Analysis of some Earth, Moon and Mars samples in terms of gamma ray energy absorption buildup...

$: Analysis of some Earth, Moon and Mars samples in terms of gamma ray energy absorption buildup factors: Penetration depth, weight fraction of constituent elements and photon energy$
Radiation Physics and Chemistry 80 (2011) 354–364

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Radiation Physics and Chemistry

0969-80

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/radphyschem

Analysis of some Earth, Moon and Mars samples in terms of gamma ray energyabsorption buildup factors: Penetration depth, weight fraction of constituentelements and photon energy dependence

Murat Kurudirek a,n, Bekir Dogan a, Yuksel Ozdemir a, Anderson Camargo Moreira b,Carlos Roberto Appoloni c

a Faculty o f Science, Department of Physics, Ataturk University, 25240 Erzurum, Turkeyb Programa de Pos Graduac- ~ao em Ciencias e Engenharia de Materiais/LMPT/EMC, Universidade Federal de Santa Catarina, P.O. Box 476, 8040-900 Florianopolis, Brazilc Departamento de Fısica, Universidade Estadual de Londrina, Centro de Ciencias Exatas, P.O. Box 6001, 86055-900 Londrina, Brazil

a r t i c l e i n f o

Article history:

Received 10 August 2010

Accepted 7 October 2010

Keywords:

Gamma ray buildup factor

Energy absorption

Astrophysical samples

Radiation dosimetry

6X/$ - see front matter & 2010 Elsevier Ltd. A

016/j.radphyschem.2010.10.001

esponding author. Tel.: +90 442 2314167; fax

ail address: [email protected] (M. Kuru

a b s t r a c t

The Earth, Moon and Mars samples have been investigated in terms of gamma ray energy absorption

buildup factors (EABF) depending on penetration depth, weight fraction of constituent elements and

photon energy. The five parameter geometric progression (G-P) fitting approximation has been used to

compute the buildup factors in the energy region 0.015–15 MeV up to a penetration depth of 40 mean free

paths (mfp). The maximum values of EABF have been observed for the Earth, Mars and Moon samples at

0.2, 0.3 and 0.2 MeV, respectively. At the corresponding energies where maximum EABF occur, the Earth

samples have the highest and the Mars samples have the lowest EABF values. There is no significant

variation in EABF for the Earth, Moon and Mars samples beyond 1 MeV, hence the values of EABF remain

constant with the variation in chemical composition for all the given materials. Finally, the buildup factors

so obtained have been discussed in function of the penetration depth, weight fraction of constituent

elements and photon energy.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

In order to evaluate the physical and chemical properties of soilsand rocks of space objects’ surfaces, the gamma ray interactionwith these types of materials has long been recognized as aneffective tool in many space missions for in situ measurements. Forexample, effects of sterilizing doses of gamma radiation on Marsanalog rocks and minerals have been studied by Allen et al. (1999)and they have concluded that the gamma photons from 60Co (1.17and 1.33 MeV) in doses as high as 3�107 rads did not induceradioactivity in the samples and produced no measurable changesin their isotopic and chemical compositions. Masarik and Reedy(1996) have studied the gamma ray production and transport inMars. Also, the gamma rays emitted from the space objects’surfaces carry information on the chemical composition of thesurface layer. Reedy et al. (1973) have focused on the expectedg-ray emission spectra from the lunar surface as a function ofchemical composition. Besides, the gamma ray transmissionmethod is widely used with success for non-destructivemeasurements of some soil and rock parameters such as water

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direk).

content, bulk density and porosity (Mudahar and Sahota, 1986;Pires et al., 2009; Subudhi et al., 2010; Appoloni and Pottker, 2004;Oliveira et al., 2010; Appoloni et al., 2004). However, the Lamber–Beer attenuation law ðI¼ I0e�mxÞ, which is often used for calculationof attenuation coefficients in gamma ray transmission studies, isviolated by buildup of gamma photons through the attenuatingmaterial. In some cases, the intensity of incident radiation is notonly attenuated but also increased by the secondary photons insidethe absorbing medium. That is called the ‘‘buildup’’ of radiation andclassified into two categories: (a) the energy absorption buildupfactor that is the buildup factor in which the quantity of interest isthe absorbed or deposited energy in the interacting material andthe detector response function is that of absorption in the inter-acting material, (b) the exposure buildup factor is the buildupfactor in which the quantity of interest is the exposure and thedetector response function is that of absorption in air (Singh et al.,2008).

Different materials have been considered as subjects to studythe gamma ray buildup factors, before. Manohara et al. (2010)studied the energy absorption buildup factors for thermo-luminescent dosimetric materials and their tissue equivalencewhich are of importance in radiation dosimetry, diagnostics andtherapy. Singh et al. (2008) have investigated the variation ofenergy absorption buildup factors with incident photon energy and

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M. Kurudirek et al. / Radiation Physics and Chemistry 80 (2011) 354–364 355

penetration depth for some commonly used solvents. Recently,chemical composition dependence of exposure buildup factors forsome polymers has been studied (Singh et al., 2009). Brar et al.(1999) have focused on the buildup factor studies of HCO materialsas a function of weight fraction of constituent elements. Also,Brar et al. (1998) have investigated the effect of weight fractionsof Fe and Si on buildup factors of some soil samples. The energydependence of energy absorption buildup factor of HCO materialshas been studied by Brar and Mudahar (1996). The effect of absorbeddose build up factor on food irradiation processing has been studiedbefore (Silva, 1996). Shin and Hirayama (2001) have calculatedgamma ray buildup factor for two-layered shields made of water,concrete and iron and discussed on application of approximatingformula. There are different available methods to calculate thebuildup factor such as the G-P fitting method (Harima et al., 1986)and the invariant embedding method (Sakamoto and Tanaka, 1988;Shimizu, 2002; Shimizu et al., 2004). Recently, American NationalStandards ANSI/ANS-6.4.3 (1991) has provided buildup factor datafor 23 elements, one compound and two mixtures (i.e. air and water)and concrete at energies in the range 0.015–15 MeV up topenetration depths of 40 mean free path using the G-P method.The developed G-P fitting formula is known to be accurate withina few percent errors (Harima et al., 1986; Harima, 1983). Recently,Harima (1993) has made an extensive historical review and anassessment for the status of buildup factor calculations andapplications.

