Study of effective atomic numbers and mass attenuation coefficients in some compounds

~

Radiat. Phys. Chem. Vol. 47, No. 4, pp. 535-541, 1996 Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All fights reserved 0969-806X(95)00057-7 0969-806X/96 $15.00 + 0.00

Pergamon

STUDY OF EFFECTIVE ATOMIC NUMBERS AND MASS ATTENUATION COEFFICIENTS IN SOME COMPOUNDS K. SINGH, RAJINDERJIT KAUR, V A N D A N A and VIJAY K U M A R Nuclear Spectroscopy Laboratory, Department of Physics, Guru Nanak Dev University, Amritsar 143005, India (Received 25 February 1994; accepted 3 February 1995)

Abstract--The effective atomic numbers and mass attenuation coefficients of some different compounds for total and partial photon interactions have been calculated in the energy range 10-2-105 MeV. The effective atomic numbers and mass attenuation coefficients have also been determined experimentally in the energy range 123-1132 keV by a transmission method. Experimental and theoretical values are in good agreement. The values of these parameters have been found to change with composition of compounds and change in energy whereas their behaviour has been found to be identical at all energies. The significant variation in mass attenuation coefficients is due to the variations in domination of different interaction processes in different energy regions.

INTRODUCTION As a sequel to our previous work (Bhandal et al., 1992; Bhandal and Singh, 1993a, b,c) in different composite materials, the present calculations are made in different compounds in order to investigate the changes in effective atomic numbers for partial and total photon interactions for their chemical composition. The parameter "effective atomic number" has a physical meaning and allows many characteristics of a material to be visualized with a number. Many attempts have been made to determine effective atomic numbers (Z,~) for partial and total gamma ray interactions in alloys and compounds (Parthasaradhi, 1968; Krishna Reddy et al., 1985; Perumallu et al., 1984; Lingam et al., 1984; EI-Kateb and Abdul Hamid, 1991). Some empirically deduced formulas have been reported in the literature (Schatzler, 1979), but their validity is limited to the experimental conditions used in that particular work. Measurements on some alloys for partial and total gamma ray interactions in the energy range 100~62keV were performed by Parthasaradhi (1968), where it was found that Zc~ for partial processes remained constant whereas for total interactions it decreased with increasing energy. Perumallu et al. (1984) measured mass attenuation coefficients and calculated the total cross sections and effective atomic numbers of some chlorides, nitrates and sulphates in the energy range 30-662keV. Lingam et al. (1984) have computed total gamma ray cross-sections and Ze~ of some halogen compounds in the energy range 33--662 keV. Their results are in conformity with the results of Parthasaradhi (1968).

Measurements on substances containing H, C and O in the energy range 54--1333 keV were also performed by EI-Kateb and Abdul Hamid (1991), where a straight line relationship between hydrogen weight fraction and total mass attenuation coefficient was obtained and irregular behavior for carbon and oxygen was evident. They concluded that the value of Zcn tends to be constant as a function of energy, whereas the total Zc~ values calculated by Parthasaradhi (1968), Krishna Reddy et al. (1985), Perumallu et al. (1984) and Lingam et al. (1984) in some alloys and compounds are dependent upon energy. Hence it is necessary to make a systematic study of various compounds having different elements with a wide range of atomic numbers. Recently Hiremath and Chikkur (1993) calculated effective atomic numbers by employing an equation developed by Massaro et al. (1982) and the mixture rule suggested by Hubbell (1982) for some chemical compounds containing H, C and O atoms in the energy range 54-1333 keV. They suggested that a systematic study of various alloys and compounds with a wide range of atomic numbers and energies can throw more light on the results of other investigations. In order to make use of the fact that scattering and absorption of gamma radiations are related to the density and effective atomic number of the matter, a knowledge of the mass attenuation coefficient is of prime importance. Accurate values of mass attenuation coefficients are necessary to establish the regions of validity of theory based parameterisation, in addition to providing essential data in such diverse fields such as tomography, gamma-ray fluorescence studies and radiation biophysics. The mass attenu535

