Applied Radiation and Isotopes 71 (2013) 11–20

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Applied Radiation and Isotopes

0969-80

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Self-absorption correction in determining the 238U activity of soil samplesvia 63.3 keV gamma ray using MCNP5 code

Ngo Quang Huy a,n, Do Quang Binh b, Vo Xuan An a, Truong Thi Hong Loan c, Nguyen Thanh Can c

a Ho Chi Minh City University of Industry, 12 Nguyen Van Bao Street, Go Vap District, Ho Chi Minh City, Vietnamb Ho Chi Minh City University of Technical Education, 1 Vo Van Ngan, Thu Duc Street, Ho Chi Minh City, Vietnamc Ho Chi Minh City University of Natural Sciences, 227 Nguyen Van Cu Street, District 5, Ho Chi Minh City, Vietnam

H I G H L I G H T S

c Determination of the 238U activity via 63.3 keV gamma rays.c Self-attenuation factors of 63.3 keV gamma rays for cylindrical sample container.c The density, chemical composition and geometry effects are taken into account.c Determination of the 238U activity in three soil types: grey, alluvial and red soils.

a r t i c l e i n f o

Article history:

Received 27 January 2012

Received in revised form

5 September 2012

Accepted 6 September 2012Available online 23 September 2012

Keywords:

Self-absorption

Self-attenuation factor238U activity

63.3 keV

MCNP5 code

HPGe detector

43/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.apradiso.2012.09.004

esponding author. Mob.: þ84 908 394 813.

ail addresses: hlchau@hcm.vnn.vn, huyhanq@

a b s t r a c t

The essential issue in analyzing the activity of 238U in an HPGe detector based gamma spectrometer via

63.3 keV line is relating to the strong self-absorption of this weak gamma ray in sample material. The

present work suggests a method of the self-absorption corrections for 63.3 keV gamma rays by a

combination of experimental measurements and Monte Carlo MCNP5 calculations. The effects of

sample chemical composition, density and geometry were calculated in terms of self-attenuation

factors. The method, developed for a cylindrical sample geometry, accounted for variable sample

heights and densities. The analysis of 238U activity was applied for three main soil types in Vietnam,

which are grey, alluvial and red soils. The results obtained with the above outlined method were in

good agreement with those derived by other methods.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The activity of 238U is commonly determined in an HPGedetector based gamma spectrometer by indirect methods. Thedirect analysis of the 238U activity is impossible because it emitstwo gamma rays with very weak intensities, namely 49.55 keV(0.0697%) and 113.5 keV (0.0174%), which lie in a large Comptonscattering background of gamma spectrum.

The indirect analysis of 238U is accomplished by means ofthe measurement of gamma rays emitted from daughter nuclidesin uranium decay chains. The daughter nuclides often used are:234Th (T1/2¼24.1 days), 234mPa (T1/2¼1.17 min), 214Pb (T1/2¼

26.8 min) and 214Bi (T1/2¼19.9 min). Among them, 214Pb and214Bi are widely applied because of large intensities of gamma

ll rights reserved.

yahoo.com (N.Q. Huy).

rays emitted from these nuclides. They are 241.9 keV (7.268%),295.2 keV (18.5%), 351.9 keV (35.6%) gamma lines emitted from214Pb and 609.3 keV (45.49%), 768.4 keV (4.891%) and 1120.3 keV(14.909%) gamma lines emitted from 214Bi. The analysis of 238Uactivity by using 214Pb and 214Bi faces with two disequilibria. Thefirst is a disequilibrium between 226Ra and 214Pb, 214Bi due to aleakage of 222Rn (T1/2¼3.825 days), which is a noble gas and is thedecay product of 226Ra. To overcome this disequilibrium, samplesare sealed for a month to attain the equilibrium between 226Raand 222Rn. Then, the average activity of 214Pb and 214Bi can beassigned to that of 226Ra as reported in Huy and Luyen (2006).This value is not considered to be 238U activity because there isstill a second geochemical disequilibrium between 226Ra and238U. The disequilibrium is caused by the different chemicalproperties of 238U and 226Ra in soil environment and a longlifetime of 1620 years for 226Ra. So, the 238U activity obtained byindirect analysis via 214Pb and 214Bi is only approximate whenneglecting the geochemical disequilibrium.

N.Q. Huy et al. / Applied Radiation and Isotopes 71 (2013) 11–2012

234Th and 234mPa are the nearest daughters of 238U and arevery short-lived nuclides compared to 238U, so radioactive equili-brium is quickly established. As a result, the geochemical dis-equilibrium between these nuclides and 238U can be ignored andthe activities obtained for these nuclides can be assigned to thatof 238U. The gamma rays preferably used for 238U analysis are63.3 keV (4.8%) and 92.6 keV (5.58%) emitted from 234Th, and766.4 keV (0.316%) and 1001.0 keV (0.839%) from 234mPa (Yucelet al., 1998, 2009; Huy and Luyen, 2004; Dowdall et al., 2004; DeCorte et al., 2005; Kaste et al., 2006). However, from the point ofview of analysis of 238U activity in soil samples with low specificactivities, the measurement of 766.4 keV and 1001.0 keV gammarays can give activities with large uncertainties because of theirweak intensities and low efficiencies of germanium detectors athigh energies. Gamma ray of 92.6 keV is a doublet, consisting of92.4 keV (2.81%) and 92.8 keV (2.77%) and is interfered by otherK-X- and gamma peaks, including 93.3 keV. So, in practice, the92.6 keV peak cannot be separated from the multiplet of about93 keV. The remaining 63.3 keV gamma ray includes contribu-tions from the 63.3 keV gamma ray (4.8%) emitted from 234Th,63.9 keV gamma ray (0.023%) from 231Th and 63.9 keV gamma ray(0.255%) from 232Th, but the contributions of 231Th and 232Th canbe neglected (Kim and Burnett, 1985; Huy and Luyen, 2004).Therefore, the 63.3 keV gamma ray is a preferred candidate fordetermination of 238U activity in environmental soil samples.

