- Email: [email protected]
Effective atomic number studies in different soils for total photon interaction in the energy region 10–5000 keV
App/. Radiar. hr. J. Radial.
Isor. Vol. 39, No. 12, pp. Appl. Insrrum. Part A
1251-1254,
0883-2889/88
1988
$3.00
+ 0.00
Copyright Q 1988 Pergamon Press plc
Printed in Great Britain. All rights reserved
Effective Atomic Number Studies in Different Soils for Total Photon Interaction in the Energy Region 104000 keV G. S. MUDAHAR’
and H. S. SAHOTA’,*
‘Department of Physics, Punjab Agricultural University, Ludhiana 141004, India and ‘Department of Physics, Punjabi University, Patiala-147002, India (Received
10 December
1987; in reoised ,form 25 March
1988)
Effective atomic numbers (Z,,) of 12 different soil samples were computed for total photon interaction cross sections using theoretical data over a wide energy region from IO to 5000 keV. It is seen that Z,, of a composite material, like soil, changes with a change in energy. With an increase in energy from 10 to 20 keV, Z,, increases, then remains nearly constant up to 40 keV but decreases sharply from 40 to 400 or 500 keV, and a further comparatively small rate of decrease up to 1500 keV. However, there is a small but continuous increase in Z,, with photon energy increases of 15OG5000 keV. This significant change in Z,, of soil is due to variations in the domination of different interaction processes in different energy regions as well as to the large number of elements present in the soil.
Introduction In our previous work (Mudahar and Sahota, 1988), the effects of grain size and compaction (achieved by pressure) on the linear and mass attenuation coefficients of soil for different y radiations were studied with a view to checking the suitability of soil as a radiation shielding material. In this connection, the study of effective atomic number (Z,,) of soil has great significance. The above study of Z,, in a composite material like soil should also be useful for comparison with similar studies in alloys, and compounds where the number of elements is much smaller and the atomic numbers of the constituents do not differ very widely. Restricted attempts have been made at studying different y-ray-energy regions in alloys and compounds. Hine (1952) reported that the Z,, of a material composed of several elements cannot be expressed by a single number. For each of the different processes by which y rays can interact with matter, the various atomic numbers in the material have to be weighted differently. In the light of Hine’s (1952) suggestion, different workers (Sastry and Jnanananda, 1958; Rama Rao et al., 1961, 1963; Parthasaradhi, 1968; Lingam et al., 1984) conducted Z,, studies in different alloys and compounds, and concluded that the statement made by Hine (1952) was justified. The present study of the Z,, of soil in which the elemental composition varies in materials bearing the *Author
for correspondence,
same name is also the first of its kind. In previous studies, the energy regions were limited to either below 662 keV (Parthasaradhi, 1968; Lingam et al., 1984) or above (Rama Rao et al., 1961, 1963). Thus the present study covers the energy regions in which the influence of all photon interaction processes (e.g. photoelectric coherent, incoherent and pair production) can be seen. In the present work the Z,, studies have been conducted in 12 different soil samples using total photon interaction cross sections in the energy region from 10 to 5000 keV in 22 energy steps. The results reported in the paper are discussed.
Calculation
Work
To study the effective atomic number of different soil samples, the total photon-interaction cross sections (barn/atom) were taken from the widely accepted and used tables of Storm and Israel (1970) for different photon energies i.e. 10, 15, 20, 30, 40, 50, 60, 80, 100, 150, 200, 300, 400, 500, 600, 800, 1000, 1500,2000, 3000,400O and 5000 keV. The more recent attenuation coefficients revised by Hubbell (1982) are available. However, these revisions will not affect the present calculations for our low- and medium-Z materials in the considered energy-range. The total interaction cross section is a sum of the cross sections of the partial processes i.e. qtotal) =
1251
o(photo)
+
o(coh)
+
ulincoh)
+
oCva~r)
G. S. MUDAHAR and
1252
Table I. Chemical comuositions
A,, Horizon (&22 cm) A,, Horizon (2240 cm) A ,3 Horizon (4&65 cm) C, Horizon (9&l 50 cm) Red soil (&lOcm) Black soil (O-15 cm) Alluvial soil (&20 cm) Sand (l&20 cm) Coarse silt (&20cm) Fine silt (&20cm) Coarse clay (O-20 cm) Fine clay (l&20 cm)
