International Journal of Latest Research in Science and Technology Volume 2, Issue 5: Page No.73-77,September-October 2013 http://www.mnkjournals.com/ijlrst.htm
ISSN (Online):2278-5299
INVESTIGATIONS OF MASS ATTENUATION COEFFICIENTS AND ENERGY ABSORPTION BUILDUP FACTORS OF SOME LOW-Z GAMMA RAY SHIELDING MATERIALS Balwinder Singh1, Vipan Kumar1*, Sukhwinder Singh2, Gurdeep Singh Sidhu3 Department of Physics, Faculty of Applied Sciences, Singhania University, Rajasthan - 333515, India 1* Department of Physics, Faculty of Applied Sciences, Singhania University, Rajasthan - 333515, India 2 Department of Physics, Govt. College for Girls, Ludhiana, Punjab - 141001, India 3 Department of Physics, Govt. Sports School Ghudda, Bathinda, Punjab -151001, India *Corresponding author:
[email protected] 1
Abstract- To check the gamma ray shielding properties of selected low-Z shielding materials such as bakelite, concrete, red sand shield and white sand shield, some parameters of dosimetric interest have been investigated in the energy range 0.015–15.0 MeV. The photon interactions with the samples have been discussed mainly in terms of mass attenuation coefficient, equivalent atomic number and energy absorption buildup factor. It has been observed that the shielding effectiveness of a sample is directly related to its effective atomic number. The shielding character of any sample is a function of the incident photon energy. Good shielding behaviour has been verified in white sand shield and red sand shield. The results have been shown graphically with more useful conclusions. Keywords: Gamma ray build-up factor, Exposure buildup factor, Equivalent atomic number and Tissues equivalent materials.
I.
INTRODUCTION
Exposure to gamma rays can occur in a range of industries, medical diagnostic centers, nuclear research establishments, nuclear reactors and nuclear weapons. Since the energetic gamma rays are hazardous for living cells and tissues, the needed precautions must be taken by shielding the radiations. But in the study of design of the gamma radiations shielding or estimating the exposure dose, there is an undesired situation faced by radiation physicists, engineers and oncologists due to secondary radiations that can occur due to buildup of photons from the collided part of the incident beam. For this reason it is of importance to determine the buildup factors to make corrections for effective energy deposition in different shielding materials. So a detailed study is required for the safe and acceptable use of gamma radiations, radioactive materials and nuclear energy. Due to numerous nuclear accidents (Fukushima, Chernobyl, Three Mile Island etc.) and the possibility of facing such issues in future, due to lost radiation sources, transportation and storage of nuclear waste, radiological terrorism and the possibility of nuclear weapons being used in a war, everybody should be encouraged to use such materials for construction of buildings (shields), which could effectively protect them from the hazardous external radiations. The gamma ray buildup factor is a multiplicative factor used to obtain the corrected response to the uncollided photons by including the contribution of scattered photons. It can be defined as the ratio of the total detector response to that of uncollided photons. The buildup factor measures the degree of violation of the Lambert–Beer law (I = Ioe-ìx), which is ISSN:2278-5299
often used in the computation of attenuation coefficients. It arises due to multiple scattering of gamma-rays or may be due to the large thickness of the interacting material or due to the divergence of the radiation beam. The modified intensity equation becomes (I = B Ioe-ìx), where B is known as buildup factor. This parameter B is always equal to or greater than unity (B = 1, in case of narrow beam geometry or interacting material is thin and the photon is assumed to be monoenergetic, else B > 1). Buildup factor has been classified into two categories viz. energy absorption buildup factor and exposure buildup factor. The energy absorption buildup factor) is the buildup factor in which the quantity of interest is the absorbed or deposited energy in the interacting material and the detector response function is that of absorption in the interacting material. There are different methods such as G.P. (Geometric Progression) fitting method (Harima et al., 1986), invariant embedding method (Shimizu, 2002; Shimizu et al., 2004), iterative method (Suteau and Chiron, 2005) and Monte Carlo method (Sardari et al., 2009) are available for computing buildup factors. Harimaet al. (1986) has also computed buildup factors using G.P. fitting method and compared the results with PALLAS code (Takeuchi and Tanaka, 1984), a good agreement was observed (discrepancy was within 7%) for penetration depth up to 40 mfp. Similarly, (Sakamoto et al., 1988) interpolated buildup factors for compounds/mixtures and reported good agreement with PALLAS code for low-Z materials (discrepancies were within 10%), whereas for high-Z materials discrepancies were found to be as large as30%.(Shimizu et al. (2004) compared the buildup factor values obtained by three 73