The important problem in the use of 63.3 keV line for analysisof 238U activity is the strong self-absorption of this weak gammaray in sample material. As reported in Hasan et al. (2002), thevalues of the self-absorption correction factor for the IAEAreference samples of 1.0 g/cm3 and 1.4 g/cm3 densities, packedin 5 cm3 tube geometry and measured with a well-type HPGedetector, are approximately 13%, 5% and 2% for the energy rangesof 40–160 keV, 200–600 keV and 4600 keV, respectively. There-fore, the self-absorption corrections must be taken into accountwhen the 63.3 keV gamma ray is used. For the volumetric samplewith a homogeneous distribution of the attenuating material andthe radioactive source, the influencing factors on self-absorptionare composed of chemical composition, density and geometryeffects. The self-absorption correction factor for a sample understudy with given chemical composition, density and geometricaldimension was determined by calculating the ratio between itscounting efficiency and that of a standard reference sample withknown self-absorption property. Some works have made correc-tions for only density and geometry effects neglecting thecomposition effect (Kitto, 1991; Melquiades and Appoloni, 2001;Abbas, 2001; Vargas et al., 2002; Huy and Luyen, 2004). The self-absorption corrections for all three effects, including the compo-sition one, were conducted in the works of Hasan et al. (2002),San Miguel et al. (2002), Nachab et al. (2004) and CarrazanaGonzalez et al. (2010). An approach to perform the self-absorption corrections is to calculate the self-attenuation factorsuggested by Debertin and Helmer (1988) and developed byKorun (1999, 2000), Korun and Vidmar (2003), Boshkova andMinev (2001) and Boshkova (2003). This factor describes theprobability of interaction between the photons and the samplematerial and is given by the ratio between the counting efficiencyfor the actual sample eV(m,E), where m, E and V denote theattenuation coefficient, the energy of photon and the samplevolume, respectively, and the counting efficiency for the samesample-detector geometry but without self-attenuation eV(0,E)(Korun, 1999):

FV ðm,EÞ ¼eV ðm,EÞ

eV ð0,EÞð1Þ

The advantage of the self-attenuation factor is that thedetector properties enter the expression via both efficiencies

and cancel out to a large extent in the ratio. Therefore, the self-attenuation factor is given as a function of sample parameters,disregarding the detector properties.

The aim of present work is to develop a method to analyze238U activity in soil samples via 63.3 keV by a combination ofexperimental measurement and Monte Carlo MCNP5 calculation.The corrections of all chemical composition, density and geome-try effects were carried out by application of the self-attenuationfactor. The method, developed for a cylindrical sample geometry,accounted for variable sample heights and densities. The analysisof 238U activity was applied for three main soil types in Vietnam,which are grey, alluvial and red soils.

2. Experimental

The measuring system used in the study was the CanberraHPGe GC1518 p-type detector based gamma spectrometerinstalled at the Center for Nuclear Techniques Ho Chi Minh City,Vietnam. It has a relative efficiency of 15% and an energyresolution of 1.8 keV at 1332 keV line. The geometry dimensionsand material compositions of the lead shield and the GC1518detector were described in Huy et al. (2007). An important parameterof the HPGe GC1518 p-type detector is its thickness of dead layer,which was 0.35 mm of germanium equivalent as provided by themanufacturer in 1996 and grown over operation time to 0.65 mm in1999, 1.15 mm in 2005 and 1.46 mm in 2009 (Huy and Ngo Quang,2010). The sample container used in the measurement had cylindricalform of 7.2 cm diameter and 5 cm height. The height of samplematerial depended on its mass and density.

3. Reliability of MCNP5 calculation of self-absorptioncorrections for 63.3 keV gamma rays

The reliability of MCNP5 calculation of self-absorption correc-tions for 63.3 keV gamma rays was controlled by using a 238Ustandard sample and a 238U water solution, chemical composi-tions of which are presented in Table 1. The 238U standard wassupplied by Institute of Nuclear Science and Technology in Hanoi(INST sample) with a specific activity of 1296712 Bq/kg. The238U water solution was prepared by addition of an amountof [238U]uranyl-acetate to water with an activity of 119397126 Bq/kg. Different samples of heights between 0.2 cm and2.4 cm with 0.1 cm increments for INST sample and between0.2 cm and 1.8 cm with 0.1 cm increments for water solutionwere measured in the spectrometer. With the model of detector,lead shield and sample cylindrical container as described in Huyet al. (2007) we simulated gamma spectra by the MCNP5calculation. The experiment of measuring the efficiencies of INSTand water samples were carried out in 2003, therefore the deadlayer thickness of GC1518 detector was taken to be 0.9 mm. TheF8 tally of the MCNP5 code is a pulse height tally, which providesthe energy distribution of pulses created in a detector by radia-tion. It was used to extract the pulse height distribution of gammaspectra, and the 63.3 keV full energy peak efficiency was deter-mined. Simulation relative error was kept under 0.3% with a totalof 3,000,000 source gamma-rays. The densities, chemical compo-sitions and geometries of INST and water samples included in theinput data of the MCNP5 code are presented in Table 1.

