Gamma-ray attenuation method as an efficient tool to investigate soil bulk density spatial variability

Annals of Nuclear Energy 36 (2009) 1734–1739

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Gamma-ray attenuation method as an efficient tool to investigate soil bulk density spatial variability L.F. Pires a,*, J.A. Rosa b, A.B. Pereira c, R.C.J. Arthur d, O.O.S. Bacchi d a

Laboratory of Soil Physics and Environmental Sciences, State University of Ponta Grossa, UEPG, C.E.P. 84.030-900 Ponta Grossa, PR, Brazil Laboratory of Soil Physics, Agricultural Research Institute of Paraná, IAPAR, C.E.P. 84.001-970 Ponta Grossa, PR, Brazil c Laboratory of Agrometeorology, State University of Ponta Grossa, UEPG, C.E.P. 84.030-900 Ponta Grossa, PR, Brazil d Laboratory of Soil Physics, Center for Nuclear Energy in Agriculture, USP/CENA, C.E.P. 13.400-970 Piracicaba, SP, Brazil b

a r t i c l e

i n f o

Article history: Received 20 May 2009 Accepted 25 August 2009 Available online 25 September 2009

a b s t r a c t The spatial variability of soil bulk density (qb) was measured by using the volumetric ring method (VRM) and the gamma-ray attenuation method (GAM). Collimated radiation from 3.7 GBq of 241Am was used to evaluate the soil mass attenuation coefficient and its bulk density. Circular lead collimators were adjusted and aligned between source (D = 1, 2 and 3 mm) and detector (D = 4.5 mm). Results of GAM for average qb provided good agreement with the corresponding values obtained gravimetrically. Variations in bulk density for different collimator dimensions can be attributed to multiple scattering after photons interaction with soil, mainly for 3 mm collimator size. The best result of qb by the nuclear technique was obtained when qb represents an average of the measurements for collimators of 1 and 2 mm. Another cause for the differences in qb by GAM and VRM is the heterogeneity of soil when the collimated beam can interact with stones or large air-filled holes or channels present in the sample. Therefore, the pattern of spatial variability obtained by VRM was confirmed by GAM for all collimator sizes. This result is a good indication that GAM can be used with success to analyze soil spatial variability. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction The gamma-ray attenuation method (GAM) represents one of the most used non-destructive tools to evaluate the soil bulk density (qb). The method is based on the probability of gamma photon interaction with the soil sample. This interaction is due to three different processes (Photoelectric absorption, Compton scattering and Pair production) whose probability depends on energy gamma radiation. When the gamma photon beam interacts with the matter the probability of all interaction process represents the linear attenuation coefficient (l) (Wang et al., 1975; Singh et al., 2004). For soil samples l is a result of the contributions from solid mineral and organic components, water and air. However, the attenuation of the beam by the air is insignificant as compared with the attenuation by soil particles and water, and can, therefore, be neglected (Ferraz and Mansell, 1979). Gamma-ray attenuation coefficients can also be expressed as mass attenuation coefficients (lm), which represents the ratio between l and qb. Two different ways can be utilized to measure qb by gamma attenuation: (1) the scattering method and (2) the transmission method. The first one is applied to depth and surface determina-

* Corresponding author. Tel.: +55 42 3220 3044; fax: +55 42 3220 3042. E-mail addresses: [email protected], [email protected] (L.F. Pires). 0306-4549/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2009.08.016