H. S.
SAHOTA
of different
soil samoles
SiO,
ALO,
Fe, 0,
TiO,
MnO
CaO
Me0
K,O
55.01 55.06 55.22 51.79 75.9 68.5 71.3 86.3 81.3 64.0 45.1 30.2
16.08 16.70 13.79 14.57 10.5 9.1 10.9 6.77 7.21 12.0 21.1 22.8
17.92 17.70 12.61 II.33 2.7 6.4 9.6 5.19 3.1 I 9.42 13.5 17.1
I .28
0.25 0.25 0.22 0.21 -
5.90 5.1 I 4.71 13.35 2.2 4.0 1.48 0.37 0.41 0.32 0.38 0.08
4.28 4.98 6.90 6.28 1.2 I.3 2.42 1.02 0.82 2.22 2.09 1.77
2.28 1.83 1.76 I.61 4.1 I.7 2.42 ~
The soil samples studied were 12 in number and different in chemical composition. Out of these, four were from different horizons* (A,, , A,,, A,? and C,) of the same profile of black soil (Gawande and Biswas, 1977). Another five were different fractions (sand, coarse silt, fine silt, coarse clay and fine clay) of the same A, horizon of Montalto silt loam soil (Joffe and Kunin, 1942). The remaining three were surface samples of red, black and alluvial soils (Krishnamoorthy and Govinda Rajan, 1977; Khangarot and Mehra, 1977). The chemical compositions of these soil samples are given in Table 1. Using theoretical cross-section data (Storm and Israel, 1970) for different soil elements, values of cross sections for SiO,, Al,O,, Fe,O,, TiO,, MnO, CaO, MgO, K,O, of which soil is largely composed, were calculated for different photon energies. Further utilizing these values, the effective cross sections for these soil samples were then computed using the following expression:
0.93 0.99 0.89
0.67 I .05 I .05 I .05 0.96 0.88
121 10
I
I
I
10’
10’
IO’
photon
energy (k eV)--
Fig. 1. Variation of effective atomic number (Z,,), for the total photon section (attenuation interaction cross coefficient), of different horizons of the same black soil, vs photon energy.
OWil= ,$, w,g, where N is the number of constituents in the soil and MI, presents the abundance by weight of the ith element such that
18
17 h
,$,W,=i. The calculations were made with the help of a computer (Hewlett-Packard 1000) and the results plotted to show the relationship between the theoretical total cross sections (Storm and Israel, 1970) in individual elements and the atomic number of the elements for all the photon energies. From these plots the effective atomic number of soil samples were obtained by interpolation. To obtain good accuracy of the results graphs of total cross sections at constant energies vs atomic numbers were drawn on an enlarged scale.
Fine clay Coarse clay Fine silt
Results and Discussion Z,, for all the soil samples are plotted against photon energy, as shown in Figs 1, 2 and 3.
the
*A “horizon” is a layer of soil approximately parallel to the soil surface, differing in properties and characteristics from adjacent layers below and above it.
11 10
I
1
lo2 photon
IO’ energy (k eV)---
10‘
Fig. 2. Variation of effective atomic number (Z,,), for the total photon interaction cross section (attenuation coefficient), of different fractions of the same Montalto soil, vs photon energy.
Effective atomic
ll, 10
10’
lo2 photon
energy (keV)-
Fig. 3. Variation of effective atomic number (Z,,), for the interaction cross section (attenuation total photon coefficient), of surface samples of red, black and alluvial soils, vs photon energy.