While the energy absorption and exposure buildup factorstudies have been widely made in different materials, there arealmost no studies in terrestrial, lunar and martian samplesalthough the gamma ray interaction with these types of samplesare used for different purposes i.e. determination of chemicalcomposition and physical properties, sterilizing. This motivated usto carry out the present study. In the present study, an attempt hasbeen made to calculate the energy absorption buildup factors byusing the G-P fitting method for some Earth, Moon and Marssamples in the energy region 0.015–15 MeV up to penetrationdepths of 40 mean free paths, for the first time. Also, effects ofpenetration depth, weight fraction of constituent elements andphoton energy on EABF have been discussed. The generated buildupfactor data should be useful in correction of the intensity of gammarays and in estimation of the real absorbed dose. The chemicalcomposition data, physical properties and the used analyticalmethods to determine the chemical compositions of the Earth,Moon and Mars samples are available in a previous study (Moreiraand Appoloni, 2006).

2. Computational work

To calculate the buildup factors, the G-P fitting parameters wereobtained by the method of interpolation from the equivalentatomic number (Zeq). Computations are illustrated step by stepas follows:

1.
Calculation of the equivalent atomic number, Zeq. 2. Calculation of geometric progression (G-P) fitting parameters. 3. Calculation of energy absorption and exposure buildup factors.
The equivalent atomic number, Zeq is a parameter describingthe properties of the composite materials in terms of equivalentelements, hence it is similar to that atomic number of elements.However, the interaction of gamma rays with materials is based ondomination of different partial photon interaction processes indifferent energy regions, thus Zeq is an energy dependent para-meter. Since the buildup factor mainly arises from multiplescattering events, Zeq is derived from the contribution of Compton

scattering process. At the first step, the equivalent atomic number,Zeq for a particular material has been calculated by matching theratio, ðm=rÞCompton=ðm=rÞTotal, of that material at a specific energywith the corresponding ratio of an element at the same energy.Thus, firstly the Compton partial mass attenuation coefficient,ðm=rÞCompton, and the total mass attenuation coefficients, ðm=rÞTotal,were obtained for the elements of Z¼4–40 and for the Earth, Moonand Mars samples in the energy region 0.015–15 MeV, using theWinXCom computer program (Gerward et al., 2001a, 2004b;initially developed as XCOM; Berger and Hubbell, 1999). It wasreported by Hubbell that the envelope of the uncertainty of massattenuation coefficient is in the order of 1–2% in the energy rangefrom 5 keV to a few MeV (Hubbell, 1999). In case of the energies of1–4 keV, the discrepancies are known to reach a value of 25–50%.Recently, Chantler has extended the investigations below 5 keVconcluding the presence of huge discrepancies below 4 keV andderived new theoretical results of substantially higher accuracy innear-edge soft X-ray regions in detail (Chantler, 2000). For theinterpolation of Zeq for which the ratio ðm=rÞCompton=ðm=rÞTotal liesbetween two successive ratios of elements, the following formulahas been employed (Sidhu et al., 1999):

Zeq ¼Z1ðlogR2�logRÞþZ2ðlogR�logR1Þ

logR2�logR1ð1Þ

where Z1 and Z2 are the atomic numbers of elements correspondingto the ratios R1 and R2, respectively, R is the ratio for the Earth, Moonand Mars samples at a specific energy. Let HIGS-1 be an example forcalculation of Zeq at the energy of 0.015 MeV. The ratio ðm=rÞCompton=

ðm=rÞTotal of HIGS-1 is 0.019, which lies between the ratios 0.016and 0.022 corresponding to the elements Z1¼12 and Z2¼13,respectively. Then, using these values in Eq. (1) the Zeq¼12.5 isobtained.

At the second step, to calculate the G-P fitting parameters a similarinterpolation procedure was adopted as in the case of the equivalentatomic number. The G-P fitting parameters for elements were takenfrom the ANSI/ANS-6.4.3 (1991) standard reference database, whichprovides the G-P fitting parameters for elements from beryllium toiron in the energy region 0.015–15 MeV up to 40 mfp. The G.P. fittingbuildup factor coefficients of the used materials were interpolatedaccording to the given formula as follows:

C ¼C1ðlogZ2�logZeqÞþC2ðlogZeq�logZ1Þ

logZ2�logZ1ð2Þ

where C1 and C2 are the values of the coefficients (G.P. fittingparameters) corresponding to the atomic numbers of Z1 and Z1,respectively, at a given energy and Zeq is the equivalent atomicnumber of the given material. The energy absorption G.P. fittingparameters for the HIGS-1 sample have been given in Table 1 as anexample.

At the final step, these parameters were used to calculate theenergy absorption and exposure buildup factors from the G-Pfitting formula (Harima et al., 1986)

BðE,XÞ ¼ 1þb�1

K�1ðKx�1Þ for Ka1 ð3Þ

BðE,XÞ ¼ 1þðb�1Þx for K ¼ 1 ð4Þ

where,

KðE,xÞ ¼ cxaþdtanhðx=Xk�2Þ�tanhð�2Þ

1�tanhð�2Þfor xr40mfp ð5Þ

where E is the incident photon energy, x is the penetration depth inmfp, a, b, c, d and Xk are the G-P fitting parameters and b is the valueof buildup factor at 1 mfp. The parameter K represents the photondose multiplication and the change in the shape of the spectrum.Here, the mean free path (mfp) represents the average distancebetween two successive interactions of photons in which the

Table 1Chemical compositions of the Earth samples (%) (Economou et al., 1970).

Chem.

comp.

Basalt BCR-1 Andesite

AGV-1

Peridotite

PCC-1

Dunite

DTS-1

Granodiorite

GSP-1

C 0.58 1.2 1.17 0.8 0.58

O 60.76 61.16 59.23 55.57 61.6

F 0 0.1 0 0 0.47

Na 2.21 2.99 0 0 1.82

Mg 1.96 0.59 21.03 25.91 1.19

Al 6 6.66 0.18 0.14 5.92

Si 19.83 21.42 15.78 14.69 23.08

S 0.62 0.76 0 0.56 0

K 1.64 0.48 0 0 3.34

Ca 2.3 2.9 0.015 0 0.86

Ti 1 0.09 0.71 0.27 0.04

Fe 2.97 1.59 1.9 2.4 1.02

Sr 0.019 0.051 0.007 0.001 0.004

Ba 0.017 0.012 0 0 0.054

Chem.

comp.