tions, by mainly using gamma/neutron surface gauges, while the second one is employed for depth or laboratory evaluations. Results of soil densitometry in the scientific literature can be found by using single and dual energy gamma-ray beams (van Bavel et al., 1957; Reginato, 1974). The latter is commonly applied for swelling soils which swell upon wetting with water and shrink upon drying. In this case qb changes during water movement through the soil and cannot be considered constant. Therefore, for stable soils, a single beam is enough for laboratory qb determinations, because is not necessary to measure simultaneously the soil water content and soil density. Physical properties of a soil can vary significantly within relatively short distances, as a few meters (Warrick and Nielsen, 1980). Physical parameters of soils vary, in part, due to the natural soil heterogeneity; this heterogeneity leads, in particular, to differences in the plant growth. Soil heterogeneity is a result of various natural processes and human activities. One of the parameters traditionally used to characterize soil structure heterogeneity is its bulk density. Soil bulk density, represented by the ratio between soil mass and soil volume, is meant to give an idea of the percentage of voids that define soil structure (Blake and Hartge, 1986). Changes in qb can cause modifications in soil water storage capacity and matric soil water potential, which are parameters used in irrigation and drainage management, and therefore have economic significance in agriculture.

L.F. Pires et al. / Annals of Nuclear Energy 36 (2009) 1734–1739

The technique traditionally used to evaluate qb in laboratory is the volumetric ring method (VRM). In this method steel cylinders are introduced by samplers into the soil and undisturbed volumetric samples are obtained. Then soil samples are conducted to the laboratory, dried and weighted in order to obtain gravimetrically the bulk density (Blake and Hartge, 1986). On the other hand, GAM is a non-invasive inspection technique that allows measurements of qb point to point on a millimetric scale without interfering with the physical integrity of the sample. Both VRM and GAM have widely been used to evaluate the soil bulk density, however VRM only allows measurements of global qb while GAM permits determinations of punctual qb as small as the collimator size. However, to obtain representative values of qb by the gamma-ray attenuation method is necessary to pay attention to: (1) the soil sample dimensions; (2) the radiation energy; (3) the collimator size and shape; (4) the distance between gamma source and detector and (5) the detector size (van Bavel et al., 1957; Ferraz and Mansell, 1979). Although, GAM has widely been used for qb evaluations the literature about the efficiency of this method to analyze the spatial variability of this physical property is very scarce. So the purpose of this research was twofold: first, to verify the possibility of GAM to give representative qb values such as those obtained by VRM in order to evaluate soil spatial variability; and second, to analyze possible causes for differences in qb values measured by GAM in comparison to VRM.

2. Material and methods Soil core samples were taken from a soil profile of a Dystrophic Dark Red Latosol (Oxisol) (12% sand, 23% silt, 65% clay) from an experimental field at the Agricultural Research Institute of Parana (IAPAR), in Ponta Grossa, PR, Brazil (25°130 S; 50°010 W; 875 m above sea level). According to Koppen’s classification the climate of Ponta Grossa is of the Cfb type, humid subtropical with mild summers. Average values for air temperature, rainfall, and relative humidity are 18 °C; 1542 mm/year; and 77%, respectively. The rainfall is distributed throughout the year without a pronounced dry period. Winters are colder than in other areas of the state and frosts are frequent. Soil samples were collected in an area submitted to the no-tillage management system. A total of 33 cylindrical samples (5.0 cm high and 4.8 cm internal diameter) were collected from the soil surface layer (0–10 cm) with steel cylinders using a stainless steel core sampler (5.5 cm high and 5.0 cm internal diameter). The sampler allows the introduction of the steel cylinders in their inner space and soil samples are collected in these cylinders by a procedure that starts with a mass pressuring the equipment in order to introduce the sampler containing the steel cylinder into the soil, down to the desired depth. After complete introduction of the set into the soil, the surrounding soil is removed with a spade. The excavation is made carefully allowing the extraction of the cylinder containing the sample for density evaluation. Caution is needed during this process to minimize vibration, shear stress and compaction effects on the structure of the soil sample. The excess of soil outside cylinder was carefully trimmed off and top and bottom surfaces of the sample were made flat to be sure that the soil volume was equal to the internal volume of the core. For evaluations and comparisons of the methods a 40 m spatial transect was chosen inside the no-tillage area on which samples were collected at 11 points (P), spaced 4 m from each other (Fig. 1). At each point three core samples with volumes of 97.8 cm3 were collected for the determination of the bulk density by the volumetric ring and gamma-ray attenuation methods. After measurements of qb by VRM the very same soil samples were utilized in GAM.