From the gamma spectra measured in the GC1518 detectorbased gamma spectrometer, the experimental efficiencies of63.3 keV full energy peaks were determined with relative uncer-tainties of less than 5% and plotted in Fig. 1 against the sampleheight. From Fig. 1 it is seen that the curves calculated by theMCNP5 code describe well experimental data. Besides, the ratios

Table 1Densities, chemical compositions and geometries of INST sample and water solution.

Sample Density (g/cm3) Chemical composition Range of sample height (cm)

INST sample 1.513 CaCO3 (71.33%), MgCO3 (24.84%), H2O (3.83%) 0.2–2.4 (23 samples)

Water solution 1.000 H2O (100%) 0.2–1.8 (17 samples)

Fig. 1. Experimental and calculated efficiencies of 63.3 keV full energy peaks for INST sample and water solution versus sample heights.

Fig. 2. The efficiencies of 63.3 keV full energy peaks plotted against the heights of the INST samples. (2.1) Narrow beam experiment: (a) measurement and its fitting curve.

(2.2) Cylindrical container: (b) measurement and its fitting curve and (c) MCNP5 calculation and its fitting curve.

N.Q. Huy et al. / Applied Radiation and Isotopes 71 (2013) 11–20 13

ecal/eexp, averaged over the height ranges of 0.2–2.4 cm for INSTsample and 0.2–1.8 cm for water solution are equal to0.97670.049 and 0.99070.024, respectively. It is clear that theseratios are very close to unity, which confirms the reliability ofefficiency calculation by using MCNP5 for different sampledensities, chemical compositions and geometries.

4. Self-attenuation factors of 63.3 keV gamma raysfor different soil types

4.1. Formulation of the self-attenuation factor

The self-attenuation factor FV ðm,EÞ ¼ ðeV ðm,EÞÞ=ðeV ð0,EÞÞ of63.3 keV gamma rays was applied for the INST sample with thechemical composition included in Table 1 and the densityr¼1.513 g/cm3, containing in the cylindrical container of 7.2 cmdiameter. Two measurements with the INST material wereperformed. The first was a direct transmission measurement ofa narrow 59.5 keV gamma beam from an 241Am source with theINST attenuating material containing in the cylindrical container.The counts of gamma rays after the absorber were plotted versus

the sample heights varied from 0.2 cm to 4.4 cm with 0.2 cmincrements (Fig. 2(2.1)). The experimental data were fitted withan exponential function of the height:

eðm,hÞ ¼ eðm,0Þ expð�mhÞ ð2Þ

where m is the linear attenuation coefficient, which is equal to0.3696 cm�1 obtained from the fitting curve (curve a). The curvea was normalized so that it is equal to the efficiency of theINST cylindrical sample measurement at the height zero, i.e.,e(m,0)¼0.0433.

The second measurement was carried out with the INSTsamples containing in the cylindrical container of the sampleheights from 0.2 cm to 2.4 cm with 0.1 cm increments. Thesample in this measurement played two roles, namely the radio-active source and the attenuating material. The experimentalcounting efficiencies were plotted against the height(Fig. 2(2.2)) and fitted with an exponential function (curve b).The MCNP5 calculation results performed for this measurementat five height values of 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm and 2.5 cmwere presented in Fig. 2(2.2) and fitted with an exponentialfunction (curve c). These two fitting curves were used for purelymathematical description of the experimental and MCNP5

N.Q. Huy et al. / Applied Radiation and Isotopes 71 (2013) 11–2014

calculation data. They showed that the data of the cylindricalsample experiment were also described by an exponential func-tion, similar to one in the narrow beam experiment (curve a). Theexponential function in this case has the following form:

eðmeff ,hÞ ¼ eð0,hÞ expð�meff hÞ ð3Þ

where e(0,h) is the efficiency without self-attenuation and meff isthe effective attenuation coefficient.

It should be noted that e(m,0) in Eq. (2) represents theefficiency in the case of a height zero, whilst e(0,h) in Eq. (3) isthe efficiency obtained at effective attenuation coefficient zero.Furthermore, the linear attenuation coefficient m in Eq. (2) havingdimension of cm�1 expresses the attenuation in the samplematrix only because the point radioactive source is locatedbehind the absorber, whilst the effective attenuation coefficientmeff having also dimension of cm�1 reflects two effects, the first ofwhich is the attenuation in the sample matrix and the second isthe volumetric distribution of radioactive source. As a result, theeffective attenuation coefficient meff can be defined as follows:

meff ðr,hÞ ¼ aðhÞr ð4Þ

where a(h) is a mass attenuation coefficient having dimension of(g/cm2)�1. In the narrow beam measurement, it depends only onmaterial matrix of the sample. In the experiment of cylindricalradioactive and attenuating samples, a(h) is dependent of thesample matrix and the height. So Eq. (3) becomes:

eðmeff ,hÞ ¼ eð0,hÞ exp½�meff ðh,rÞh� ¼ eð0,hÞ exp½�aðhÞhr� ð5Þ

where e(0,h) is determined at r¼0, i.e., at meff¼0.The MCNP5 code was used for calculating the counting

efficiencies as functions of the INST densities from 0.2 g/cm3 to1.8 g/cm3 with 0.2 g/cm3 increments for the sample heights from0.5 cm to 2.5 cm with 0.5 cm increments (Fig. 3). The calculateddata of counting efficiencies were fitted with exponential function(5), from which the values of e(0,h) and a(h)h were determined(Table 2, rows 1 and 2). The values of a(h) and meff¼a(h)rat r¼1.513 g/cm3 were calculated and reported in rows 3 and 4