Philippinite

Po-300

Granite

(G-2)

V25-1-T91 HIGS-1 Syenite

C 0.41 0.47 0.57 0.36 0

O 63.08 61.73 60.81 59.43 61.7

F 0.1 0.11 0.03 0.025 0.21

Na 0.65 2.65 2.01 1.3 2.59

Mg 1.95 1.52 3.38 7.13 3.2

Al 5.28 6.22 6.88 4.54 3.9

Si 24.78 23.29 19.07 18.27 21.5

S 0.11 0 0.47 0.13 0

K 0.22 2.66 0.99 0.92 4.1

Ca 1.68 0.62 4.2 3.45 4.1

Ti 0.3 0 0.55 0.93 0.6

Fe 1.41 0.71 2.37 3.51 2.2

Sr 0.013 0.012 0 0.014 0

Ba 0.006 0.05 0 0 0.1

Table 2Chemical compositions of lunar samples (%) (Turkevich et al., 1969; Franzgrote et al.,

1970; Paterson et al., 1969).

Chem. comp. Surveyor V-1 Surveyor V-2 Surveyor VI Surveyor VII

C 0.2 0.9 o2

O 61.6 60.9 59.3 58

F 0.06 0.05 0.07

Na 0.34 0.45 0.59 o3

Mg 2.8 2.4 3.7 4

Al 6.2 6.2 6.5 9

Si 16.3 17.4 18.5 18

S 0.3 0 0 6

Ca 6.3 5.4 5.2

Ti 1.9 2.3 1

Fe 3.7 3.7 3.9 2

Zn o0.16 o0.09 o0.13

Sr o0.07 o0.06 o0.13

Zr–In o0.05 o0.06 o0.16

Sn–U o0.07 o0.07 o0.10

Table 3Chemical compositions of four samples of martian rocks analyzed by the Viking 1

and 2 missions (Massambani and Mantovani, 1997).

Chem. comp. Viking 1-A Viking 1-B Viking 1-C Viking 2

Mg 5 5.2

Al 3 2.9

Si 20.9 20.8 20.5 30

S 3.1 3.8 3.8 2.6

Cl 0.7 0.8 0.9 0.6

K o0.25

Ca 4 3.8 3.6

Ti 0.5 0.61

Fe 12.7 12.6 13.1 14.2

O 50 49.7 50.4

M. Kurudirek et al. / Radiation Physics and Chemistry 80 (2011) 354–364356

intensity of incident photon beam is reduced by the factor of 1/e.The ratio of the total value of a specified radiation quantity at anypoint to the contribution to that value from radiation reaching the

Table 4Chemical compositions (in oxides) of samples from the surface of Mars (Economou,

2001).

Chem.

comp.

Soil A-

2

Soil A-

4

Soil A-5 Soil A-8 Soil A-9 Soil A-

10

Soil A-

15

Na2O 3.1 3.1 3.8 2.4 2.3 2.5 2.9

MgO 10.3 9.5 8.4 7.6 7.7 8.8 8

Al2O3 10 10.2 10 10.2 9.9 9.4 9.6

SiO2 40.9 40.9 40.5 45.4 41.9 41 43.1

P2O5 0.9 1.1 0.5 0.5 0.7 0.6 0.5

SO3 6 7 5.7 5.6 6.7 6.4 5.3

Cl 0.7 0.8 0.8 0.9 1.3 0.9 0.8

K2O 0.5 0.5 0.5 0.9 0.7 0.4 0.7

CaO 6.1 5.6 6.1 7.1 6.5 6 5.6

TiO2 0.8 1.3 0.7 0.9 1.1 1 1

Cr2O3 0.3 0.4 0.5 0.1 0.2 0.3 0.3

MnO 0.5 0.4 0.2 0.3 0.1 0.4 0.3

FeO 20 19.2 22.2 18.2 21 22.4 21.9

Chem.

comp.

Rock A-

3

Rock A-

7

Rock A-

16

Rock A-

17

Rock

A�18

Na2O 3.4 3.6 4.3 2.5 4.3

MgO 2.5 6.2 4.8 4.6 4

Al2O3 12.2 10.9 11 10.3 11.7

SiO2 53.5 47.2 47.5 53.8 49.2

P2O5 0.7 0.5 0.5 0.4 0.5

SO3 2 4.5 3 1.7 3

Cl 0.5 0.9 0.7 0.5 0.7

K2O 1.2 0.8 0.8 0.9 1

CaO 5.7 6.6 6.9 7.7 5.9

TiO2 0.7 0.9 0.9 0.7 0.9

Cr2O3 0.1 0.1 0 0.1 0.1

MnO 0.4 0.4 0.3 0.4 0.4

FeO 17.3 17.8 19.3 16.5 18.5

Table 5Energy absorption G.P. fitting coefficients for HIGS-1 sample in the energy range

0.015–15 MeV.

E (MeV) Energy absorption buildup factor coefficients

a b c d Xk

1.50E�02 0.225 1.033 0.383 �0.1517 13.72

2.00E�02 0.222 1.077 0.375 �0.1165 14.34

3.00E�02 0.203 1.238 0.420 �0.1110 14.09

4.00E�02 0.170 1.512 0.496 �0.0937 14.86

5.00E�02 0.147 1.927 0.571 �0.0879 14.71

6.00E�02 0.112 2.411 0.675 �0.0784 14.63

8.00E�02 0.039 3.335 0.906 �0.0358 14.09

1.00E�01 �0.013 3.922 1.118 �0.0129 13.59

1.50E�01 �0.070 4.107 1.409 0.0156 14.14

2.00E�01 �0.095 3.685 1.553 0.0287 14.24

3.00E�01 �0.105 3.105 1.610 0.0321 14.35

4.00E�01 �0.101 2.786 1.582 0.0302 14.66

5.00E�01 �0.095 2.588 1.535 0.0277 15.15

6.00E�01 �0.093 2.431 1.508 0.0301 14.91

8.00E�01 �0.082 2.240 1.431 0.0275 14.90

1.00E+00 �0.072 2.122 1.362 0.0249 15.02

1.50E+00 �0.053 1.938 1.251 0.0203 14.40

2.00E+00 �0.034 1.844 1.155 0.0125 14.73

3.00E+00 �0.009 1.706 1.050 �0.0011 10.70

4.00E+00 0.009 1.614 0.983 �0.0119 13.15

5.00E+00 0.019 1.542 0.946 �0.0149 12.69

6.00E+00 0.024 1.480 0.928 �0.0271 15.94

8.00E+00 0.033 1.389 0.903 �0.0230 12.28

1.00E+01 0.036 1.325 0.893 �0.0285 13.93

1.50E+01 0.038 1.226 0.890 �0.0329 14.72

Table 6(a–c) Equivalent atomic numbers of the given Earth, Moon and Mars samples.