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different approaches (G.P. fitting, invariant embedding and Monte Carlo method) and only small discrepancies were observed for low-Z elements up to 10 mfp. Singh et al., 2008 studied buildup factors for some commonly used solvents. Hence one can use any of these methods/codes for computing buildup factors for low-Z materials. Engineers require these build-up factors while performing calculations for radiation shielding design. These samples are called low-Z as the equivalent atomic numbers remain less than 18 in the selected energy range. Since the buildup factors of selected samples are not found in any compilation or tabulation, so in the present study by using G.P. fitting formula an attempt has been made to compute energy absorption build-up factor values for these building materials in the energy range 0.015–15 MeV and up to penetration depth of 40 mfp. Such data will be of prime importance for those who are working with scattering of photons and related phenomena like radiation shield designing (Suteau and Chiron, 2005) and production of a new materials for gamma radiation shielding (Mortazavi and Mosleh Shirazi, 2010. Recently, a study has been made for the purpose of updating gamma-ray build-up factors for highZ engineering materials that are presented in the current ANS standard (Ruggieri and Sanders, 2008). Recently, the mass attenuation coefficients and exposure buildup factors (EBFs) have been studied by different researchers; Singh et al. (2008),Kurudirek and Topcuoglu (2011), Kurudirek and Ozdemir (2011), Manohara et al. (2011), Mann et al., (2011, 2012), Kumar V. et al.(2012). II. Materials and methods
III. Computational work To compute the value of the buildup factors, the G-P fitting function parameters were obtained by the method of interpolation from the equivalent atomic number (Zeq).The results so obtained have been shown in the tabular form for (Zeq) the selected shielding materials (Table 3). Table III.Equivalent atomic numbers of different shielding materials in the energy range of 0.015-15.0 MeV.
Table IV. Energy absorption G-P fitting parameters of Bakelite and Concrete.
In the present analysis selected samples are bakelite, concrete, red shield and white shield. The elemental composition by weight of the samples bakelite and concrete has been taken from literature Nat. Stand. Ref. Data Ser., Nat. Bur. Stand. (U. S), 29, page 8, (August 1969) and listed in the Table 1. The elemental composition by weight of the samples red sand shield and white sand shield is obtained from the journal of Energy and Power Engineering, 2010, pages 6-9 and listed in the table 2. Table I. Element composition of concrete and Bakelite
Table II. Elemental composition of red sand shield and white sand shield
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I. Computation of equivalent atomic number Firstly the values of Compton partial attenuation coefficient (ìcomp) and total attenuation coefficients (ì)tot in cm2/g were obtained for elements from Z = 1 to 25 and chosen samples in the energy of 0.015–15.0 MeV, using the state-of-the-art and convenient computer program XCOM and WinXCom (Berger and Hubbell, 1987; http://physics.nist.gov/xcom; Gerward et al.,2004).Further, by using a simple computer program, the ratio R (ìcomp/ìtot) was obtained for selected samples. Then the value of equivalent atomic number (Zeq) 74
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for these samples was calculated by matching the ratio R (ìcomp/ ìtot) of particular sample at a given energy with corresponding ratios of elements at the same energy. For the case the ratio lies in between the two ratios of known elements. The value of Zeq was interpolated by using the following formula of interpolation (Harima, 1993) given in the following equation.
Z eq
Z1 (log R2 log R ) Z 2 (log Rlog R1 )
(1)
log R2 log R1
Table V. Energy absorption G-P fitting parameters of Red shield and White shield.
elemental atomic numbers between which the equivalent atomic number Z of the chosen samples lies. The computed G.P. parameters of bakelite, concrete, red sand shield and white sand shield are listed in Tables 4 and 5 respectively. 3. Computation of EABFs Further, the computed G-P fitting function parameters (b, c, a, Xk and d) were then used to compute the energy absorption buildup factors for the selected samples at some standard incident photon energies in the range of 0.015–15.0 MeV and up to a penetration depth of 40 mean free path, with the help of G-P fitting formula (2) as given by the following eqs. 3–5.
