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Gamma-ray double-layered transmission exposure buildup factors of some engineering materials, a comparative study
Radiation Physics and Chemistry 125 (2016) 27–40
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Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
Gamma-ray double-layered transmission exposure buildup factors of some engineering materials, a comparative study Kulwinder Singh Mann a,b,n, Manmohan Singh Heer c, Asha Rani d a
Department of Applied Sciences, Punjab Technical University, Kapurthala 144601, India Department of Physics, D.A.V. College, Bathinda 151001, Punjab, India c Department of Physics, Kanya Maha Vidyalaya, Jalandhar 144001, India d Department of Applied Sciences, Ferozpur College of Engineering and Technology, Ferozshah, Ferozpur 142052, India b
H I G H L I G H T S
G.P. fitting formula accurately reproduces the EBF values for low-Z materials. Lin and Jiang empirical formula computes DLEBF with minimum differences. For low-Z followed by high-Z, DLEBF values are smaller than the reverse order. Two-materials protect γ-rays effectively than a single material of same thickness. Al-LS seem to be the best γ-ray protective shield in energy range 0.5–3.0 MeV.
art ic l e i nf o
a b s t r a c t
Article history: Received 22 July 2015 Received in revised form 28 February 2016 Accepted 1 March 2016 Available online 3 March 2016
Comparative study on various deterministic methods and formulae of double layered transmission exposure buildup factors (DLEBF) for point isotropic gamma-ray sources has been performed and the results are provided here. This investigation has been performed on some commonly available engineering materials for the purpose of gamma-ray shielding. In reality, the presence of air around the gamma-ray shield motivated to focus this study on exposure buildup factor (EBF). DLEBF have been computed at four energies viz. 0.5, 1.0, 2.0 and 3.0 MeV for various combinations of the chosen five samples taken two at a time with combined optical thickness up to 8 mean free path (mfp). For the necessary computations for DLEBF, a computer program (BUF-toolkit) has been designed. Comparison of Monte Carlo (EGS4-code) and Geometric Progression (G.P.) fitting point kernel methods were done for DLEBF computation. It is concluded that empirical formula given by Lin and Jiang using EBF computed by G.P. fitting formula is the most accurate and easiest method for DLEBF computations. It was observed that DLEBF values at selected energies for two layered slabs with an orientation (low-Z material followed by high-Z material) were lower than the opposite orientation. For optical thickness up to 8 mfp and chosen energy range (0.5–3.0 MeV), Aluminum-Lime Stone shield, appears to provide the best protection against the gamma-rays. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Buildup factors Empirical formulae Lin and Jiang formula BUF-toolkit
1. Introduction Buildup factor of a material for gamma-rays exposure is an important parameter in the investigation of material’s radiation protection ability. The exposure buildup factor (EBF) for gammarays at a point is the ratio of the correct value of photon flux after
n Corresponding author at: Department of Physics, D.A.V. College, Bathinda 151001, Punjab, India. E-mail address: [email protected] (K.S. Mann).
http://dx.doi.org/10.1016/j.radphyschem.2016.03.001 0969-806X/& 2016 Elsevier Ltd. All rights reserved.
transmission through a material-slab to the uncollided photon flux (without the slab) measured at that point. The value of EBF depends on the atomic number (Z) of the attenuating material, energy of gamma-ray photon (E), optical thickness (number of mean free paths penetrated by the photon) and geometrical form of the radiation source. One mean free path (mfp) is the average distance that a photon traveled between two successive scattering points inside the material. Goldstein and Wilkins (1954) firstly reported data of photon buildup factors. The significance of EBF is indicated by the available literature on it (Harima, 1986; Harima et al., 1986;
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K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
50
(a)
40
EBF
30
Water G.P. fitting formula 0.5 MeV 1.0 MeV 2.0 MeV 3.0 MeV
ANSI 6.4.3. (1991) 0.5 MeV 1.0 MeV 2.0 MeV 3.0 MeV
G.P. fitting formula 0.5 MeV 1.0 MeV 2.0 MeV 3.0 MeV
ANSI 6.4.3. (1991) 0.5 MeV 1.0 MeV 2.0 MeV 3.0 MeV
20 10 15
(b)
EBF
10
Iron
5
0
1
2
3
4
5
6
7
8
Optical Thickness (mfp) Fig. 1. Standardization of BUF-toolkit for EBF calculations using corresponding standard values of EBF (a) for water and (b) for iron.