Energy (MeV) Equivalent atomic number

(a) Earth samplesBCR-1 AGV-1 PCC-1 DTS-1 GSP-1 Po-300 G-2 V25-1-T91 HIGS-1 Sye.

1.50E�02 12.3 11.7 11.3 11.5 11.6 11.5 11.4 12.2 12.5 12.5

2.00E�02 12.5 11.9 11.4 11.6 11.7 11.6 11.5 12.4 12.6 12.6

3.00E�02 12.6 12.0 11.5 11.7 11.8 11.8 11.6 12.5 12.8 12.8

4.00E�02 12.8 12.1 11.6 11.8 12.0 11.9 11.8 12.6 12.9 13.1

5.00E�02 12.9 12.2 11.7 11.9 12.1 11.9 11.8 12.7 13.0 13.2

6.00E�02 12.9 12.3 11.7 11.9 12.1 12.0 11.9 12.7 13.1 13.2

8.00E�02 13.0 12.3 11.8 12.0 12.2 12.0 12.0 12.8 13.2 13.4

1.00E�01 13.1 12.4 11.8 12.1 12.3 12.1 12.0 12.9 13.2 13.4

1.50E�01 13.2 12.5 11.9 12.1 12.4 12.1 12.1 13.0 13.3 13.6

2.00E�01 13.2 12.5 12.0 12.2 12.4 12.2 12.2 13.0 13.4 13.6

3.00E�01 13.3 12.6 12.0 12.2 12.5 12.2 12.2 13.1 13.5 13.7

4.00E�01 13.4 12.6 12.0 12.2 12.5 12.3 12.3 13.1 13.5 13.8

5.00E�01 13.4 12.6 12.1 12.3 12.6 12.3 12.3 13.1 13.5 13.8

6.00E�01 13.4 12.6 12.1 12.3 12.6 12.3 12.3 13.1 13.5 13.9

8.00E�01 13.4 12.7 12.1 12.3 12.6 12.3 12.3 13.1 13.5 13.9

1.00E+00 13.4 12.7 12.1 12.3 12.6 12.3 12.3 13.1 13.5 13.9

1.50E+00 11.4 10.9 10.6 10.8 10.9 10.8 10.7 11.3 11.5 11.7

2.00E+00 10.9 10.6 10.3 10.5 10.6 10.5 10.4 10.9 11.0 11.2

3.00E+00 10.8 10.5 10.2 10.4 10.5 10.4 10.4 10.8 10.9 11.0

4.00E+00 10.8 10.5 10.2 10.4 10.4 10.4 10.3 10.8 10.9 11.0

5.00E+00 10.8 10.5 10.2 10.4 10.4 10.4 10.3 10.8 10.9 11.0

6.00E+00 10.8 10.5 10.2 10.4 10.4 10.3 10.3 10.7 10.9 11.0

8.00E+00 10.8 10.4 10.2 10.4 10.4 10.3 10.3 10.7 10.9 11.0

1.00E+01 10.7 10.4 10.2 10.4 10.4 10.3 10.3 10.7 10.9 11.0

1.50E+01 10.7 10.4 10.2 10.4 10.4 10.3 10.3 10.7 10.9 11.0


(b) Mars samplesV. 1-A V. 1-B V. 2 S. A-2 S. A-5 S. A-8 R. A-3 R. A-16 R. A-17

1.50E�02 14.9 14.8 15.1 15.6 15.9 15.4 15.2 15.6 15.2

2.00E�02 15.1 15.1 15.4 15.9 16.2 15.7 15.5 15.8 15.4

3.00E�02 15.3 15.3 15.6 16.1 16.4 15.9 15.7 16.0 15.7

4.00E�02 15.5 15.5 15.8 16.3 16.6 16.1 15.9 16.2 15.8

5.00E�02 15.6 15.6 15.9 16.4 16.7 16.2 16.0 16.3 15.9

6.00E�02 15.7 15.7 16.0 16.5 16.8 16.3 16.1 16.4 16.0

8.00E�02 15.8 15.8 16.1 16.6 16.9 16.4 16.2 16.5 16.1

1.00E�01 15.9 15.9 16.2 16.7 17.0 16.5 16.3 16.6 16.2

1.50E�01 16.1 16.1 16.3 16.8 17.1 16.6 16.4 16.7 16.3

2.00E�01 16.1 16.1 16.4 16.9 17.2 16.7 16.5 16.8 16.4

3.00E�01 16.2 16.2 16.5 17.0 17.3 16.8 16.5 16.9 16.5

4.00E�01 16.3 16.3 16.5 17.1 17.4 16.8 16.6 17.0 16.5

5.00E�01 16.3 16.3 16.6 17.1 17.4 16.8 16.6 17.0 16.6

6.00E�01 16.3 16.3 16.6 17.1 17.4 16.9 16.6 17.0 16.6

8.00E�01 16.3 16.3 16.6 17.1 17.4 16.9 16.7 17.0 16.6

1.00E+00 16.3 16.3 16.6 17.1 17.4 16.9 16.7 17.0 16.6

1.50E+00 13.9 13.8 14.2 14.8 15.1 14.6 14.3 14.7 14.3

2.00E+00 13.0 12.9 13.3 13.8 14.0 13.7 13.4 13.7 13.5

3.00E+00 12.8 12.7 13.0 13.5 13.7 13.4 13.2 13.5 13.2

4.00E+00 12.7 12.6 12.9 13.4 13.7 13.3 13.1 13.4 13.1

5.00E+00 12.7 12.6 12.9 13.4 13.6 13.3 13.1 13.4 13.1

6.00E+00 12.6 12.6 12.9 13.4 13.6 13.3 13.1 13.3 13.1

8.00E+00 12.6 12.6 12.9 13.4 13.6 13.3 13.1 13.3 13.1

1.00E+01 12.6 12.6 12.9 13.4 13.6 13.2 13.1 13.3 13.1

1.50E+01 12.6 12.5 12.9 13.3 13.6 13.2 13.0 13.3 13.1


(c) Moon samples

Surveyor V-1 Surveyor V-2 Surveyor VI Surveyor VII

1.50E�02 13.0 12.9 12.9 11.7

2.00E�02 13.2 13.2 13.3 11.8

3.00E�02 13.6 13.6 13.8 11.9

4.00E�02 13.8 13.7 14.0 12.0

5.00E�02 13.9 13.8 14.2 12.0

6.00E�02 14.0 13.9 14.3 12.1

8.00E�02 14.1 14.1 14.5 12.1

1.00E�01 14.2 14.2 14.6 12.2

1.50E�01 14.9 14.9 15.6 12.2

2.00E�01 15.1 15.1 15.8 12.3

3.00E�01 15.4 15.3 16.1 12.3


Table 6 (continued )