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Fig. 1. Distribution of soil sampling position points (P) along a 40 m spatial transect.

Evaluation of qb by VRM was made with samples placed in a drying oven at 110 °C for 24 h. Details about the method used to measure qb can be found in Blake and Hartge (1986). In relation to GAM, qb was obtained solving the following equation (Hopmans and Dane, 1986):

I ¼ I0 expðlms qb x  lmw hqw xÞ

ð1Þ

where I0 and I (cps) are the incident and the transmitted beam intensities, x (cm) is the sample thickness, lms and lmw (cm2 g1) represent the mass attenuation coefficients of soil and water, and h (cm3 cm3) and qw (g cm3) are the volumetric water content and the water density, respectively. As soil samples were dried in an oven at 60 °C for 96 h the second term in the right side of Eq. (1) can be eliminated. For the measurement of soil mass attenuation coefficient, airdried soil samples were passed through a 2.0 mm sieve and packed into thin wall acrylic containers (183.6 cm3). Monoenergetic photon intensities were measured at different positions of the container (x = 5.1 cm). The lms value represents an arithmetic mean value of five replications. The Beer–Lambert equation (Wang et al., 1975) was used to obtain the linear attenuation coefficient of soil and the following equation was utilized to evaluate lm:

lm ¼

l qgb

ð2Þ

where l (cm1) is the linear attenuation coefficient and qgb (g cm3) represents the global physical density of the material analyzed. In the case of soil qgb was obtained by the volumetric ring method (Blake and Hartge, 1986). In order to use Eq. (2) and after Eq. (1), first we evaluated qgb data for each soil sample utilized in the experiment. The soil bulk density by GAM was monitored using a radioactive gamma-ray source of 241Am having an activity of 3.7 GBq emitting monoenergetic photons of 59.54 keV. The detector was a 7.62  7.62 cm NaI(Tl) scintillation crystal coupled to a photomultiplier tube. Circular lead collimators were adjusted and aligned between source (D = 1, 2 and 3 mm) and detector (D = 4.5 mm). As the source and the detector are fixed, the soil sample was moved across the beam and scanned at two different vertical positions (p1 = 1.5 and p2 = 2.5 cm below the upper surface of the sample). The radioactive source and detector were mounted 25.0 cm apart and the counting time was 20 s with three replications for

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Statistical softwares were used for data processing. Normality tests were performed on the data prior to their statistical processing. An analysis of variance (ANOVA) and the Scheffé’s multiple range test (P < 0.05) were performed to analyze statistical differences and to discriminate means. 3. Results

Fig. 2. Schematic diagram of the gamma-ray beam attenuation system: (1) lead collimators, (2) 241Am source, (3) Pb holding, (4) NaI(Tl) detector, (5) soil sample, p1 and p2 measuring points.

1.40 1.20

b

ρ (g.cm-3 )

1.00 0.80 0.60

Average between p1 and p2 GAM 1 mm GAM 2 mm GAM 3 mm VRM Average 1 and 2 mm

0.40 0.20 0.00 0

6

12

18

24

30

36

42

P (m) Fig. 3. Distribution of average soil bulk density (qb) values along a 40 m spatial transect (positions P) determined by the volumetric ring method (VRM) and the gamma-ray attenuation method (GAM). p1 and p2 represent the positions of gamma-ray beam passage inside the soil sample and 1–3 mm the collimator sizes positioned in the radioactive source.

each collimator and position of beam scanning (Fig. 2). The experiments were conducted at constant temperature (21 °C) to avoid any shift of the primary peak of 241Am gamma source.