536

K. Singh et al.

ation coefficients (cm2/g) of gamma rays in materials are of great interest for industrial, biological, agricultural and medical studies. The mass attenuation coefficients are also widely used in the calculations of photon penetration and energy deposition in biological shielding and other materials (Davisson and Evans, 1951; Conner et aL, 1977; Goswami and Chaudhuri, 1973; EI-Kateb et al., 1987, 1989, 1991; Bradley et al., 1985, 1986; Perumallu et al., 1985). Measurements on hydrocarbons in the energy range 33-662 keV were performed by Bradley et al. (1986), where a regularity in relationship between mass attenuation coefficients and the hydrogen weight fraction was revealed. Zavel'skii (1964) proposed a direct relationship of mass attenuation coefficients with heavy metals in rocksalt for low photon energies. Joga Rao et al. (1985) measured total photon attenuation coefficients in certain alloys and compounds in the energy region 6.4-12.1 keV employing the Si(Li) detector system and deduced photoelectric mass absorption coefficients after subtracting from data, contributions due to coherent and incoherent scattering. A large number of photon attenuation measurements, calculations and compilations in elements have been made available by several standard laboratories and institutes such as National Institute of Standards and Technology, Gaithersburg, U.S.A. Compared to the elements, the availability of data on attenuation coefficients for composite materials is very limited. Some papers such as that of Hubbell (1982), Nageswara Rao (1984) and E1-Kateb and Abdul-Hamid (1991) are available in literature for composite materials. But the available studies are only for limited energy range for one or another interactions process only. THEORY

For materials composed of various elements, the total attenuation coefficient (/~/p )T is related to (#/p ) values of constituents by the following mixture rule

(t,/p)~ =f~(#/p), +A(~Ip)~ +A(/~/p)~...

(l)

where f~ are weight fractions of constituent elements such that f~ +f2 +f3 . . . . 1 (2) From the measured values of/~/p, the total atomic cross-section trtotis obtained by the following relation (Perumallu et al., 1984) O'tot

= (~/p)r .-~s/vA

(3)

where

EniAi Ar ~

i

Zn,

N^ is Avogadro's number, A~ is the average atomic mass of the compound, n~ is the number of atoms

(with respect to mass number), A i is the atomic mass of the ith element in a molecule. The total cross-section in turn can be written as the sum of the partial cross-sections: Crtot= acoh + trincoh + ~ + x + trp~.n

(4)

in which trcoh, O'incoh are the coherent (Rayleigh) and incoherent (Compton) scattering cross sections respectively, z is the atomic photoelectric cross-section, x is the positron electron pair production cross-section and trph.n is the photonuclear cross-section. The total electronic cross-section is related to (I~/P)T as given by the following relation:

1 Ai ~T,E = ~ x f,. Z (~IP)'

(5)

Total electronic cross-section is also related to effective atomic number (Ze~) of the compound through the formula ~ niz i O'T, E

zoo- '

(6) i nitYT,E

as given by EI-Kateb and Hamid (1991). Other expressions for the effective atomic numbers are found in Perumallu et al. (1984), Jackson and Hawkes (1981) and Parthasardhi (1968). EXPERIMENTAL SET-UP

In the present investigations the satisfactory geometrical arrangement similar to that of Goswami and Chaudhuri (1973) has been employed. The sources 57Co, tuBa, Z2Na, 137Cs, 54Mn and 6°Co were obtained from Bhabha Atomic Research Centre, Trombay, Bombay (India). Each source was housed in a properly shielded lead container. A 1.5"x 1.5" NaI(T1) crystal having an energy resolution of 12.5% at 662 keV gamma ray from the decay of 137Cs was used for the measurements of the total mass attenuation coefficients. The samples were contained in perspex boxes 5 cm wide under natural compactness. The errors in (/~/P)T values were calculated from errors in the intensities I0 (without absorber), I (with absorber), and the densities using the following relation, also used by EI-Kateb and Hamid (1991).

~(~,/p)T =

-~

{[(too - Io~t)/Ito)

+ x~p In t/tol} (7) where 61o and M a r e the errors in the intensities I0 and I respectively and x is the thickness of the sample in centimeters. Determination o f mass attenuation coefficients and effective atomic numbers To determine the total mass attenuation coefficients, we measured the density values of the compounds using a mass/volume relation. These values were used to calculate total cross sections of

537

Effective atomic numbers and mass attenuation coefficients compounds which in turn were used to find the effective atomic numbers. The results are shown in Tables 1 and 2. The experimental values of mass attenuation coefficients were compared with the theoretical values that were calculated using the chemical composition (Table 3) with the help of computer program and data base developed by Berger and Hubbell (1987) for partial and total photon interaction processes in square centimeters per gin. The results are shown in Table 4. It is clear that there is good agreement between the theoretical and experimental values.