(c) Moon samples


4.00E�01 15.5 15.5 16.3 12.4

5.00E�01 15.6 15.6 16.5 12.4

6.00E�01 15.7 15.7 16.6 12.4

8.00E�01 15.8 15.7 16.7 12.4

1.00E+00 15.8 15.8 16.7 12.4

1.50E+00 12.5 12.5 13.0 10.9

2.00E+00 11.5 11.5 11.7 10.6

3.00E+00 11.3 11.2 11.4 10.5

4.00E+00 11.2 11.2 11.3 10.5

5.00E+00 11.2 11.1 11.3 10.5

6.00E+00 11.2 11.1 11.3 10.5

8.00E+00 11.2 11.1 11.2 10.5

1.00E+01 11.2 11.1 11.2 10.5

1.50E+01 11.1 11.1 11.2 10.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.010-2 10-1 100 101

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Energy (MeV)

1 mfp

1

10

1

10E

nerg

y ab

sorp

tion

build

up f

acto

r

Energy (MeV)

5 mfp

100

101

102

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Energy (MeV)

10 mfp

SyeniteEne

rgy

abso

rptio

n bu

ildup

fac

tor

Energy (MeV)

20 mfp

Basalt BCR-1 Andesite AGV-1 Peridotite PCC-1 Dunite DTS-1 Granodiorite GSP-1 Philippinite Po-300 Granite G-2 V25-1-T91 HIGS-1 Syenite

100

101

102

100

101

102

100

101

102

10-2 10-1 100 101

10-2 10-1 100 101 10-2 10-1 100 101

10-2 10-1 100 101 10-2 10-1 100 101

10-2 10-1 100 101 10-2 10-1 100 101

Bas. BCR-1 And. AGV-1 Per. PCC-1 Dun. DTS-1 Gra. GSP-1 Phil. Po-300 Gran. G-2 V25-1-T91 HIGS-1 Syenite


Bas. BCR-1 And. AGV-1 Per. PCC-1 Dun. DTS-1 Gra. GSP-1 Phil. Po-300 Gran. G-2 V25-1-T91 HIGS-1

103

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Energy (MeV)

40 mfp

100

101

102

103

100

101

102

10-2 10-1 100 101

10-2 10-1 100 101


Fig. 1. (a–e) Energy absorption buildup factors for Earth samples in the energy region 0.015–15 MeV at 1, 5, 10, 20, 40 mfp.



point without having undergone any collision is called the ‘‘buildupfactor’’. The energy absorption buildup factor, EABF refers to theabsorbed or deposited energy in the attenuating material.

3. Results and discussion

3.1. Energy absorption buildup factors of Earth, Moon and Mars

samples

The chemical compositions of the given materials have beengiven in Tables 1–4. Table 5 presents the energy absorption G.P.fitting coefficients for HIGS-1 sample in the energy range 0.015–15 MeV. The equivalent atomic numbers of the Earth, Moon andMars samples are tabulated in Table 6(a–c). The gamma ray

1.0

1.5

2.0

2.5

3.0

3.5

4.0

10-2 10-1 100 101

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Energy (MeV)

1 mfp

1

10

1

10

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Energy (MeV)

10 mfp

10-2 10-1 100 101

10-2 10-1 100 101

10-2 10-1 100 101

Viking 1-A Viking 1-B Viking 2 SOIL A-2 SOIL A-5 SOIL A-8 ROCK A-3 ROCK A-16 ROCK A-17


103

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Energy

40 mfp

100

101

102

10-2 10-1

10-2 10-1

Vik Vik Vik SOI SOI SOI ROC ROC ROC

Fig. 2. (a–e) Energy absorption buildup factors for Mars samples

buildup, which represents the collided part of the incidentgamma rays, mainly arises from the larger penetration depths(especially for materials of larger thickness) and divergence of theincident beam. It can be clearly seen from the figures that the valuesof EABF are always larger than unity.

Figs. 1–3(a–e) show the energy absorption buildup factors atfixed penetration depths from 0.015 to 15 MeV. It is seen thatinitially, the EABF values start increasing with the increase inphoton energy up to a maximum value at intermediate energies,then starts decreasing further with the increase in energy. Thisstate can be clearly explained by the domination of differentphoton interaction processes at different energy regions. Theabsorption processes, namely photoelectric absorption and pairproduction lead to completely removal of photons, hence thelifetime of photons in the material are small, thus they do not

1

10

1

10

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Energy (MeV)

5 mfp

100

101

102

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Energy (MeV)

20 mfp

100

101

102

10-2 10-1 100 101

10-2 10-1 100 101

10-2 10-1 100 101

10-2 10-1 100 101



(MeV)

103

100

101

102

100 101

100 101

ing 1-Aing 1-Bing 2L A-2L A-5L A-8K A-3K A-16K A-17

in the energy region 0.015–15 MeV at 1, 5, 10, 20, 40 mfp.

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.50.01

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5E

nerg

y ab

sorp

tion

build

up f

acto

r

Energy (MeV)

1 mfp

1

10

1

10

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Energy (MeV)

5 mfp

100

101

10210-2 10-1 100 101

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Energy (MeV)

10 mfp

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Energy (MeV)

20 mfp

0.1 1 10

100

101

102

0.01 0.1 1 10

0.01 0.1 1 10 0.01 0.1 1 10

10-2 10-1 100 101

10-2 10-1 100 101 10-2 10-1 100 101100

101

102

100

101

102




Surveyor VI

Surveyor V-1 Surveyor V-2

Surveyor VII

103

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Energy (MeV)

40 mfp

100

101

102

10-2 10-1 100 101

10-2 10-1 100 101

103

100

101

102


Fig. 3. (a–e) Energy absorption buildup factors for Moon samples in the energy region 0.015–15 MeV at 1, 5, 10, 20, 40 mfp.


exist for a longer period of time, resulting in less buildup factor atlower and high energy regions, whereas in the case of the scatteringprocesses i.e. Compton scattering, the photons are not completelyremoved but their energies are only degraded, resulting in theaccumulation of photons. They exist for a long time in the material,thus this process results with more multiple scattered photons whichlead to increase in buildup factor in the medium. The maximumvalues of EABF for Earth, Mars and Moon samples occur at energies0.2, 0.3 and 0.2 MeV where the Compton scattering is the maininteraction process, respectively. The corresponding energies wheremaximum EABF occur, shift to higher energies for high Zeq samples.