The mass attenuation coefficient of the soil was calculated from Eq. (1) for known physical density (determined gravimetrically, 0.89 g cm3) by using gamma-ray transmission measurements. The lms obtained for the Oxisol was 0.3122 ± 0.0006 cm2 g1, for the 59.54 keV photons. The width (x) of soil samples to evaluate both lms and qb was measured with vernier calipers in order to improve the precision of the nuclear method. In Fig. 3 the spatial variability of soil bulk density values with the respective standard deviations is presented along the 40-m spatial transect for GAM and VRM. It is important to recognize that VRM is considered the pattern method herein. Analyzing Fig. 3, it is possible to verify that qb values are not homogeneous along the spatial transect for VRM. The same behavior can be observed for GAM for the different size of collimators. By the results the increase in the collimator size caused an over-estimation of qb. However, considering the average of qb obtained for 1 and 2 mm collimators the values of this soil physical property present only slight variation between methods. So, the pattern of spatial variability measured with VRM could be confirmed by GAM (Table 1). The same behavior is observed for the different collimator sizes, but with lower and higher bulk densities than those of VRM. The region with higher bulk densities was at position (P) 12 m, which could be due to the presence of a compacted soil strip. The same result was observed for both methods. Differences between maximum and minimum qb ranged from 0.14 g cm3 (GAM1) to 0.18 g cm3 (GAM3), slightly smaller and greater than in the case of VRM (0.15 g cm3). According to the Scheffé’s multiple range test no statistical differences along the qb spatial transect for both treatments and collimator sizes was found (Table 1). These results show that the gamma-ray attenuation method can give representative values of qb for spatial variability studies when compared with the volumetric ring one. The same spatial variability tendency of qb presented by GAM in relation to VRM (Fig. 3) indicates that the nuclear method can be applied with success for soil physical properties

Table 1 Average soil bulk density (qb) values and relative errors (RE) determined through the volumetric ring method (VRM) and the gamma-ray attenuation method (GAM) along the spatial transect (different positions). Position

P1-0 m P2-4 m P3-8 m P4-12 m P5-16 m P6-20 m P7-24 m P8-28 m P9-32 m P10-36 m P11-40 m

a

RE(%)b

qb (g cm3) GAM1a

GAM2a

GAM3a

VRM

GAM12a

GAM1

GAM2

GAM3

GAM12

0.82a,C 0.89a,C 0.89a,C 0.96a,C 0.85a,C 0.88a,B 0.90a,E 0.91a,C 0.92a,A 0.94a,C 0.91a,C

0.99a,AB 1.10a,AB 1.11a,A 1.16a,AB 1.01a,AB 1.07a,AB 1.11a,B 1.15a,AB 1.14a,A 1.15a,AB 1.11a,AB

1.06a,A 1.16a,A 1.16a,A 1.24a,A 1.07a,A 1.15a,A 1.18a,A 1.21a,A 1.22a,A 1.21a,A 1.17a,A

0.93a,B 0.95a,BC 0.96a,BC 1.05a,BC 0.90a,BC 0.96a,AB 0.95a,D 0.98a,C 1.03a,A 1.03a,BC 0.95a,BC

0.90a,BC 1.00a,ABC 1.00a,B 1.06a,BC 0.93a,BC 0.97a,AB 1.00a,C 1.03a,BC 1.03a,A 1.04a,BC 1.01a,ABC

11.83 6.32 7.29 8.57 5.56 8.33 5.26 7.14 10.68 8.74 4.21

6.45 15.79 15.63 10.48 12.22 11.46 16.84 17.35 10.68 11.65 16.84

13.98 22.11 20.83 18.10 18.89 19.79 24.21 23.47 18.45 17.48 23.16

3.23 5.26 4.17 0.95 3.33 1.04 5.26 5.10 0.00 0.97 6.32

MAXc MINc

11.83 4.21

6.45 17.35

13.98 24.21

3.23 6.32

GAM1, GAM2, GAM3, and GAM12 = gamma-ray attenuation method with 1, 2, 3 mm and 1 mm plus 2 mm collimators. RE = Relative error calculated as: REð%Þ ¼ ðqbVRM  qbGAM =qbVRM Þ  100. MAX and MIN = maximum and minimum; mean soil bulk density values are the average of three samples for each position (P); means followed by the same letter are not significant different by the Scheffé’s multiple range test (P < 0.05); capital and normal letters represent the application of the statistical test among methods and among positions within a same method, respectively. b

c

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(a) 1.40 1.30

(a)