HgO op~.Qf@/I.....'~I-

" o~_o~o~o~

O

60 ,e /

50

?-: -----oJ°"~"O

Eu203 o~oBaF 2

40

Calculation work The following relation was used to compute the atomic cross sections in barns/atoms from the calculated mass attenuation coefficients O'tot

(8)

30 0~0~0*'--0~0

•

•

•

NaBr o~O-

Na2WO4.2H20 20 -

o/

0~6

•

i

•

0~0Na2SeO3 TiO~

i

These calculations were made with the help of a PC/XT computer (WIPRO). The values of effective atomic numbers of present compounds were obtained from the calculated effective cross sections for all the photon interaction processes by a piece wise interpolation program.

NaC1

KC1

]o

NaF

o-O, .o-O~o

0-3

KCI+NaF •

I 10-2

Q

I i i 10-1 100 101

•

,

i 102

•

oml~

H3BO 3 I I I 103 104 105

Photon energy (MeV) RESULTS AND DISCUSSION

The computed values of the effective atomic numbers of the compounds are graphically shown in Figs 1-7.

Fig. 1. Variation of Zen of inorganic compounds with photon energy for photoelectric absorption. 100-662 keV. Similar results have also been reported by Singh (1992) for soils and alloys.

(a) Photoelectric interaction process The variation in effective atomic numbers with energy for photoelectric effect as shown in Fig. 1 is characteristic showing jumps in Z ~ for low energy photons. In case of H2BO3, NaF, A1203 and NaC1, the variation in Zen with energy is small. The variations may be due to the fact that in high Z materials the domination of the photoelectric process extends to higher energies than for low Z materials. The results for photoelectric process explain the variation in ~/p for the total interaction process (Fig. 6) with chemical composition in low energy region. These variations are attributed to the fact that the photoelectric effect varies as Z 45. Similar results were also obtained by Perumallu et al. (1985) in multielement materials of biological importance. Singh (1992) found that the photoeffect extends to high energies for high Z materials (such as alloys) compared to low Z materials to give the same value of attenuation coefficient. He also observed that variation in/~/p due to chemical composition is large in alloys in comparison with all other materials. Our theoretical results are in line with the experimental findings of Perumallu et al. (1985) and not with those of Parthasaradhi (1968) who reported that Z,~ values of alloys remain nearly constant in the energy region RPC47,4--B

(b) Coherent scattering The results for this interaction are found to be similar to the findings of Bhandal and Singh (1993) in fatty acids and cements. The variation of Ze~ with the photon energy is shown in Fig. 2. From the graph it is clear that variations in Zon are not similar for all compounds in low energy region. In some materials it decreases with an increase in energy and becomes minimum in the energy range 3-10keV and starts increasing. It remains constant with increase in energy and sharply falls to a minimum value. The point at which Ze~ value becomes minimum is different for different materials. The non similarity of Z,n values may be due to contributions of elements of different Z values. Similar results have been reported by Khayyoom and Parthasaradhi (1970) for incoherent scattering in bronze, aluminium and bronze ordinary in the energy range 20--800 keV. The present results are also similar to theoretical results of Singh (1992) in different composite materials and experimental findings of Parthasaradhi (1968) who reported constancy of Z~n in the energy range from 100 to 662 keV for tungsten steel, solder and bell metal.

K. Singh et al.

538 60

of•

~°

°-

•

o•f

O''--'O ~ O ' ' "

48

tt

O~o~o~o~o~o~o~o~

O'''-" O

•

O~O

° Na2BiO2

•.

~o-----o~o~o~o~O~o~o~

O ~ I

~ o

o!~ l j ~ v ~

Eu203

'

•

• KI

•

• BaF2

36 N"

/o~_~.~.~. toO.T 24

~.__0~0__

o~O-----O

•

•

•

•

•

•

O~o

•

NaBr

~

• Na2SeO3 .

.

12 6-1~o~ . l ~ ~ o ~ O b~l~O~O~O

'

0-3

_

•

.

_

•

•

.

_

°~o~o

.

_

.

....

. _ . o~o~o

_

.

I

I

I

I

10-1

100

101

lIT-~•~•~¢l 102 103

.

•'---"-'O KCI

:'--':=1=8=1=-::

10-2

.

ii. I 104

A12o 3

• NaF

iI H3BO3 105

Photon energy (MeV) Fig. 2. Variation of Ze~ of inorganic compounds with photon energy for coherent scattering.