B ( E , x) 1
(b 1)( K x 1) K 1
B (E,x) = 1 + (b-1)
for
for K≠1
(3)
K=1
(4)
Where K ( E, x) cx a d
tanh(x / X k 2) tanh(2) , x 40mfp 1 tanh(2)
(5)
where a, b, c, d and Xk are the G-P fitting parameters and x is source to detector distance in the medium (mfp). The parameter K (E, x) represents photon dose multiplication
IV. RESULTS AND DISCUSSION 1. Dependence of shielding effectiveness on mass WhereZ1 and Z2 are the atomic numbers of elements corresponding to the (ìcomp/ìtotal) ratios, R1 and R2, respectively; and R (ìcomp/ìtotal) is the ratio for the selected samples at a particular energy which lies between ratios R1 and R2. 2. Computation of G.P. fitting parameters American National Standard has provided the energy exposure G.P. fitting parameters of 23 elements (Be, B, C, N, O, Na, Mg, Al,Si, P, S, Ar, K, Ca, Fe, Cu, Mo, Sn, La, Gd, W, Pb and U), one compound(water) and two mixtures (air and concrete) in the energy range of 0.015–15.0 MeV and up to a penetration depth of 40 mfp (ANSI/ANS-6.4.3-1991). Using the interpolation formula, five G.P. fitting parameters (b, c, a, Xk and d) for selected samples were computed at the different incident photon energies using equivalent atomic number (Zeq), in the chosen energy range (0.015–15.0 MeV) up to penetration depth of 40 mfp. The formula used for the purpose of interpolation (Sidhu et al., 1999 a,b) is as follows:
P
P1(log Z2 log Zeq ) P2 (log Zeq log Z1 )
(2)
log Z2 log Z1
Here P1 and P2 are the values of G.P. fitting parameters corresponding to the atomic numbers Z1 and Z2 respectively at a fixed energy, whereas Z is the equivalent atomic number of the chosen sample at the same energy. Z1 and Z2 are the ISSN:2278-5299
attenuation coefficient Figure1. Show the results of mass attenuation coefficients for photoelectric process ìm(photo) of all the chosen low-Z composite shielding materials against the incident photon energy. This figure clearly shows the most significant variation in ìm due to chemical composition of the shielding materials. These results of ìm(photo) explain the variation of ìm(total) with chemical composition in the low energy region because in the low energy region photoelectric effect is predominant. The variation in ìm(total) are interpreted as being due to the Z-dependence of the partial interaction processes, since the cross-section for photoelectric absorption is proportional to Z4-5.There is a sudden jump in ìm(photo) at about 2 keV for red sand shield and white shield and at about 4 keV for white sand shield which contains larger percentage of comparatively heavy elements like Ca (Z= 20), Mn (Z=25) and Fe (Z=26) and resulting larger Zeq. It is also observed that the materials which contain comparatively larger percentages of heavier elements have relatively larger value of ìm(photo). 2. Buildup factor of Shielding Materials as a Function of Penetration Depth Figures 2-5 show the variation of energy absorption buildup factor with penetration depth for different shielding materials at fixed incident photon energies 0.015, 0.15, 1.5 and 15.0 MeV Figure 2 show the variation of energy absorption buildup factor with penetration depths for all the selected shielding materials at fixed incident photon energy of 0.015 75
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MeV. At low incident photon energies there are significant variations of energy absorption buildup factor for all the selected materials. It has also been observed that for the materials with low values of (Zeq) i.e. bakelite and white sand shield have larger values of energy absorption buildup factor while the materials with higher values of (Zeq) i.e concrete and red sand shield the values of energy absorption buildup factors are comparatively lower. The energy absorption buildup factor depends on the nature of the materials at incident photon energy of 0.015 MeV.
From Figure 3 it is noted that the dependence of buildup factor on the nature of materials reduces at the incident photon energy 0.15 MeV. From Figure 4.it is also observed that the energy absorption buildup factor values are practically the same for different selected materials at the energy value of 1.5 MeV. Thus, the buildup factor values become almost independent of the chemical composition of the given materials at this energy region, where compton scattering process dominate. From Figure 5, it is further noted that at penetration depth greater than 15 mfp, the trend of dependence of energy absorption buildup factor on Zeqhas also been reversed at the incident photon energy of 15.0 MeV.
V. Acknowledgements The authors are grateful to Prof. L. Gerward for providing user friendly computer programs WinXCom, and also Prof. M. J. Berger for the encouragement to carry out this work. VI. Conclusions From the present investigations, we have found that among the selected samples, white sand shield acts as best gamma ray shielding material, due to its higher values for mass
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International Journal of Latest Research in Science and Technology. 11. Mortazavi, S., Mosleh-Shirazi, M.A., 2010. Production of a datolitebased heavy concrete for shielding nuclear reactors and megavoltage radiotherapy rooms. Iran. J. Radiat. Res. 8, 11–15.
attenuation coefficient and least values for energy absorption buildup factor in the selected energy range. Lambert–Beer law’s violation is less in the selected energy region. Where photon absorption process is dominating over the scattering process. The computed data G.P. fitting parameters and energy absorption buildup factors for selected four low-Z shielding materials (25 energies and 40 penetration depths) may be useful in the future study of variety of shielding configurations. References:
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ANSI, 1991. American National Standard Gamma-Ray Attenuation Coefficient and Buildup Factors or Engineering Materials. ANSI/ANS6.4.3.
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Gerward, L., Guilbert, N., Jensen, K.B., Levring, H., 2004. WinXCom – a program for 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 the gamma ray buildup factors. Nucl. Sci. Eng. 94, 24–35.
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