Fig. 3. The counting efficiencies calculated for the INST material densities fro

Table 2MCNP5 calculation results of counting efficiencies for the INST sample with r¼1.513

No. h (cm) 0.5

1 e(0,h) 0.0431

2 a(h)h 0.0898

3 a(h) 0.1796

4 meff¼a(h)r (r¼1.513 g/cm3) 0.2717

5 ecal(meff,h) 0.0376

6 eexp(meff,h) (75%) 0.0361

of Table 2. It is noted that e(0,h) was obtained at r¼0, i.e., at meff¼0according to Eq. (4). From rows 1 and 4 of Table 2 it is revealed thate(0,h) and meff¼a(h)r decrease with the increasing height, whilste(m,0) and m are constant in the narrow beam experiment. Thecalculated counting efficiencies ecal(meff,h) for five h values from0.5 cm to 2.5 cm were obtained (Table 2, row 5), which are in goodagreement with the experimental ones eexp(meff,h) (Table 2, row 6).

Based on the good agreement of the counting efficiencycalculated by Eq. (5) with the experimental data, the attenuationfactor can be expressed as follows:

Fðmeff ,hÞ ¼eðmeff ,hÞ

eð0,hÞ¼ exp �meff ðr,hÞh

� �¼ exp �aðhÞhr

� �ð6Þ

It is noted that the effective attenuation coefficients meff of0.2717 cm�1, 0.2495 cm�1, 0.2306 cm�1, 0.2148 cm�1 and0.2006 cm�1 at the heights of 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm and2.5 cm, respectively (Table 2, row 4), are less than the linearattenuation coefficient m¼0.3696 cm�1. This difference resultsfrom the difference of the two experiments, where the linearattenuation coefficient m was obtained in an experiment with acollimated gamma beam from the point radioactive source placedbehind the attenuating material, whilst the effective attenuationcoefficient meff was obtained in the case, when the attenuatingmaterial of cylindrical form is also radioactive source. Because thecylindrical radioactive source of a given height is placed close todetector, its counting efficiency is larger than that of the pointradioactive source in the narrow beam measurement with theattenuating material of the same height placed between thesource and the detector. Then the effective product (mh)eff ofcylindrical container measurement should be less than theproduct mh of the narrow beam experiment. The first productcan be written as (mh)eff¼meffh¼mheff, where meff is the effectiveattenuation coefficient and heff is the effective height or the photonsaverage path length (Korun, 1999). The inequality (mh)effomh leadsto meffom if the height h is fixed or heffoh if the linear attenuationcoefficient m is kept unchanged. In the experiment with the INSTsamples, m¼0.3696 cm�1 and meff¼0.2717 cm�1, 0.2495 cm�1,

m 0.2 g/cm3 to 1.8 g/cm3 and the sample heights from 0.5 cm to 2.5 cm.

g/cm3.

1.0 1.5 2.0 2.5

0.0406 0.0381 0.0358 0.0336

0.1649 0.2286 0.2839 0.3314

0.1649 0.1524 0.1419 0.1326

0.2495 0.2306 0.2148 0.2006

0.0316 0.0270 0.0233 0.0204

0.0330 0.0279 0.0241 0.0220

Table 3The measured chemical compositions of grey soil 1, grey soil 2, alluvial soil and

red soil samples, collected in Southern Vietnam.

Chemical

composition

Percentage (%)

Grey soil 1 Grey soil 2 Alluvial soil Red soil

SiO2 83.16 89.32 83.30 33.08

Al2O3 5.34 4.42 4.90 25.46

Fe2O3 0.84 0.5 2.83 18.06

FeO 1.59 0.97 3.55 2.32

TiO2 0.82 0.50 0.69 4.52

MnO – – 0.05 0.22

MgO 1.07 0.04 0.49 0.49

CaO 0.37 0.74 0.68 -

Na2O 0.12 0.12 0.48 0.11

K2O 0.15 0.21 1.04 0.14

P2O5 0.13 0.04 0.10 0.08

Loss of ignition 4.98 2.96 1.58 14.56

N.Q. Huy et al. / Applied Radiation and Isotopes 71 (2013) 11–20 15

0.2306 cm�1, 0.2148 cm�1 and 0.2006 cm�1, so the ratios betweenthe photons average path lengths and the geometrical thicknessesare heff/h¼meff/m¼0.735, 0.675, 0.624, 0.581, and 0.543 at theheights of 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm and 2.5 cm, respectively.

For comparison purpose, we consider the self-attenuationfactor obtained by Debertin and Helmer (1988). For a planesource of thickness h with a homogeneous distribution of theattenuating material and the activity, placed coaxially with thedetector at a far distance, it has the following form:

F 0ðm,hÞ ¼1�e�mh

mhð7Þ

The function F0(m,h) was calculated for the INST sample withthe linear attenuation coefficient m¼0.3696 cm�1 and the sampleheights of 0.01 cm, 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm and 2.5 cm(Fig. 4). Because the source plane is placed at a far distance fromthe detector, we can consider the effective attenuation coefficientmeff independent of the height. In this case, the obtained data ofself-attenuation factor F0(m,h) could be fitted with the functionF(meff,h)¼exp(�meffh) with a constant value of meff. The fittingresult showed that meff¼0.1707 cm�1 with R2

¼0.9994. So, wecan conclude that the self-attenuation factor (7), obtained byDebertin and Helmer (1988) with a given linear attenuationcoefficient m, can be expressed by Eq. (6) with an appropriateeffective attenuation coefficient meff. It is seen that heff/h¼meff/m¼0.46270.046. This value is in good agreement with the ratio of0.46170.027 between the average path sðmÞ and the geometricalthickness h for a slab-shape sample, obtained from the formula(Korun, 1999)

sðmÞ ¼ 1

m1�

mhe�mh

1�e�mh

� �ð8Þ

and averaged over the heights from 0.5 cm to 2.5 cm withm¼0.3696 cm�1.