(c) Incoherent scattering In case of incoherent scattering no significant variations are seen in l~/P due to the types of compounds. This is due to the linear Z dependence of the Compton scattering. This also explains the constancy of l~/P in medium energy region for all types of materials for the total interaction process. Similar results have also been obtained by Singh (1992) in HgO Of 40

30

/

o o/O/

//

o/

o~

o

10

O~O~O~o

/"

• KI

~ o ~ o ~ o

Eo2o3

•

BaF2

i l i a / / ! / " Na2BiO2 /?~

NaCI

Ili:L I'|~OnnmmmO

TO ~ °

I I 0-3 10-2 10-1 l00

J

|

I l01

I l02

• •

•

Na2SeO3 NaF O O~'~"'O A1203 H3BO3 KCI I l03

I 104

I l05

Photon energy (MeV) Fig. 3. Variation of Zar of inorganic compounds with photon energy for incoherent scattering.

alloys, compounds and soils. In this energy region the Compton scattering process is dominant. The variation of Zar with photon energy for Compton scattering (Fig. 3) displays some interesting results below 100keV. In the low energy region (10--100 keV) the value of Ze~ increases with increase in energy. Above 10 MeV, Z~g becomes constant for all compounds. However, in some compounds, it attains constant value at about 100keV (A1203, NaF). The variation of Zar depends on the respective proportions and range of atomic numbers of the elements of which the compound is composed.

(d) Pair production in nuclear and electric fieM The results for the mass attenuation coefficients for pair production interaction processes in nuclear and electron fields show a significant variation in l#P values of the chosen compounds due to chemical composition. The variation may be due to the fact that pair production in the nuclear field is Z 2 dependence. This explanation also extends to the variation in the total interaction process (Fig. 6) in the high energy region because pair production is the most dominant process in the high energy region. Significant variations due to chemical compositions are observed in Zen for pair production in nuclear and electron fields (Figs 4 and 5, respectively). It may be because of the fact that pair production in nuclear field is Z 2 dependent. Below 1 MeV, the fall in the effective atomic numbers with energy is more for compounds containing a large range of atomic numbers of its constituent elements.

Effective atomic numbers and mass attenuation coetficients

6055 I

e~o

• •

•

•

•

•

HgO

50 45 -

40

I0~1~8=S~8=8~8=8.__.8__..8_..

KI Eu203

35 %,. ~ 30 --

O"-..-o--O~O--o-- o ~ • ~ O ~ O ~

BaF 2

25 ~ o ~ o ~ o _ o ~ O ~ O ~ O _ O _ _ o _ _ e ~

NaBr

20 --

]5

.,~

----

O ~ O ~ • ~ O ~ O ~ O ~ O ~ O ~ O ~

~-

/

Na~SeO. z

/TiO 2 "NaCI

Na2WO42H20 10 -AI20~ ~8~8~:~1~8~8=8~8 - - ' ~ | ' ~ - | ~ - NaF j .o~o~o~o~o--O~O~O~O~o~ KCI 5 To~o~O~O~o--o~o~o~o~o~H3

539

heavy metals in rocksalt for low energy. In the intermediate energy region, where incoherent scattering is the most dominant process, the mass attenuation coefficient is found to be constant and is due to the linear Z-dependence of incoherent scattering and insignificant role played by pair production. Singh (1992) also found a negligible variation between 150 keV and 5 MeV for biological materials. In the high energy region, the significant variation in #/p due to compound type is related to the Z-dependence of pair production, which is of the order of Z 2, In case of compounds which are made of medium and high Z materials, the constancy of I~/P was observed in the narrow energy region of 1.25-2.5 MeV (Singh, 1992). This was attributed to the fact that some of the alloys are composed of medium Z-elements and others are of high Z-elements. The variation of Ze~ with photon energy for total photon interactions (Fig. 7) shows dominance of different interaction processes in different energy regions. The behaviour of all compounds is almost identical. The significant variation in Z ~ is because of the relative dominance of the partial photon interaction processes. This confirms that Z ~ depends upon number of elements and the range of atomic numbers in a compound. The present results are in

BO3 45 O

0100

I

I

I

I

I

101

102

103

104

105

~

o

~

°~o%

HgO • " " - ' O ~ O ~ O - -

40 Photon energy (MeV) KI

Fig. 4. Variation of Z~ of inorganic compounds with photon energy for pair production in nuclear field.