The values of EABF have been shown as a function of penetrationdepth in Figs. 4–6(a–d). It has been shown that with the increasingpenetration depths, the EABF also increases for the given materials

due to increase in number of scattered photons. The maximumvalues of EABF which are in the order of 103, have been obtained atthe largest penetration depth (40 mfp). While the value of EABF forEarth, Mars and Moon samples lies between 1–1.2, 1–1.3 and 1–1.2at the lowest energy (0.015 MeV), respectively, it can reach to amaximum value in the order of 103 at 40 mfp.

The variation of EABF with the weight fractions of silicon andiron has been given in Figs. 7 and 8(a and b) for Earth and Marssamples, respectively. It has been shown that the values of EABF arepractically the same for given materials at higher energies beyond1 MeV (Figs. 1–3(a–e) and Figs. 4–6(c,d)). This can be due to the factthat in the low energy region the chemical composition (Zeq) has asignificant effect on attenuation properties whereas at higherphoton energies the effect of chemical composition (Zeq) is less.

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

1.18

1.20

0

1.00

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

1.18

1.20

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Energy (MeV)

0.015 MeV103

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Energy (MeV)

0.15 MeV

100

101

102

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Energy (MeV)

1.5 MeV

1

10

1

10

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Energy (MeV)

15 MeV

Basalt BCR-1 Andesite AVG-1 Pendotite PCC-1 Dunite DTS-1 Granodiorite GSP-1 Philippinite Po-300 Granite G-2 V25-1-T91 HIGS-1 Syenite


Phil. Po-300 Gran. G-2 V25-1-T91 HIGS-1 Syenite

Bas. BCR-1 And. AGV-1 Per. PCC-1 Dun. DTS-1 Gra. GSP-1


100

101

102

100

101

102

103

100

101

102

10 20 30 40 0 10 20 30 40

0 10 20 30 40 0 10 20 30 40

0 10 20 30 40 0 10 20 30 40

0 10 20 30 40 0 10 20 30 40

Fig. 4. (a–d) Energy absorption buildup factors for Earth samples up to 40 mfp at 0.015, 0.15, 1.5, 15 MeV.

1.02

1.04

1.06

1.080

1.02

1.04

1.06

1.08

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Penetration depth (mfp)

0.015 MeV103

Ene

rgy

abso

rptio

n bu

ildup

fac

tor


0.15 MeV

100

101

102

Ene

rgy

abso

rptio

n bu

ildup

fac

tor


1.5 MeV

1

10

1

10

Ene

rgy

abso

rptio

n bu

ildup

fac

tor


15 MeV

100

101

102

100

101

102

103

100

101

102

10 20 30 40 0 10 20 30 40

0 10 20 30 40 0 10 20 30 40

0 10 20 30 40 0 10 20 30 40

0 10 20 30 40 0 10 20 30 40





Fig. 5. (a–d) Energy absorption buildup factors for Mars samples up to 40 mfp at 0.015, 0.15, 1.5, 15 MeV.


1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

1.18

0

1.02

1.04

1.06

1.08

1.10

1.12

1.14

1.16

1.18E

nerg

y ab

sorp

tion

build

up f

acto

r


0.015 MeV

101

102

103

Ene

rgy

abso

rptio

n bu

ildup

fac

tor


0.15 MeV

100

101

102

Ene

rgy

abso

rptio

n bu

ildup

fac

tor


1.5 MeV

2

4

6

810

2

4

6

810

Ene

rgy

abso

rptio

n bu

ildup

fac

tor


15 MeV



101

102

103



100

101

102

10 20 30 40 0 10 20 30 40

0 10 20 30 40 0 10 20 30 40

0 10 20 30 40 0 10 20 30 40

0 10 20 30 40 0 10 20 30 40

Fig. 6. (a–d) Energy absorption buildup factors for Moon samples up to 40 mfp at 0.015, 0.15, 1.5, 15 MeV.

100

101

102

103

18

40 mfp

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Weight fraction of Si (%)

0.5

40 mfp

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Weight fraction of Fe (%)

100

101

102

103

100

101

102

103

100

101

102

103

19 20 21 22 23 24 25

18 19 20 21 22 23 24 25

1.0 1.5 2.0 2.5 3.0 3.5

0.5 1.0 1.5 2.0 2.5 3.0 3.5

0.02 0.06 0.151.5 15

0.015 0.02 0.060.15 1.5

Fig. 7. (a and b) Energy absorption buildup factors for Earth samples as a function of weight fractions of Si and Fe.


However, at lower and intermediate energies there are significantvariations in EABF when chemical compositions of the sampleschange. From the Figs. 7 and 8(a and b), it can be clearly seen that atenergies 0.15 MeV or lower, the EABF increases with the increase inweight fraction of Si whereas the EABF decreases with the increasein weight fractions of Fe. Also, among the given materials themaximum values for EABF are observed in Earth samples and theminimum values for EABF are observed in Mars samples. Thepossible explanations behind this could be that, the high Z element

Fe is abundantly present in Mars samples thus leading to high Zeq

values when compared with the Earth and Moon samples. It is wellknown that the photoelectric absorption cross section isproportional with tpZ4�5=E7=2, hence at lower energies the photo-electric absorption is more dominant for high Zeq materials.Consequently, the increase in weight fraction of Si which is arelatively low Z element, increases the EABF while the increase inweight fraction of Fe which is a relatively high Z element, decreasesthe EABF at lower energies.

100

101

102

18

40 mfp

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Weight fraction of Si (%)

12

Ene

rgy

abso

rptio

n bu

ildup

fac

tor

Weight fraction of Fe (%)

40 mfp

20 22 24 26 28 30

18 20 22 24 26 28 30

13 14 15 16 17 18

12 13 14 15 16 17 18100

101

102

100

101

102

100

101

102

0.02 0.06 0.151.5 15

0.02 0.06 0.151.5 15

Fig. 8. (a and b) Energy absorption buildup factors for Mars samples as a function of weight fractions of Si and Fe.

-5.0-4.5-4.0-3.5-3.0-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.53.03.54.04.55.0

0

-5.0-4.5-4.0-3.5-3.0-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.53.03.54.04.55.0

0.015 0.6 0.8 1 3

4 5 8 10 15

Dif

fere

nce

(%)

Penetration depth (MFP)

Energy absorption buildup factor for air Energy (MeV)

10 20 30 40

0 10 20 30 40

Fig. 9. (a and b) Difference (%) between ANSI database and present work with respect to the calculated values of EABF and EBFfor air at some energies up to 40 mfp.