It is clear from our results that in line with alloys and compounds, in soil too, no definite atomic number exists, which supports the view point of Hine (1952). Further, the behaviour of Z,, with respect to energy is rather interesting. From the plots it is seen that with an increase in energy from 10 to 20 keV there is a small increase in Z,, of soils and that this is nearly constant between 20- and 40-keV photon energies. Then there is a sharp decrease with a further increase in energy from 40 to 400 or 500 keV. After this, Z,, decreases with increasing energy up to 1500 keV but at a comparatively slower rate. Beyond this, Z,, increases with further increases in energy from 1500 to 5000 keV. This increase in Z,, is small but continuous. This significant variation in Z,, is because of the relative domination of the partial photon interaction processes (photo, scattering and pair production). This variation also depends upon the range of the atomic number of the constituent elements, and number of elements in the composite material. The atomic numbers of elements of present soils vary from 8 (0,) to 26 (Fe) and a total of nine elements are considered. Parthasaradhi (1968) reported that the Z,, of alloys is different for partial processes such as photoelectric effect and scattering. In the first region where Z,, seems to be nearly constant, photoelectric interactions are dominant, so that here nearly constant Z,, may result. After 40 keV there is a sharp decrease in Z,, up to 400 or 500 keV. In this region the contribution of scattering increases, resulting in a decrease in Z,,. This point is confirmed by the results of Sastry and Jnanananda (1958) who reported that the Z,, for composite materials (e.g. tungsten steel etc.) is greater for photoelectric interactions than for other processes. The further decrease in Z,, with an
number
1253
of soils
increase in energy up to 1500 keV is small. This may be because in this region the dominant incoherent scattering falls off with a similar trend. Near 1500 keV, Z,, is least of all. With further increases in energy (from 1500 to 5000 keV) there is slight but continuous increase in Z,,. In this region the dominant processes are incoherent scattering and pair production. This behaviour of the curve may be due to the mixed contribution of these two processes. Rama Rao et al. (1963) reported that Z,, of rhodium-platinum alloys remains constant for pair-production cross sections in the energy region 1119-2000 keV. As the energy region presently considered extends up to 5000 keV our results show an increasing trend in Z,, with energy. This is because of the mixed contribution of scattering and pairproduction interaction processes in which, unlike the region covered by Rama Rao ef al. (1963), the contribution of pair production is increasing rapidly with energy. The energy region Z,, also depends upon the range of atomic number of the constituents which is clear from the results of Parthasaradhi (1968) Lingam et al. (1984) and Rama Rao et al. (1961). For water, Perspex and Monel metal no change in Z,, is seen, whereas for tungsten steel there is significant change. This is due to the fact that tungsten steel is composed of such elements which have a wider range of atomic numbers. In the present work, the change in Z,, of soil with energy is significant and comparable with the case of tungsten steel (Parthasaradhi, 1968; Rama Rao et al., 1961) which is a composition of W (23%) C (0.77%) Cr (4.25%) V (1.6%) Co (11%) and Fe (59.38%). Figure 4 shows the results of Parthasaradhi (1968) and Rama Rao et al. (1961) for tungsten steel for total photon interaction cross sections in the energy range covered by these two publications. The similarity in the pattern for soils and tungsten steel is evident. Another conclusion which may also be drawn from the present studies is that, along with the range of atomic number of the constituent elements, Z,, also
o Parthasaradhi l
251 0
(1968)
Rama Rao et al( 1961 )
I I 1000 500 photon energy (k eV)-
Fig. 4. Variation of effective interaction total photon coefficient), of tungsten
I 1500
atomic number (Z,,), for the section (attenuation cross steel, vs photon energy.
G. S. MUDAHAR and H. S. SAHOTA
1254
deoends won the number of elements Dresent. This may be the reason for the similarity in the behaviour of Z,, for soil and tungsten steel, both having large numbers of constituent elements. 1
1
Acknowledgement--The authors are thankful to Sh. Gurbakash Singh, Computer Centre, Punjab Agricultural University, Ludhiana for kind help in the computational work.