Average p1 and p2 - 1 mm ρb =0.18+0.73.ρ b GAM VRM r=0.72 Upper 95% Confidence Limit Lower 95% Confidence Limit

1.40 1.30

-3

GAM

1.10

1.00

ρb

GAM

1.10

ρb

1.20

(g.cm )

-3

(g.cm )

1.20

0.90

0.80

0.90

1.00

ρb

(b)

1.00 0.90 0.80

0.80 0.70 0.70

1.10

1.20

1.30

0.70 0.70

1.40

1.40 1.30

-3

(g.cm )

1.00 Average p1 and p2 - 2 mm =0.17+0.95.ρb ρb GAM VRM r=0.70 Upper 95% Confidence Limit Lower 95% Confidence Limit

0.90 0.80

1.00

(c)

1.10

1.20

1.30

-3

(g.cm )

1.30

1.40

(g.cm ) VRM

Position 2 (p2) - Average 1 and 2 mm ρb =-0.09+0.93.ρ b GAM VRM r=0.65 Upper 95% Confidence Limit Lower 95% Confidence Limit

1.00 0.90 0.80

1.40

0.70 0.70

-3

0.80

0.90

VRM

1.00

ρb

1.10

1.20

1.30

1.40

-3

(g.cm ) VRM

1.40

(c)

1.40

1.20

1.30 1.10 -3

0.80 0.70 0.70

(g.cm )

Average p1 and p2 - 3 mm =0.18+1.01.ρb ρb GAM VRM r=0.71 Upper 95% Confidence Limit Lower 95% Confidence Limit

0.90

0.80

0.90

1.00

ρb

1.10

1.20

1.30

1.40

Average p1 and p2 - Average 1 and 2 mm ρb =0.17+0.86. ρ b GAM VRM r=0.72 Upper 95% Confidence Limit Lower 95% Confidence Limit

1.20 1.10 GAM

1.00

ρb

GAM

1.20 -3

1.10

(g.cm )

1.30

ρb

1.10

1.20

GAM

ρb

GAM

1.10

ρb

-3

(g.cm )

1.20

ρb

1.00

ρb

-3

1.30

0.90

0.90

(g.cm )

(b)

0.80

0.80

VRM

1.40

0.70 0.70

Position 1 (p1) - Average 1 and 2 mm =-0.26+0.77.ρ b GAM VRM r=0.68 Upper 95% Confidence Limit Lower 95% Confidence Limit

ρb

1.00 0.90 0.80

-3

(g.cm ) VRM

Fig. 4. Relation between the average values of soil bulk density (qb) evaluated by the volumetric ring method (VRM) and the gamma-ray attenuation method (GAM) along a 40 m spatial transect. p1 and p2 represent the positions of gamma-ray beam passage inside the soil sample; and 1, 2, and 3 mm the collimator sizes positioned in the radioactive source.

variability studies. The relative error (RE) in the last column of Table 1 also shows that the average of 1 and 2 mm collimators presents the best values of qb in comparison to VRM. The very same result can be confirmed by the statistical agreement between GAM12 and VRM (Table 1). The CV, ranged from 4.3% (GAM1) to 5.1% (GAM2), slightly lower and higher than in the case of VRM (4.8%), represents an indication that observations of qb present a certain spatial homogeneity along the spatial transect. Figs. 4 and 5 show the relations among the values of soil bulk density obtained by VRM and GAM and also the linear correlations. The relation between methods was obtained comparing: first, qb