4.2. Application of the self-attenuation factor to some soil types of

Vietnam

The self-attenuation factor (6) was applied for determining theself-absorption corrections of some soil types of Vietnam. Accord-ing to the soil classification of Vietnam based on the method ofFAO-UNESCO classification, Vietnam has three main soil types,which encompass 93.3% soil area of Vietnam (Ton That Chieuet al., 1991; Vietnam Soil Scientific Society, 1996; Pham QuangKhanh, 1995). They are grey soil (63.8%), alluvial soil (19.9%) andred soil (9.6%). The key chemical compositions of these soil typeswere reported in Pham Quang Khanh (1995). The main composi-tions of grey soil and alluvial soil are SiO2 and Al2O3 with their

Fig. 4. Function F0(m,h)¼ð1�e�mhÞ=mh calculated for the INST sample with m¼0.369

F(meff,h)¼exp(�meffh).

total percentage of about 85–95%. Whilst the main compositionsof red soil are composed of two groups, the first consists of SiO2

and Al2O3 with their total percentage of about 55–65%, and thesecond consists of Fe2O3, FeO and TiO2 with their total percentageof about 25–35%. Other compositions have negligible contribu-tions. Table 3 presents the chemical compositions of four soilsamples, collected in Southern Vietnam and measured by theSouth Vietnam Geological Mapping Division. From Table 3 it isnoted that the measured composition percentages are close tothose given in Pham Quang Khanh (1995).

The self-attenuation factor was calculated by MCNP5 codeusing Eq. (6) for four samples of grey soil 1, grey soil 2, alluvialsoil and red soil. Then the effective attenuation coefficientdepends on chemical composition (c), sample height (h) andsample density (r):

meff ðc,h,rÞ ¼ aðc,hÞr ð9Þ

The counting efficiency has the following form:

eðmeff ,c,h,rÞ ¼ eð0,c,h,0Þ exp½�meff ðc,h,rÞh� ¼ eð0,c,h,0Þ exp½�aðc,hÞhr�ð10Þ

where e(0,c,h,0) is the counting efficiency without self-attenuation obtained at r¼0, i.e., at meff¼0. The self-attenuationfactor can be described by the expression:

F1ðmeff ,c,h,rÞ ¼eðmef f ,c,h,rÞeð0,c,h,0Þ

¼ exp �meff ðc,h,rÞh� �

¼ exp �aðc,hÞhr� �

ð11Þ

The counting efficiencies were calculated for 5 values of thesample heights of 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm and 2.5 cm, and

6 cm�1 depending on the height. The calculated data are fitted with function

Table 4The values of e(0,c,h,0), a(c,h)h and a(c,h) in Eq. (10) for grey soil 1, grey soil 2,

alluvial soil and red soil in the case of sample height h¼2 cm.

Sample e(0,c,h,0) a(c,h)h a(c,h)¼a(c,h)h/h

Grey soil 1 (GS1) 0.0359 0.2424 0.1212

Grey soil 2 (GS2) 0.0359 0.2369 0.1185

Alluvial soil (AS) 0.0358 0.2634 0.1317

Red soil (RS) 0.0355 0.3477 0.1738

Average for GS1, GS2 and AS 0.2476 (75.65%) 0.1239 (75.65%)

(RS-Average)/RS 28.80% 28.80%

N.Q. Huy et al. / Applied Radiation and Isotopes 71 (2013) 11–2016

9 density values from 0.2 g/cm3 to 1.8 g/cm3 with 0.2 g/cm3

increments. They are expressed as functions of the density fordifferent values of the sample height. As an example, in Fig. 5 thecalculated efficiencies for the height of 2 cm are plotted versusthe density for grey soil 1, grey soil 2, alluvial soil and red soil.From Fig. 5 the values of e(0,c,h,0), a(c,h)h and a(c,h) are obtainedand presented in Table 4. It is revealed from Table 4 that theefficiencies without self-attenuation e(0,c,h,0) have almost thesame values for the three soil types at a given thickness. It isbecause that these values are obtained at r¼0, i.e., they areindependent of soil types. From Fig. 5 it is seen that three curvesfor the grey soil 1, grey soil 2 and alluvial soil are close each toother, which clearly differ from the curve for the red soil. Theaverage values of a(c,h)h and a(c,h) for the grey and alluvial soilsare 0.2476 and 0.1239 with their relative uncertainties of 5.65%,whilst the relative differences between these average valuescompared to the corresponding values of red soil of 0.3477 and0.1738 are 28.8%. So, three soil types can be categorized into2 groups, one is the group of grey and alluvial soils and another isthe red soil one.