References Gawande S. P. and Biswas T. D. (1977) Characterisation and classification of black soils developed on basalt in relation to micro-relief. J. fnd. Sot. Soil Sci. 25, 233. Hine G. J. (1952) The effective atomic numbers of materials for various y-ray interactions. Phys. Reo. 85, 725. Hubbell J. H. (1982) Photon mass attenuation and energy absorption coefficients from 1 keV to 20 MeV. In?. J. A&. Radiat. Isot. 33, 1269. Joffe J: ‘S. and Kunin R. (1942) Mechanical separates and their fractions in the soil mofile: I. Variability in chemical composition and its pedogenic and agropedogic implications. Soil Sci. Sot. Proc. 187. Khangarot A. S. and Mehra R. K. (1977) Characterization
of alluvial 25, 241.
soils of Udaipur
Krishnamoorthy
Valley. J. Ind. Sot. Soil Sci.
P. and Govinda
Rajan S. V. (1977)
Genesis and classification of associated red and black soils under Rajolibunda diversion irrigation scheme (Andhra Pradesh). J. Ind. Sot. Soil Sci. 25, 239. Lingam S. C., Basu K. S. and Reddy D. V. K. (1984) Total gamma ray cross sections and effective atomic numbers in compounds in the energy region 32 to 662 keV. Ind. J. Phys. 58A, 285. Mudahar G. S. and Sahota H. S. (1988) Soil: A radiation shielding material. Int. J. Appl. Radial. ISOI. 39, 21. Parthasaradhi K. (1968) Studies on the effective atomic numbers in alloys for gamma ray interactions in the energy region 100-662 keV. Ind. J. Pure Appl. Phys. 6, 609. Rama Rao J., Lakshminarayana V. and Jnanananda S. (1961) Effective atomic number of alloys and compounds. J. Sci. Indust. Res. ZOB, 587. Rama Rao J., Lakshminarayana V. and Jnanananda S. (1963) Effective atomic number of alloys for pair creation. Ind. J. Pure Appl. Phys. 1, 315. Sastry K. S. R. and Jnanananda S. (1958) Attenuation coefficients for gamma rays from wCO. J. Sci. Indusf. Res. 17B, 389. Storm E. and Israel H. I. (1970) Photon cross sections from I keV to 100 MeV for elements Z = 1 to Z = 100. Nucl. Data Tables A7, 565.
Isor. Vol. 39, No. 12, pp. Appl. Insrrum. Part A
1251-1254,
0883-2889/88
1988
$3.00
+ 0.00
Copyright Q 1988 Pergamon Press plc
Printed in Great Britain. All rights reserved
Effective Atomic Number Studies in Different Soils for Total Photon Interaction in the Energy Region 104000 keV G. S. MUDAHAR’
and H. S. SAHOTA’,*
‘Department of Physics, Punjab Agricultural University, Ludhiana 141004, India and ‘Department of Physics, Punjabi University, Patiala-147002, India (Received
10 December
1987; in reoised ,form 25 March
1988)
Effective atomic numbers (Z,,) of 12 different soil samples were computed for total photon interaction cross sections using theoretical data over a wide energy region from IO to 5000 keV. It is seen that Z,, of a composite material, like soil, changes with a change in energy. With an increase in energy from 10 to 20 keV, Z,, increases, then remains nearly constant up to 40 keV but decreases sharply from 40 to 400 or 500 keV, and a further comparatively small rate of decrease up to 1500 keV. However, there is a small but continuous increase in Z,, with photon energy increases of 15OG5000 keV. This significant change in Z,, of soil is due to variations in the domination of different interaction processes in different energy regions as well as to the large number of elements present in the soil.