3.2. Calculation uncertainty

Fig. 9 shows the relative difference between ANSI (1991)database and the present work with respect to the calculatedvalues of EABF for air. We have checked our calculations bycomparing EABF for air present in ANSI (1991) database with ourcalculated EABF for air in the energy region 0.015–15 MeVand penetration depths up to 40 mfp. From Fig. 9 it can beclearly seen that our calculated values for air agree well withthat of ANSI (1991) database within a few percent uncertainty.Recently, Asano and Sakamoto (2007) have evaluated the buildupfactors of two typical heavy concretes to improve the capability ofthe various materials for the shielding wall by using the MonteCarlo simulation code, EGS4. They also compared their calculatedvalues by that of concrete in ANSI/ANS-6.4.3 (1991) standardreference database. Both of the calculations are in goodagreement except for the slight differences which may be due to(a) the ANSI/ANS data are based on the calculation result data by

using the moments method (Eisenhauer and Simmons, 1975)with parallel beam source and the Monte Carlo code, EGS4 withisotropic emission source, (b) the development of the low energyphoton treatments in EGS4 such as K-X-ray, L-X-ray andBremsstrahlung. It was shown by Shimizu et al. (2004) that themethods based on invariant embedding, G.P fitting and MonteCarlo simulation agree well for 18 low-Z materials withinsmall discrepancies. In the present study, the Zeq values of Earth,Moon and Mars samples lie in the range 10–18. Hence, the usedmaterials can be considered as low Zeq materials. When comparedwith other available approximations such as Berger, Taylorand three exponential, the geometric progression (G.P) fittingseem to reproduce the buildup factors with better accuracy.Harima et al. (1986) have shown that the absolute values ofmaximum deviations of exposure build factors for water in G.P.fitting is within 0.5–3%, in three-exponential approach is within0.4–9.3%, in Berger approach is within 0.9–42.7% and in Taylorapproximation is within 0.4–53.2%.


4. Conclusions

From the present study it can be concluded that

�
The gamma ray energy absorption buildup factors have beencalculated using the five parameter geometric progression (G-P)fitting formula for some Earth, Moon and Mars samples in theenergy region 0.015–15 MeV up to a penetration depth of 40mean free paths, for the first time. � The maximum values of EABF occur in the intermediate energy
region where Compton scattering is the main interactionprocess whereas the minimum values of EABF occur at lowerand higher energy regions where absorption processes namelyphotoelectric absorption and pair production start dominating.
� In general, the Earth samples have the larger values of EABF
whereas the Mars samples have the lower values of EABF amongthe all samples. Beyond 1 MeV, there is no significant variation inEABF for the Earth, Moon and Mars samples, hence the values ofEABF remain constant with the variation in chemical compositionfor all the given materials at the higher incident photon energies.
� For the photon energies 0.15 MeV or lower, it was seen that the
increase in weight fraction of Si lead to higher values of EABF

while the increase in weight fraction of Fe lead to lower values ofEABF for the Earth and Mars samples. After 1 MeV, the EABF doesnot vary with the change in weight fractions of both Si and Fe.

Finally, in order to evaluate the effective doses given to thesematerials and evaluate the soil and rock parameters such as watercontent, bulk density and porosity with higher accuracy, thebuildup factors of gamma rays should be taken into account sincethe energy absorption buildup factor may reach to significantlyhigher values in Earth, Moon and Mars samples.

References

Allen, C., Albert, F.G., Combie, J., Banin, A., Yablekovitch, Y., Kan, I., Bodnar, R.J.,Hamilton, V.E., Jolliff, B.L., Kuebler, K., Wang, A., Lindstrom, D.J., Morris, P.A.,Morris, R.V., Murray, R.W., Nyquist, L.E., Simpson, P.D., Steele, A., Symes, S.J.,1999. Effects of sterilizing doses of gamma radiation on Mars analog rocks andminerals. J. Geophys. Res. 104 (E11), 27043–27066.

ANSI/ANS-6.4.3, 1991. Gamma ray attenuation coefficient and buildup factors forengineering materials. American Nuclear Society, La Grange Park, Illinois.

Appoloni, C.R., Pottker, W.E., 2004. Non-destructive porosity profile measurement ofamorphous materials by gamma-ray transmission. Appl. Radiat. Isot. 61,1133–1138.

Appoloni, C.R., Fernandes, C.P., Innocentini, M.D.M., Macedo, A., 2004. Ceramicfoams porous microstructure characterization by X-ray microtomography.Mater. Res. 7 (4), 557–564.

Asano, Y., Sakamoto, Y. 2007. Gamma ray buildup factors for heavy concretesJAEData/Code 2007–006.

Berger, M.J., Hubbell, J.H., 1999. XCOM: photon cross sections database. Web version1.2, available at/http://physics.nist.gov/xcomS, National Institute of Standardsand Technology, Gaithersburg, MD 20899, USA, August 1999. Originallypublished as NBSIR 87-3597, XCOM: Photon cross sections on a personalcomputer (July 1987) 1987–1999.

Brar, G.S., Mudahar, G.S., 1996. Energy dependence of the energy absorption buildupfactor of HCO materials. Radiat. Phys. Chem. 47, 795–799.

Brar, G.S., Sidhu, G.S., Singh, P.S., Mudahar, G.S., 1999. Buildup factor studies of HCO-materials as a function of weight fraction of constituent elements. Radiat. Phys.Chem. 54, 125–129.

Brar, G.S., Sidhu, G.S., Sandhu, P.S., Mudahar, G.S., 1998. Variation of buildup factorsof soils with weight fractions of iron and silicon. Appl. Radiat. Isot. 49, 977–980.

Chantler, C.T., 2000. Detailed tabulation of atomic form factors, photoelectricabsorption and scattering cross section and mass attenuation coefficients inthe vicinity of absorption edges in the soft X-ray (Z¼30–36, Z¼60–89, E¼0.1–10 keV), Addressing convergence issues of earlier work detailed tabulationof atomic form factors, photoelectric absorption and scattering cross section,and mass attenuation coefficients in the vicinity of absorption edges in the soft

X-ray (Z¼30–36, Z¼60–89, E¼0.1–10 keV), addressing convergence issues ofearlier work. J. Phys. Chem. Ref. Data 29, 597.