35

The present theoretical results are consistent with the experimental results obtained by Visweswara Rao and Parthasaradhi (1968) and Rama Rao et al. (1963).

(e) Total photon interactions (with coherent) Figure 6 shows the results of the total mass attenuat•on coefficients of some of the chosen composite materials against the photon energy. It is seen that the variation in #/p with chemical composition is large below 500 keV and negligible between 1-10 MeV, and further there is again significant variation in p/p up to 100MeV photon energy. Variations are interpreted as being due to the dominance of Z-dependence of partial photon interaction processes in different energy regions. In the low region variations in ~/p are due to (i) photoelectric effect which varies as Z* 5 and (ii) less but significantly due to coherent scattering which varies as Z 2-3. This fact has also been verified experimentally by Singh (1992) by measuring total mass attenuation coefficients of some soils. Similar observations were also made by Zavel'skii (1964) who proposed a direct relationship of #/p with

30

--

• ....

O----.~ •

•

~u2v3 •

O ~ O

25 --

BaF 2 Q

vq~

•

O'-,~Q

•

•

•

•

Na2S~O3

NaCl

TiO~

AI203/NaF

,. o ~ o ~ 9 ~ o , , - ~ r . . . - e

•

z0

0100

qt,--

Na2WO4.2H20 •

5 --

.... O ~

NaBr

20 15 _

O~

•

O ~ 0

I~I

•

•

•

H3BO 3 .... | KCI

"I--l--l--I

0--

"O ~-

I

i

L

l

I

t01

102

103

I04

I05

Photon energy (MeV) Fig. 5. Variation of Z~r of inorganic compounds with photon energy for pair production in electric field.

540

K. Singh et al.

,04 103

10 2

A" 1o I .-a iNa2BiO 2 tEu203 /NaBr /Na2WO4"2H20 /KCI iTiO2

100

l0 -1

10-2 10 3

~-w~l~S~---

I

I

I

l

10-2

10-I

100

102

101

. . . .

o----.-.~.

I

]

j

103

104

105

H3BO3

Photon energy (MeV) Fig. 6. Variation of Ze~ of inorganic compounds with photon energy for total attenuation with coherent scattering.

48

.:TL'~.\ r+ 36

}

~ ,11: .....

-

~qt

o--o

~ e

,

~o

o--o

O--o

. . . . .

o--o

o--o

-,

•

BaF 2

•

NaBr

"' •

? ~---o--o~o

0-3

,=t

\~.

•

24

12

:--,.

I 10-2

NaCI

\o %o~R0~_|--_$ I 10-I

o ~

,.---,

*

•

~o--o~s

I 100

I 101

I 102

o--, o--o -• o--o--o I 103

r 104

• NaF KCI • H31303 I 105

Photon energy (MeV) Fig. 7. Variation of mass attenuation coefficients with photon energy for total photon interaction processes (with coherent).

Effective atomic numbers and mass attenuation coefficients line with the results o f L i n g a m et al. (1984) in their covered energy region in case o f c o m p o u n d s .

REFERENCES Berger M. J. and Hubbell J, H. (1987) XCOM: photon cross sections on a personal computer. Report NBSIR 87-3597. Bhandal G. S. and Singh K. (1993a) Effective atomic number studies in different biological samples for partial and total photon interactions in the energy region 10 -3 to 105 MeV. Int. J. Appl. Radiat. lsot. 44, 505. Bhandal G. S. and Singh K. (1993b) Study of mass attenuation coefficients and effective atomic numbers in some multielement materials. Int. J. AppL Radiat. lsot. 44, 429. Bhandal G. S. and Singh K. (1993c) Photon attenuation coefficient and effective atomic number study of cements. Int. J. Appl. Radiat. Isot. 44, 1231. Bhandal G. S., Ahmed I. and Singh K. (1993) Determination of effective atomic numbers and electron density of fatty acids by gamma ray attenuation. Int. J. Appl, Radiat. Isot. 43, 1183. Bradley D. A., Chong C. S. and Ghose A. M. (1985) Photon absorption of bone and bone standards. Int. J. Appl. Radiat. Isot. 37, 1195. Bradley D. A., Chong C. S. and Ghose A. M. (1986) Photon absorption of hydrocarbons. Int. J. Appl. Radiat. Isot. 37, 1195. Conner A. L., Atwater H. F., Plassman E. H. and McCrary J. H. (1977) Gamma ray attenuation measurements. Phys. Rev. AI, 539. Corey J. C., Peterson S. F. and Wakat M. A. (1971) Measurements of attenuation of ~37Csand 24~Amgamma rays for soil density and water content determination. Soil SeL Soc. Am. Proe. 35, 215. Davisson C. M. and Evans R. D. (1951) Measurements of gamma ray absorption coefficients. Phys. Rev. 81, 104. EI-Kateb A. H. and Abdul Hamid A. S. (1991) Photon attenuation coefficient study of some materials containing hydrogen, carbon and oxygen. Int. J. AppL Radiat. Isot. 42, 303. EI-Kateb A. H., Hassan A. F. and Abdul Hamid A. S. (1987) Back scattering and transmission of gamma radiation on cellulose acetate in the energy range 0.08-1.25 MeV. 1st Egyptian-British Conf on Biophysics, Cairo University, p. 442. E1-Kateb A. H., Hassan A. F., EI-Hennawi S. A. and Abdul Hamid A. S. (1989) Effects of paraffin wax on gamma ray spectra. Nucl. Sci. J. 26, 133, Goswami B. and Chaudhuri N. (1973) Measurement of gamma ray attenuation coefficients (0.662-1.332 MeV). Phys. Rev. A7, 1912. Hiremath S. S. and Chikkur G, C. (1993) Computation of effective atomic number of some hydrocarbons containing H, C and O atoms in the energy range 54-1333 keV. Indian J. Pure Appl. Phys. 31, 855.