Introduction In our previous work (Mudahar and Sahota, 1988), the effects of grain size and compaction (achieved by pressure) on the linear and mass attenuation coefficients of soil for different y radiations were studied with a view to checking the suitability of soil as a radiation shielding material. In this connection, the study of effective atomic number (Z,,) of soil has great significance. The above study of Z,, in a composite material like soil should also be useful for comparison with similar studies in alloys, and compounds where the number of elements is much smaller and the atomic numbers of the constituents do not differ very widely. Restricted attempts have been made at studying different y-ray-energy regions in alloys and compounds. Hine (1952) reported that the Z,, of a material composed of several elements cannot be expressed by a single number. For each of the different processes by which y rays can interact with matter, the various atomic numbers in the material have to be weighted differently. In the light of Hine’s (1952) suggestion, different workers (Sastry and Jnanananda, 1958; Rama Rao et al., 1961, 1963; Parthasaradhi, 1968; Lingam et al., 1984) conducted Z,, studies in different alloys and compounds, and concluded that the statement made by Hine (1952) was justified. The present study of the Z,, of soil in which the elemental composition varies in materials bearing the *Author
for correspondence,
same name is also the first of its kind. In previous studies, the energy regions were limited to either below 662 keV (Parthasaradhi, 1968; Lingam et al., 1984) or above (Rama Rao et al., 1961, 1963). Thus the present study covers the energy regions in which the influence of all photon interaction processes (e.g. photoelectric coherent, incoherent and pair production) can be seen. In the present work the Z,, studies have been conducted in 12 different soil samples using total photon interaction cross sections in the energy region from 10 to 5000 keV in 22 energy steps. The results reported in the paper are discussed.
Calculation
Work
To study the effective atomic number of different soil samples, the total photon-interaction cross sections (barn/atom) were taken from the widely accepted and used tables of Storm and Israel (1970) for different photon energies i.e. 10, 15, 20, 30, 40, 50, 60, 80, 100, 150, 200, 300, 400, 500, 600, 800, 1000, 1500,2000, 3000,400O and 5000 keV. The more recent attenuation coefficients revised by Hubbell (1982) are available. However, these revisions will not affect the present calculations for our low- and medium-Z materials in the considered energy-range. The total interaction cross section is a sum of the cross sections of the partial processes i.e. qtotal) =
1251
o(photo)
+
o(coh)
+
ulincoh)
+
oCva~r)
G. S. MUDAHAR and
1252
Table I. Chemical comuositions
A,, Horizon (&22 cm) A,, Horizon (2240 cm) A ,3 Horizon (4&65 cm) C, Horizon (9&l 50 cm) Red soil (&lOcm) Black soil (O-15 cm) Alluvial soil (&20 cm) Sand (l&20 cm) Coarse silt (&20cm) Fine silt (&20cm) Coarse clay (O-20 cm) Fine clay (l&20 cm)
H. S.
SAHOTA
of different
soil samoles
SiO,
ALO,
Fe, 0,
TiO,
MnO
CaO
Me0
K,O
55.01 55.06 55.22 51.79 75.9 68.5 71.3 86.3 81.3 64.0 45.1 30.2
16.08 16.70 13.79 14.57 10.5 9.1 10.9 6.77 7.21 12.0 21.1 22.8
17.92 17.70 12.61 II.33 2.7 6.4 9.6 5.19 3.1 I 9.42 13.5 17.1
I .28
0.25 0.25 0.22 0.21 -
5.90 5.1 I 4.71 13.35 2.2 4.0 1.48 0.37 0.41 0.32 0.38 0.08
4.28 4.98 6.90 6.28 1.2 I.3 2.42 1.02 0.82 2.22 2.09 1.77
2.28 1.83 1.76 I.61 4.1 I.7 2.42 ~
The soil samples studied were 12 in number and different in chemical composition. Out of these, four were from different horizons* (A,, , A,,, A,? and C,) of the same profile of black soil (Gawande and Biswas, 1977). Another five were different fractions (sand, coarse silt, fine silt, coarse clay and fine clay) of the same A, horizon of Montalto silt loam soil (Joffe and Kunin, 1942). The remaining three were surface samples of red, black and alluvial soils (Krishnamoorthy and Govinda Rajan, 1977; Khangarot and Mehra, 1977). The chemical compositions of these soil samples are given in Table 1. Using theoretical cross-section data (Storm and Israel, 1970) for different soil elements, values of cross sections for SiO,, Al,O,, Fe,O,, TiO,, MnO, CaO, MgO, K,O, of which soil is largely composed, were calculated for different photon energies. Further utilizing these values, the effective cross sections for these soil samples were then computed using the following expression:
0.93 0.99 0.89
0.67 I .05 I .05 I .05 0.96 0.88
121 10
I
I
I
10’
10’
IO’
photon
energy (k eV)--
Fig. 1. Variation of effective atomic number (Z,,), for the total photon section (attenuation interaction cross coefficient), of different horizons of the same black soil, vs photon energy.