The similar calculations were performed for four remainingheight values of 0.5 cm, 1.0 cm, 1.5 cm and 2.5 cm. The MCNP5calculation data were plotted versus the density and fitted withthe Eq. (10). From the fitting results, the values e(0,c,h,0), a(c,h)hand a(c,h) were obtained and presented in Table 5. From Table 5 itis revealed that e(0,c,h,0) have the similar values for the red soil(column 2) and the average of grey soil and alluvial soil (column3) at a given height. The average value for 4 soil samples isreported in column 4 of Table 5, plotted in Fig. 6 versus the heightand fitted with a linear function of the sample height:

eð0,c,h,0Þ ¼ �0:004843hþ0:045442 ð12Þ

The values of a(c,h)h and a(c,h) were presented in Table 5,which are different for the red soil and the average of grey soiland alluvial soil. In Fig. 7 the values of a(c,h) are plotted versus thesample height and are fitted with the functions:

aðc,hÞ ¼ ph2þqhþr ð13Þ

where p, q and r depend on soil types and are equal to:

p¼ 0:00467, q¼�0:04587, r¼ 0:24639 ð14Þ

for the red soil; and

p¼ 0:00254, q¼�0:02738, r¼ 0:16825 ð15Þ

for the average of grey and alluvial soils. The relative uncertain-ties of the parameters p, q, r are about 5% as estimated for

Fig. 5. The calculated efficiencies plotted versus the density for grey so

uncertainty of a(c,h). Then the effective attenuation coefficient isexpressed by the formula:

meff ðc,h,rÞ ¼ aðc,hÞr¼ ðph2þqhþrÞr ð16Þ

where p, q and r depend on chemical compositions.

5. Propagation of uncertainties in chemical composition,sample height and sample density to the uncertaintyof the self-attenuation factor

The self-attenuation factor is expressed by the exponentialfunction (11), explicitly depending on the sample height (h) andthe sample density (r). However, the self-attenuation factor is animplicit function of the chemical composition (c). In order todetermine the propagation of the uncertainties in chemicalcomposition, sample height and sample density to the uncer-tainty of the self-attenuation factor we suggest an explicit func-tion of the self-attenuation factor depending on the chemicalcomposition, sample height and sample density as follows:

F2ðmeff ,c,h,rÞ ¼X11

i ¼ 1

aiðcÞ � f iðmef f ,h,rÞ ð17Þ

where 11 is the number of oxides, ai denotes the percentage of ithoxide and fi is the self-attenuation factor of the sample containingonly ith oxide. Note that ai depends on the chemical compositionof soil, whilst fi depends on the sample height and the sampledensity. The correctness of Eq. (17) is checked by comparison ofthe self-attenuation factor calculated by the expressionF2 ¼

P11i ¼ 1 aif i (row 12 of Table 6) and that calculated for the

real matrix of sample, expression F1¼exp[�meff(c,h,r)h] (row 13of Table 6). From Table 6, it is evident that these two values matchfor grey, alluvial and red soils. So Eq. (17) can be used fordetermining the propagation of uncertainties instead of Eq. (11).

The relative uncertainty of the self-attenuation factor F2

is described via the relative uncertainties sai=ai and sf i

=f i as

il 1, grey soil 2, alluvial soil and red soil in the case of 2 cm height.

Table 5The values e(0,c,h,0), a(c,h)h and a(c,h) for red soil and the average of grey and alluvial soils. Note: RS, GS and AS denote the red soil, grey soil and alluvial soil, respectively.

h (cm) e(0,c,h,0) a(c,h)h a(c,h)

RS Average of GS and AS Average of GS, AS and RS RS Average of GS and AS RS Average of GS and AS

(1) (2) (3) (4) (5) (6) (7) (8)

0.5 0.0431 0.0431 0.0431 0.1124 0.0776 0.2248 0.1551

1.0 0.0405 0.0407 0.0406 0.2049 0.1436 0.2049 0.1436

1.5 0.0379 0.0382 0.0381 0.2819 0.1990 0.1879 0.1327

2.0 0.0355 0.0359 0.0357 0.3477 0.2476 0.1739 0.1238

2.5 0.0332 0.0337 0.0335 0.4017 0.2892 0.1607 0.1157

Fig. 6. The average value e(0,c,h,0) for 4 soil samples plotted versus the sample height.

Fig. 7. The values a(c,h) for the red soil (curve a) and the average of grey soil and alluvial soil (curve b) plotted versus the sample height.

N.Q. Huy et al. / Applied Radiation and Isotopes 71 (2013) 11–20 17

follows:

sF2

F2

� �2

¼

P11i ¼ 1ðf

2i s2

aiþa2

i s2f iÞP11

j ¼ 1 ajf j

� �2¼X11

i ¼ 1

aif iP11j ¼ 1 ajf j

!2sai

ai

� �2

þsf i

f i

� �2" #

ð18Þ

The calculation based on the MCNP5 code shows that thefunction fi has an exponential form

f iðmeff ,i,h,rÞ ¼ exp½�meff ,iðh,rÞh� ¼ exp½�aiðhÞrh� ð19Þ

where meff,i is the effective attenuation coefficient of ith oxide,which is expressed by a function of density, similar to Eq. (16):

meff ,iðh,rÞ ¼ aiðhÞr¼ ðpih2þqihþriÞr ð20Þ

The parameters pi, qi and ri are calculated for 5 main oxidesSiO2, Al2O3, Fe2O3, FeO and TiO2 (Table 7).