0.70 0.70

0.80

0.90

1.00

ρb

1.10

1.20

1.30

1.40

-3

(g.cm ) VRM

Fig. 5. Relation between the average values of soil bulk density (qb) evaluated by the volumetric ring method (VRM) and the gamma-ray attenuation method (GAM) along a 40 m spatial transect. p1 and p2 represent the positions of gamma-ray beam passage inside the soil sample; and 1, 2, and 3 mm the collimator sizes positioned in the radioactive source.

average values between p1 plus p2 and collimators of 1, 2, and 3 mm (Fig. 4); and second, qb average values for collimators of 1 mm plus 2 mm for p1 (Fig. 5a) and p2 (Fig. 5b) and qb average values for p1 plus p2 and 1 mm plus 2 mm (Fig. 5c). According to the observed in Fig. 4, based on the linear coefficient of correlation (r) a high positive adjustment of data was observed for all collimator sizes when compared to the volumetric ring method. The collimator of 1 mm presented under-estimated

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values of qb when compared to VRM (Fig. 4a) while the others (2 and 3 mm) provided over-estimated ones (Figs. 4b and c). The standard deviation in relation to the adjustment straight line was 0.04 (N = 33, P < 0.0001) for 1 mm collimator and 0.06 for 2 and 3 mm, respectively. Analyzing the confidence intervals 11 (GAM3), 12 (GAM1), and 14 (GAM2) qb values are inside of their limits at 95% of probability. From graphs of Fig. 5, it can be seen that for position 1 the major part of bulk density values are over-estimated in relation to VRM (Fig. 5a), while for position 2 the values of qb are almost equally distributed along the 1:1 straight line (Fig. 5b). The same results of p1 were found for p1 plus p2 with the major part of qb over-estimated in comparison to the pattern method. The standard deviation in relation to the adjustment straight line was 0.05 (N = 33, P < 0.0001) for p1, 0.06 for p2, and 0.05 for p1 plus p2, respectively. Analyzing the confidence intervals 10 (p1 and p2) and 13 (p1 plus p2) qb values are inside of their limits at 95% of probability. The highly significant correlation among the values of soil bulk density observed in Figs. 4 and 5 shows that the data evaluated by the gamma-ray attenuation method are reliable when compared to those from the volumetric ring method. These results are also a good indication that GAM can be used with success to analyze the pattern of soil spatial variability.

the increase in qb values for great collimator sizes can be attributed to the fact of the number of photons detected in the photopeak, after soil interaction, be smaller than the expected in the absence of multiple scattering. Since soils are not homogeneous even over short distances (Warrick and Nielsen, 1980) it is expected that qb will be variable in the region of measurement when the gamma-ray attenuation method is used. Probably, different collimator sizes will also give distinct bulk density values because stones or large air-filled holes or channels could be present in the soil sample. As the soil is rarely homogeneous the gamma-ray beam will follow a straight path from source to detector founding layers of differing density. However, because the volumetric ring method considers the whole soil bulk density (Blake and Hartge, 1986) it is natural to expect differences between methods mainly due to the size of soil portions analyzed by each technique. For example, Pereira and Rezende (2001) performed, in three areas with different type of soils, measurements of qb by GAM and VRM. These authors found qb values over-estimated by up to 0.12 g cm3 in relation to the traditional technique (VRM) for two soils and under-estimated by up to 0.06 g cm3 for the other soil.

4. Discussion

We can conclude by the results presented in this work that the gamma-ray attenuation method (GAM) for measuring bulk density agrees quite well with the volumetric ring method (VRM) and the pattern of spatial variability obtained by VRM could also be confirmed by GAM. Variations in bulk density for different collimator dimensions by GAM can be attributed to multiple scattering after photon interaction with soil, mainly for 3 mm collimator size. The best result of soil bulk density (qb) by the nuclear technique is obtained when qb represents an average of the measurements for collimators of 1 and 2 mm. The significant correlation among qb values determined through GAM and VRM indicates that the data measured by the nuclear technique can give adequate and reliable values of this soil physical property for studies of spatial variability. The best correlation between methods is obtained when qb represents an average of several measurements by the nuclear technique along the soil sample and an average of the evaluations for 1 and 2 mm collimator sizes.