OWil= ,$, w,g, where N is the number of constituents in the soil and MI, presents the abundance by weight of the ith element such that
18
17 h
,$,W,=i. The calculations were made with the help of a computer (Hewlett-Packard 1000) and the results plotted to show the relationship between the theoretical total cross sections (Storm and Israel, 1970) in individual elements and the atomic number of the elements for all the photon energies. From these plots the effective atomic number of soil samples were obtained by interpolation. To obtain good accuracy of the results graphs of total cross sections at constant energies vs atomic numbers were drawn on an enlarged scale.
Fine clay Coarse clay Fine silt
Results and Discussion Z,, for all the soil samples are plotted against photon energy, as shown in Figs 1, 2 and 3.
the
*A “horizon” is a layer of soil approximately parallel to the soil surface, differing in properties and characteristics from adjacent layers below and above it.
11 10
I
1
lo2 photon
IO’ energy (k eV)---
10‘
Fig. 2. Variation of effective atomic number (Z,,), for the total photon interaction cross section (attenuation coefficient), of different fractions of the same Montalto soil, vs photon energy.
Effective atomic
ll, 10
10’
lo2 photon
energy (keV)-
Fig. 3. Variation of effective atomic number (Z,,), for the interaction cross section (attenuation total photon coefficient), of surface samples of red, black and alluvial soils, vs photon energy.
It is clear from our results that in line with alloys and compounds, in soil too, no definite atomic number exists, which supports the view point of Hine (1952). Further, the behaviour of Z,, with respect to energy is rather interesting. From the plots it is seen that with an increase in energy from 10 to 20 keV there is a small increase in Z,, of soils and that this is nearly constant between 20- and 40-keV photon energies. Then there is a sharp decrease with a further increase in energy from 40 to 400 or 500 keV. After this, Z,, decreases with increasing energy up to 1500 keV but at a comparatively slower rate. Beyond this, Z,, increases with further increases in energy from 1500 to 5000 keV. This increase in Z,, is small but continuous. This significant variation in Z,, is because of the relative domination of the partial photon interaction processes (photo, scattering and pair production). This variation also depends upon the range of the atomic number of the constituent elements, and number of elements in the composite material. The atomic numbers of elements of present soils vary from 8 (0,) to 26 (Fe) and a total of nine elements are considered. Parthasaradhi (1968) reported that the Z,, of alloys is different for partial processes such as photoelectric effect and scattering. In the first region where Z,, seems to be nearly constant, photoelectric interactions are dominant, so that here nearly constant Z,, may result. After 40 keV there is a sharp decrease in Z,, up to 400 or 500 keV. In this region the contribution of scattering increases, resulting in a decrease in Z,,. This point is confirmed by the results of Sastry and Jnanananda (1958) who reported that the Z,, for composite materials (e.g. tungsten steel etc.) is greater for photoelectric interactions than for other processes. The further decrease in Z,, with an
number
1253
of soils
increase in energy up to 1500 keV is small. This may be because in this region the dominant incoherent scattering falls off with a similar trend. Near 1500 keV, Z,, is least of all. With further increases in energy (from 1500 to 5000 keV) there is slight but continuous increase in Z,,. In this region the dominant processes are incoherent scattering and pair production. This behaviour of the curve may be due to the mixed contribution of these two processes. Rama Rao et al. (1963) reported that Z,, of rhodium-platinum alloys remains constant for pair-production cross sections in the energy region 1119-2000 keV. As the energy region presently considered extends up