541

Hubbell J. H. (1982) Photon mass attenuation and energy absorption coefficients from I keV to 20 MeV. Int. J. Appl. Radiat. lsot. 33, 1269. Jackson D. F. and Hawkes D. J. (1981) X-ray attenuation coefficients of elements and mixtures. Phys. Rev. 70, 169. Joga Rao K., Nageswara Rao. G., Prem Chand K., Thrimula Rao B. V., Raju M. L. N. and Parthasardhi K. (1985) Total photon attenuation coefficients in alloys and compounds in the energy region 6.4-22.1 keV. Indian J. Appl. Phys. 23, 160. Khayyoom A. and Parthasaradhi K. (1970) Effective atomic numbers in alloys for incoherent scattering of gamma rays. Indian J. Pure Appl. Phys. 8, 845. Krishna Reddy D. V., Chandra Lingam S. and Suresh Babu K. (1985) Photoelectric cross sections in heavy elements derived from total attenuation measurements. Can. J. Phys. 63, 1421. Lingam S. C., Baku K. S. and Reddy D. V. K. (1984) Total gamma ray cross sections and effective atomic numbers in compounds in the energy region 32~62 keV. Indian J. Phys. 58A, 285. Massaro E., Costa E. and Salvati M. (1982) Semiempirical formula for gamma ray absorption coefficient. Nucl. Instrum. Methods 192, 423. Murty R. C. (1965) Effective atomic numbers of hetrogeneous materials. Nature (London) 207, 398. Nageswara Rao A. S., Perumallu A. and Krishana Rao G. (1984) Photon cross section measurements in compounds and elements in the energy range 30~562 keV. Physica 124C, 96. Parthasaradhi K. (1968) Studies on the effective atomic numbers in alloys for gamma ray interactions in the energy region 1004562 keV. Indian J. Pure Appl. Phys. 6, 609. Perumallu A., Nageswara Rao A. S. and Krishna Rao G. (1984) Photon interaction measurements of certain compounds in the energy range 3(b660 keV. Can. J. Phys. 62, 454. Perumallu A., Nageswara Rao A. S. and Krishna Rao G. (1985) Z dependence of photon interactions in multielement materials. Physica 132C, 388. Rama Rao J., Lakshminarayana V. and Jnanananda S. (1963) Effective atomic number of alloys for pair production. Indian J. Pure AppL Phys. 1, 375. Schatzler H. P. (1979) Basic aspects in the use of elastic to inelastic radiation for the determination of binary system with effective atomic number less than 10. Int. J. Appl. Radiat. Isot. 30, I 15. Singh M. (1992) Behaviour of gamma ray interactions in composite materials. Ph.D. thesis, Pbi. Univ. Patiala, India (unpublished). Visweswara Rao V. and Parthasaradhi K. (1968) Effective atomic numbers of alloys for pair production process. Indian J. Pure Appl. Phys. 6, 643. Zavel'skii F. S. (1964) Mass absorption coefficients of gamma radiations in soils and errors in measurements made by the gamma method. At. Energy 16, 266~