Taking into account Eqs. (19) and (20), Eq. (18) becomes:

sF2

F2

� �2

¼X11

i ¼ 1

aif iP11j ¼ 1 ajf j

!2sai

ai

� �2

þðpih3rÞ2

spi

pi

� �2(

þðqih2rÞ2

sqi

qi

� �2

þðrihrÞ2sri

ri

� �2

þ ð3pih3rþ2qih

2rh

þrihrÞ2þðpih3rþqih

2rþrihrÞ2i sh

h

� �2g ð21Þ

According to Pham Quang Khanh (1995), the grey and alluvialsoils are mainly composed of SiO2 and Al2O3 with the relativeuncertainties of their percentages sai

=aiE0.05 and the red soil ofSiO2, Al2O3, Fe2O3, FeO and TiO2 with sai

=aiE0.10. The relativeuncertainties of the parameters pi, qi, ri are spi

=pi � sqi=qi � sri

=

r3i � 0.05 as stated in Section 4. The sample heights weremeasured with the uncertainty of 0.05 cm. Then the maximalrelative uncertainties sF2

=F2 obtained from Eq. (21) are equal to

Table 7Parameters pi, qi and ri of Eq. (20) for 5 main soil oxides SiO2, Al2O3, Fe2O3, FeO

and TiO2.

i Oxide pi qi ri

1 SiO2 0.00198 �0.02434 0.15051

2 Al2O3 0.00106 �0.02053 0.14152

3 Fe2O3 0.02218 �0.16327 0.50819

4 FeO 0.02427 �0.18011 0.54579

5 TiO2 0.00733 �0.06979 0.30469

Table 6The measured chemical compositions of grey 1, alluvial and red soil samples, collected in Southern Vietnam (columns 4, 6, 8). The self-attenuation factor fi (column 3)

calculated for the sample containing only ith oxide with 2 cm height and 1 g/cm3 density. The products aifi for grey 1, alluvial and red soils are presented in columns 5, 7, 9,

respectively.

i Oxide fi Grey soil 1 Alluvial soil Red soil

ai aifi ai aifi ai aifi

(1) (2) (3) (4) (5) (6) (7) (8) (9)

1 SiO2 0.8033 0.8932 0.7175 0.8330 0.6692 0.3308 0.2657

2 Al2O3 0.8454 0.0442 0.0374 0.0490 0.0414 0.2546 0.2153

3 Fe2O3 0.6328 0.0050 0.0032 0.0283 0.0179 0.1806 0.1143

4 FeO 0.6982 0.0097 0.0068 0.0355 0.0248 0.0232 0.0162

5 TiO2 0.7616 0.0050 0.0038 0.0069 0.0053 0.0452 0.0344

6 MnO 0.6693 0.0000 0.0000 0.0005 0.0003 0.0022 0.0015

7 MgO 0.8715 0.0004 0.0003 0.0049 0.0043 0.0049 0.0043

8 CaO 0.7175 0.0074 0.0053 0.0068 0.0049 0.0000 0.0000

9 Na2O 0.8692 0.0012 0.0010 0.0048 0.0042 0.0011 0.0010

10 K2O 0.7266 0.0021 0.0015 0.0104 0.0076 0.0014 0.0010

11 P2O5 0.8493 0.0004 0.0003 0.0010 0.0008 0.0008 0.0007

12F2¼

P11

i ¼ 1

ai f i

0.7772 0.7806 0.6543

13 F1¼exp(�meff h) 0.7847 0.7684 0.7063

N.Q. Huy et al. / Applied Radiation and Isotopes 71 (2013) 11–2018

5.2% for grey and alluvial soils and 5.9% for red soil. In summary,we consider that the maximal relative uncertainties of the self-attenuation factors are about 6% for all soil types.

6. Determination of the 238U activity for soil samples

Specific activity A (Bq/kg) of 238U is determined through theefficiency e as follows:

A ðBq=kgÞ ¼S

eITmð22Þ

where S, I, T and m denote the area of the 63.3 keV experimentalfull energy peak, intensity of 63.3 keV gamma emissionI¼0.048470.0048 (Firestone and Shirley, 1996; Yucel et al.,2009), measuring time in second and sample mass in kg, respec-tively. The determination of 238U activity was validated for somesoil samples and an IAEA reference sample. The efficiency isdetermined from Eq. (10), in which e(0,c,h,0) from Eq. (12),a(c,h) from Eqs. (13)–(15) and meff(c,h,r) from Eq. (16).

The relative uncertainty of the activity A is determined fromEq. (22):

sA

A

� �2¼

sS

S

� �2þ

see

� �2þ

sI

I

� �2þ

sT

T

� �2þ

sm

m

� �2ð23Þ

where sS=S¼ 5%; se=e¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðseð0,c,h,0Þ=eð0,c,h,0ÞÞ2þðsF1

=F1Þ2

q�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðseð0,c,h,0Þ=eð0,c,h,0ÞÞ2þðsF2=F2Þ

2q

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0:012

þ0:062p

¼ 6%;

sI=I¼10%; sT=T and sm=m are less than 1% and can be neglected.So, the relative uncertainty of the activity is:

sA

A¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffisS

S

� �2þ

see

� �2þ

sI

I

� �2r

¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0:052

þ0:062þ0:102

q� 12:7%:

6.1. Grey, alluvial and red soils

Grey, alluvial and red soils were added with amounts of[238U]uranyl-acetate to enhance their counting statistics. Themeasurement was carried out for two grey soil samples withthe densities of 1.077 g/cm3 and 1.347 g/cm3, one alluvial soilsample with the density of 1.069 g/cm3 and one red soil samplewith the density of 0.918 g/cm3. For each sample, 4 configurationswith the height values of 0.5 cm, 1.0 cm, 1.5 cm and 2.0 cm weremeasured and calculated. In Table 8, the parameters S, T, m and eare presented for each sample with 4 height values. Here theefficiency was determined according to formula e�e(meff,c,h,r)¼e(0,h)exp(�meffh), in which e(0,h)�e(0,c,h,0) are taken fromcolumn 4 of Table 5 and meff(h,r)�meff(c,h,r)¼a(h)r, wherea(h)�a(c,h) are taken from columns 7 and 8 of Table 5 for thered soil and the average of grey and alluvial soils, respectively.From Table 8 it is revealed that average activities over 4 sampleheights are in good agreement with reference activities, whichwere determined by quantities of [238U]uranyl-acetate added tosoil samples. The activity of the sample matrix is neglected incomparison to that of [238U]uranyl-acetate.

6.2. IAEA reference sample

The reference sample IAEA-368 of 31 Bq/kg 238U activity,1.291 g/cm3 density, 0.4 cm height and 0.021 kg mass was mea-sured for 40 h. The area of 63.3 keV full energy peak was 169717.Chemical composition of IAEA-368 marine sediment is close tothat of grey and alluvial soils. The values e(0,h)¼0.0435 anda(h)¼0.1577 were taken from Eqs. (12) and (13), so the effectiveattenuation coefficient meff¼a(h)r¼0.2036 cm�1 and the effi-ciency e¼e(0,h)exp(�meffh)¼0.0401. The specific activity of thissample was equal to 29.174.4 Bq/kg according to Eq. (22). Thisvalue is in good agreement with that of 31 Bq/kg ranged within25.0–33.0 Bq/kg for the IAEA-368 reference sample.

7. Conclusion

The present work assumes a method for analyzing the 238Uspecific activity in soil samples via the 63.3 keV gamma rays byexperimental measurement in the HPGe GC1518 p-type detectorbased gamma spectrometer and calculation with using MCNP5code. In order to complete this analysis, it is important to make

Table 8Specific activities of 238U for 2 grey soils, 1 alluvial soil and 1 red soil.

Height (cm) 0.5 1.0 1.5 2.0 Average activity (Bq/kg) Reference activity (Bq/kg)

Grey soil 1 r¼1.077 g/cm3

S 3212 938 1318 1573

T (h) 6 1 1 1

m (kg) 0.0219 0.0439 0.0659 0.0879

e¼e(0,h)e�mef f h 0.0396 0.0348 0.0307 0.0273

A(Bq/kg) 3568.1 3555.0 3764.1 3787.4 3668.67249.5 3664

Grey soil 2 r¼1.347 g/cm3

S 19102 937 1173 1435

T (h) 36 1 1 1

m (kg) 0.0275 0.0549 0.0824 0.1099

e¼e(0,h)e�mef f h 0.0388 0.0335 0.0291 0.0256

A(Bq/kg) 2876.0 2951.9 2827.1 2954.5 2902.47197.4 2963

Alluvial soil r¼1.069 g/cm3

S 532 844 1208 28401

T (h) 0.5 0.5 0.5 10

m (kg) 0.0218 0.0436 0.0654 0.0872

e¼e(0,h)e�meff h 0.0397 0.0348 0.0308 0.0274

A(Bq/kg) 7119.8 6434.0 6941.6 6879.5 6843.77465.4 7137

Red soil r¼0.918 g/cm3

S 7849 359 396 626

T (h) 13 0.333 0.333 0.333

m (kg) 0.0187 0.0375 0.0562 0.0749

e¼e(0,h)e�mef f h 0.0382 0.0326 0.0282 0.0246

A(Bq/kg) 4888.7 5101.2 4344.1 5900.7 5058.77645.6 4896

N.Q. Huy et al. / Applied Radiation and Isotopes 71 (2013) 11–20 19

self-absorption corrections, which consist of chemical composition,geometry and density effects of these weak gamma rays in samplematerials. The study of the above-mentioned effects was per-formed by application of self-attenuation factor, which is definedas the ratio between the counting efficiency for the actual sampleand the counting efficiency for the same sample-detector geometryin the absence of self-attenuation. This factor was expressedby an exponential function F(meff,c,h,r)¼exp[�meff(c,h,r)h], wheremeff, c, h and r are the effective attenuation coefficient, chemicalcomposition, sample height and sample density in the cylindricalcontainer, respectively. The effective attenuation coefficient meff¼

(ph2þqhþr)r reflects the self-attenuation property of volu-

metric radioactive and attenuating samples. The self-attenuationfactor F(meff,c,h,r)¼exp[�meff(c,h,r)h] and the counting efficiencye(meff,c,h,r)¼e(0,c,h,0)F(meff,c,h,r), where e(0,c,h,0) is the efficiencywithout self-attenuation, were calculated by MCNP5 code for themain soil types of Vietnam, which are grey, alluvial and red soils.The efficiency e(meff,c,h,r) was applied for determining the 238Uactivities in some soil samples via 63.3 keV gamma rays. Theobtained 238U activities were in good agreement with those derivedby other methods.

Acknowledgments

The authors express their thanks to Mr. Nguyen Van Mai andMr. Ninh Duc Tuyen for their help in use of the GC1518 detectorbased gamma spectrometer.

This work is completed with the financial support from theVietnam’s National Foundation for Science and Technology Devel-opment (NAFOSTED), code 103.04.01.09.

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