Limitations on precision and resolution of the gamma-ray attenuation method can mainly be attributed to the random nature of photon emission from 241Am radioactive source and the absorption and scattering characteristics of the gamma-ray beam in the soil. These limitations are present in any type of nuclear measurements e.g. soil mass attenuation and bulk density evaluations. In order to improve the method and to reduce possible errors due to the random nature of photon emission, the total counts in the photopeak must be taken for sufficient time periods depending on the radioactive source activity (Ferraz and Mansell, 1979). The statistical accuracy obtained in this work for lms measurement was better than 1% for the container and the soil plus container. It is important to recognize that the soil container should be constructed with a rigid material to maintain the soil thickness and to attenuate as little as possible the radiation. The container used in this work was constructed from 0.4 cm thick acrylic. On the other hand, statistical accuracies involved in qb evaluations were better than: (1) 2% without any absorber and 4% with the soil sample for GAM1; (2) 1% without any absorber and 3% with the soil sample for GAM2 and (3) 1% without any absorber and with the soil sample for GAM3. Therefore, analyzing statistical accuracies related to lms and qb evaluations it is possible to conclude that the total counts in the photopeak were taken for sufficient time periods in order to obtain reliably values of soil bulk density and mass attenuation coefficient (Varier et al., 1986). Differences in qb values for different collimator sizes (Figs. 3–5 and Table 1) could be attributed to the contribution of multiple scattered photons for large thickness samples (Gopal and Sanjeevaiah, 1973; Abdel-Rahman et al., 2000; Singh et al., 2008). According to Gopal and Sanjeevaiah (1973), large sample thicknesses improve multiple scattering affecting evaluations of lms and qb. Varier et al. (1986) describe that beyond the thickness of samples another factor influencing lms is its transverse dimension. Sidhu et al. (1999) show the effect of collimator size in the attenuation coefficient and demonstrate that when the solid angle is decreased the effect of multiple scattered photons is reduced and it can be neglected for large absorber thickness. However, in this work the thickness and transverse dimensions of soil samples was maintained constant for all collimator sizes. Therefore,

5. Concluding remarks

Acknowledgment The authors are grateful to Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for the scientific grants. References Abdel-Rahman, M.A., Badawi, E.A., Abdel-Hady, Y.L., Kamel, N., 2000. Effect of sample thickness on the measured mass attenuation coefficients of some compounds and elements for 59.54, 661.6 and 1332.5 keV gamma-rays. Nucl. Instrum. Methods Phys. Res. A 447, 432–436. Blake, G.R., Hartge, K.H., 1986. Bulk density. In: Klute, A. (Ed.), Methods of Soil Analysis: Physical and Mineralogical Methods. American Society of Agronomy, Madison, pp. 363–375. Ferraz, E.S.B., Mansell, R.S., 1979. Determining water content and bulk density of soil by gamma ray attenuation methods. Technical Bulletin 807 IFAS. Institute of Food and Agricultural Sciences, University of Florida. 51 p. Gopal, S., Sanjeevaiah, B., 1973. Gamma-ray attenuation coefficient measurements. Phys. Rev. 8, 2814–2818. Hopmans, J.W., Dane, J.H., 1986. Calibration of a dual-energy gamma radiation system for multiple point measurements in a soil. Water Resour. Res. 22, 1109– 1114. Pereira, J.R.A., Rezende, M.A., 2001. Determinação da densidade do solo para diferentes tipos de manejos e metodologias. Irriga 6, 1–9. Reginato, R.J., 1974. Gamma radiation measurements of bulk density changes in a soil pedon following irrigation. Soil Sci. Soc. Am. Proc. 38, 24–29.

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