M. Asai, K. Tsukada, A. Toyoshima,
N. Sato, K. Ooe, Y. Miyamoto, K. Yasuda, K. Ninomiya,
M. Matsuda, S. Mitsuoka, H. Ishiyama, and Y. Nagame (tobe published).
(3) D. S. Andreev, K. I. Erokhina, V. S. Zvonov, and I. Kh.
Lemberg, Instr. Expt. Techn. 15, 1358 (1972).
(4) D. S. Andreev, K. I. Erokhina, V. S. Zvonov, and I. Kh.
Lemberg, Izv. Akad. Nauk. SSSR, Ser. Fiz. 37, no. 8, 1609
(1973).
(5) G. J. McCallum and G. E. Coote, Nucl. Instrum. Methods
130, 189 (1975).
(6) K. Debertin and U. Schötzig, Nucl. Instrum. Methods 158,471 (1979).
(7) Z. J. Li, A. Toyoshima, K. Tsukada, and Y. Nagame,Radiochim. Acta 98, 7 (2010).
(8) R. Griffiths, Nucl. Instrum. Methods 91, 377 (1971).
(9) R. B. Firestone, Table of Isotopes, 8th ed., 1998 Update(John Wiley & Sons, New York, 1998).
(10) P. De Felice, P. Angelini, A. Fazio, and R. Biagini, Appl.
Radiat. Isot. 52, 745 (2000).
(11) D. Arnord and O. Sima, J. Radioanal. Nucl. Chem. 248,
365 (2001).
(12) M.-C. Lépy, L. Ferreux, and S. Pierre, Appl. Radiat. Isot.
70, 2137 (2012).
(13) P. Dryák, J. Šolc, and P. Kovář, Appl. Radiat. Isot. 70, 2130
(2012).
(14) M.-C. Lépy, T. Altzitzoglou, M. J. Anagnostakis, M.
Capogni, A. Ceccatelli, P. De Felice, M. Djurasevic, P.
Dryak, A. Fazio, L. Ferreux, A. Giampaoli, J. B. Han, S.
Hurtado, A. Kandic, G. Kanisch, K. L. Karfopoulos, S.
Klemola, P. Kovar, M. Laubenstein, J. H. Lee, J. M. Lee,K. B. Lee, S. Pierre, G. Carvalhal, O. Sima, Chau Van Tao,
Tran Thien Thanh, T. Vidmar, I. Vukanac, and M. J. Yang,
Appl. Radiat. Isot. 70, 2112 (2012).