Economou, T., 2001. Chemical analyses of martian soil and rocks obtained by thepathfinder alpha proton X-ray spectrometer. Radiat. Phys. Chem. 61, 191–197.

Economou, T.E., Turkevich, A.L., Sowinski, K.P., Paterson, J.H., Franzgrote, E.J., 1970.Alpha–scattering technique of chemical analysis. J. Geophys. Res 75,6514–6523.

Eisenhauer, C.M., Simmons, G.L., 1975. Point isotropic gamma ray buildup factors inconcrete. Nucl. Sci. Eng. 56.

Franzgrote, E.J., Paterson, J.H., Turkevich, A.L., Economou, T.E., Sowinski, K.P., 1970.Chemical composition of the lunar surface in Sinus Medii. Science 167, 376–379.

Gerward, L., Guilbert, N., Jensen, K.B., Levring, H., 2001a. X-ray absorption in matter.Reengineering XCOM. Radiat. Phys. Chem. 60, 23–24.

Gerward, L., Guilbert, N., Jensen, K.B., Levring, H., 2004b. WinXCom—a programfor calculating X-ray attenuation coefficients. Radiat. Phys. Chem. 71, 653–654.

Harima, Y., Sakamoto, Y., Tanaka, S., Kawai, M., 1986. Validity of the geometric-progression formula in approximating gamma ray build up factors. Nucl. Sci.Eng. 94, 24–35.

Harima, Y., 1983. An approximation of gamma ray buildup factors by modifiedgeometrical progression. Nucl. Sci. Eng. 83, 299–309.

Harima, Y., 1993. A historical review and current status of build-up factorcalculations and applications. Radiat. Phys. Chem. 41, 631–672.

Harima, Y., Sakamoto, Y., Tanaka, S., Kawai, M., Fujita, T., Ishikawa, T., Kinno, M.,Hayashi, K., Matsumoto, Y., Nishimura, T. 1986. Applicability of geometricalprogression approximation (G-P method) of gamma-ray buildup factors, JapanAtomic Energy Research Institute (JAERI)-M 86-071.

Hubbell, J.H., 1999. Review of photon interaction cross section data in the medicaland biological context. Phys. Med. Biol. 44, R1.

Manohara, S.R., Hanagodimath, S.M., Gerward, L., 2010. Energy absorption buildupfactors for thermoluminescent dosimetric materials and their tissue equiva-lence. Radiat. Phys. Chem. 79, 575–582.

Masarik, J., Reedy, R., 1996. Gamma ray production and transport in Mars.J. Geophys. Res. 101 (E8), 18891–18912.

Massambani, O., Mantovani, M.S.M., 1997. In: Marte: Novas Descobertas, Sa\wide-tildeo Paulo: Diagrama & Texto: Instituto Astrono\widehat mico e Geofı�sico,IAG/USP.

Moreira, A.C., Appoloni, C.R., 2006. Mass attenuation coefficient of the Earth, Moonand Mars samples over 1 keV–100 GeV energy range. Appl. Radiat. Isot. 64,1065–1073.

Mudahar, G.S., Sahota, H.S., 1986. A new method for simultaneous measurementof soil bulk density and water content. Int. J. Appl. Radiat. Isot. 37 (7), 563–565.

Oliveira Jr., J.M., Filho, N.A., Chaud, M.V., Angiolucci, T., Aranha, N., Martins, A.C.G.,2010. Porosity measurement of solid pharmaceutical dosage forms by gamma-ray transmission, Appl. Radiat. Isot. 68 (12), 2223–2228.

Paterson, J.H., Franzgrote, E.J., Turkevich, A.L., Anderson, W.A., Economou, T.E.,Griffin, H.E., Crotch, S.L., Sowinski, K.P., 1969. Alpha-scattering experimenton Surveyor 7: comparison with Surveyor 5 and 6. J. Geophys. Res. 74,6120–6148.

Pires, L.F., Rosa, J.A., Pereira, A.B., Arthur, R.C.J., Bacchi, O.O.S., 2009. Gamma-rayattenuation method as an efficient tool to investigate soil bulk density spatialvariability. Ann. Nucl. Energy 36, 1734–1739.

Reedy, R., Arnold, J., Trombka, J., 1973. Expected g Ray Emission Spectra from theLunar Surface as a Function of Chemical Composition. J. Geophys. Res. 78 (26),5847–5866.

Sakamoto, Y., Tanaka, S., 1988. Interpolation of gamma ray buildup factors for pointisotropic source with respect to atomic number. Nucl. Sci. Eng. 100, 33–42.

Shimizu, A., 2002. Calculations of gamma-ray buildup factors up to depths of 100mfp by the method of invariant embedding, (I) analysis of accuracy andcomparison with other data. J. Nucl. Sci. Technol. 39, 477.

Shimizu, A., Onda, T., Sakamoto, Y., 2004. Calculations of gamma-ray buildup factorsup to depths of 100 mfp by the method of invariant embedding, (III) generationof an improved data set. Nucl. Sci. Technol. 41, 413–424.

Shin, K., Hirayama, H., 2001. Calculation of gamma-ray buildup factor for two-layered shields made of water, concrete and iron and discussed on application ofapproximating formula. Radiat. Phys. Chem. 61, 583–584.

Sidhu, G.S., Singh, P.S., Mudahar, G.S., 1999. Energy absorption buildup factor studiesin biological samples. Radiat. Prot. Dosim. 86, 207–216.

Silva, H., 1996. The effect of absorbed dose build-up factor on food irradiationprocessing. Radiat. Phys. Chem. 35, 845–849.

Singh, S.P., Singh, T., Kaur, P., 2008. Variation of energy absorption buildup factorswith incident photon energy and penetration depth for some commonly usedsolvents. Ann. Nucl. Energy 35, 1093–1097.

Singh, T., Kumar, N., Singh, S.P., 2009. Chemical composition dependence ofexposure buildup factors for some polymers. Ann. Nucl. Energy 36, 114–120.

Subudhi, R.K., Hussein, Esam M.A., Al, T.A., 2010. Measurement of spatial distribu-tion of total and accessible porosity in sedimentary rocks using isotopicradiation transmission: Device design and testing. Appl. Radiat. Isot. 68,496–504.

Turkevich, A.L., Franzgrote, E.J., Paterson, J.H., 1969. Chemical composition of thelunar surface in mare tranquillitatis. Science 165, 277–279.

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Analysis of some Earth, Moon and Mars samples in terms of gamma ray energy absorption buildup...

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