to 5000 keV our results show an increasing trend in Z,, with energy. This is because of the mixed contribution of scattering and pairproduction interaction processes in which, unlike the region covered by Rama Rao ef al. (1963), the contribution of pair production is increasing rapidly with energy. The energy region Z,, also depends upon the range of atomic number of the constituents which is clear from the results of Parthasaradhi (1968) Lingam et al. (1984) and Rama Rao et al. (1961). For water, Perspex and Monel metal no change in Z,, is seen, whereas for tungsten steel there is significant change. This is due to the fact that tungsten steel is composed of such elements which have a wider range of atomic numbers. In the present work, the change in Z,, of soil with energy is significant and comparable with the case of tungsten steel (Parthasaradhi, 1968; Rama Rao et al., 1961) which is a composition of W (23%) C (0.77%) Cr (4.25%) V (1.6%) Co (11%) and Fe (59.38%). Figure 4 shows the results of Parthasaradhi (1968) and Rama Rao et al. (1961) for tungsten steel for total photon interaction cross sections in the energy range covered by these two publications. The similarity in the pattern for soils and tungsten steel is evident. Another conclusion which may also be drawn from the present studies is that, along with the range of atomic number of the constituent elements, Z,, also
o Parthasaradhi l
251 0
(1968)
Rama Rao et al( 1961 )
I I 1000 500 photon energy (k eV)-
Fig. 4. Variation of effective interaction total photon coefficient), of tungsten
I 1500
atomic number (Z,,), for the section (attenuation cross steel, vs photon energy.
G. S. MUDAHAR and H. S. SAHOTA
1254
deoends won the number of elements Dresent. This may be the reason for the similarity in the behaviour of Z,, for soil and tungsten steel, both having large numbers of constituent elements. 1
1
Acknowledgement--The authors are thankful to Sh. Gurbakash Singh, Computer Centre, Punjab Agricultural University, Ludhiana for kind help in the computational work.
References Gawande S. P. and Biswas T. D. (1977) Characterisation and classification of black soils developed on basalt in relation to micro-relief. J. fnd. Sot. Soil Sci. 25, 233. Hine G. J. (1952) The effective atomic numbers of materials for various y-ray interactions. Phys. Reo. 85, 725. Hubbell J. H. (1982) Photon mass attenuation and energy absorption coefficients from 1 keV to 20 MeV. In?. J. A&. Radiat. Isot. 33, 1269. Joffe J: ‘S. and Kunin R. (1942) Mechanical separates and their fractions in the soil mofile: I. Variability in chemical composition and its pedogenic and agropedogic implications. Soil Sci. Sot. Proc. 187. Khangarot A. S. and Mehra R. K. (1977) Characterization
of alluvial 25, 241.
soils of Udaipur
Krishnamoorthy
Valley. J. Ind. Sot. Soil Sci.
P. and Govinda
Rajan S. V. (1977)
Genesis and classification of associated red and black soils under Rajolibunda diversion irrigation scheme (Andhra Pradesh). J. Ind. Sot. Soil Sci. 25, 239. Lingam S. C., Basu K. S. and Reddy D. V. K. (1984) Total gamma ray cross sections and effective atomic numbers in compounds in the energy region 32 to 662 keV. Ind. J. Phys. 58A, 285. Mudahar G. S. and Sahota H. S. (1988) Soil: A radiation shielding material. Int. J. Appl. Radial. ISOI. 39, 21. Parthasaradhi K. (1968) Studies on the effective atomic numbers in alloys for gamma ray interactions in the energy region 100-662 keV. Ind. J. Pure Appl. Phys. 6, 609. Rama Rao J., Lakshminarayana V. and Jnanananda S. (1961) Effective atomic number of alloys and compounds. J. Sci. Indust. Res. ZOB, 587. Rama Rao J., Lakshminarayana V. and Jnanananda S. (1963) Effective atomic number of alloys for pair creation. Ind. J. Pure Appl. Phys. 1, 315. Sastry K. S. R. and Jnanananda S. (1958) Attenuation coefficients for gamma rays from wCO. J. Sci. Indusf. Res. 17B, 389. Storm E. and Israel H. I. (1970) Photon cross sections from I keV to 100 MeV for elements Z = 1 to Z = 100. Nucl. Data Tables A7, 565.