Guvendik and Nicholas, 2000; Kazuo and Hirayama, 2001; Saadi, 2012). To compute the buildup factors for a material, there are numerous methodologies available such as: Moments method by Eisenhauer and Simmons (1975); G.P. fitting method by Harima et al. (1986); Invariant embedding method by Sakamoto et al. (1988) and Shimizu (2002); Iterative method by Suteau and Chiron (2005) and Monte Carlo method by Sardari et al. (2009). Various codes exist for computation of the buildup factors such as: ASFIT (Anisotropic Source-Flux Iteration Technique) (Gopinath and Samthanam, 1971), PALLAS (Takeuchi and Tanaka, 1984) and Monte Carlo Code EGS4 (Nelson et al. 1985). Harima et al. (1986) reported that G.P. (Geometric Progression) fitting method using five fitting parameters for point kernel calculations reproduce the basic buildup factor data over the whole range of energy, atomic number and shield thickness within a few percent errors. He further reported that G.P. fitting method can reproduce the EBF with better accuracy. Sakamoto et al. (1988), Harima (1993) and Shimizu et al. (2004) confirmed that for EBF calculations, G. P. fitting method agreed well with simple differences for low-Z materials to other methods (invariant embedding and Monte Carlo calculation). Thus the G.P. fitting method can be used for precise computations of EBF for shield made from low-Z material.
American National Standards report (ANSI/ANS-6.4.3-1991) provided database of gamma-ray buildup factors and G.P. fitting parameters for 23 elements (4Be, 5B, 6C, 7N, 8O, 11Na, 12Mg, 13Al, 14Si, 15P,16S, 18Ar, 19K, 20Ca, 26Fe, 29Cu, 42Mo, 50Sn, 57La, 64Gd, 74W, 82Pb and 92U), one compound (H2O), two mixtures (i.e. air and concrete) at 25 energies among 0.015–15 MeV and 16 optical thicknesses between 0.5 and 40 mfp. Numerous attempts have been made to determine EBF of different materials (single slab) using G.P. fitting method (Manohara et al., 2010; Medhat, 2011; Icelli et al., 2013; Kurudirek et al., 2013; Kavanoz et al., 2014). In selection of suitable materials for manufacturing of an efficient gamma-rays protective shield, double layered transmission exposure buildup factors (DLEBF) for two-layered slabs is required. Kalos (1956, 1957) for the first time proposed an empirical formula for double layer buildup factors from those of single layered slabs; Kalos and Goldstein (1959) explained fundamental aspects of reactor shielding; Burke and Beck (1974) using results of transport calculations made some modifications to Kalos formula; Shin and Hariyama (1995) validated the formula using Monte Carlo method; Lin and Jiang (1996) confirmed the empirical method used for double layer shields in point isotropic source. Suteau and Chiron (2005 , ) proposed an iterative method for calculating gamma-ray build-up factors in multi-layer shields. Schirmers (2006) proposed an improvement of photon buildup factors formula using optical thickness of materials. Trontl et al. (2007)
K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
29
Table 1 Percentage deviations in DLEBF obtained by various formulae from Monte Carlo calculations in Fe-H2O slabs (High-Z followed by low-Z material) for point isotropic sources. EBF computed from G.P. fitting formula (Harima et al., 1986)
Fe
H2O
EBF-data from EGS4-code (Lin and Jiang, 1996)
X1 (mfp)
X2 (mfp)
Lin and Jiang
Burke and Beck
Kalos
Lin and Jiang
Burke and Beck
Kalos
E ¼0.5 MeV 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4
1 2 3 4 5 6 1 2 3 4 5 1 2 3 4
4.02 2.83 3.65 3.04 3.87 3.43 1.79 0.12 0.88 0.83 0.60 1.05 2.13 1.56 2.57
10.93 3.72 3.52 10.69 13.13 16.55 7.05 2.57 11.31 18.92 24.67 5.93 6.88 18.34 29.48
1.78 15.63 24.39 31.23 32.51 34.64 8.38 26.55 37.65 45.64 50.07 11.32 34.57 50.23 62.45
4.08 4.80 5.65 6.62 8.03 9.49 2.77 2.83 4.02 4.43 5.93 1.71 0.96 0.58 1.09
13.40 10.76 7.80 5.93 6.03 7.11 11.81 7.09 3.68 0.48 1.07 10.40 3.59 4.08 9.10
1.45 5.05 8.44 9.39 7.84 5.29 2.67 13.07 17.48 21.14 20.05 5.87 20.06 30.30 35.06
E ¼1.0 MeV 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4
1 2 3 4 5 6 1 2 3 4 5 1 2 3 4
1.52 0.17 0.43 0.69 0.17 1.01 1.00 1.03 1.24 0.65 2.47 0.72 0.80 1.23 2.44
6.50 1.22 2.23 4.42 3.76 6.90 6.05 0.16 4.17 5.05 10.16 5.92 0.49 4.36 9.25
6.19 16.17 20.22 21.81 19.75 21.26 9.12 21.99 27.33 27.68 31.44 11.03 24.20 31.49 36.32
2.27 4.10 5.29 6.35 7.51 8.24 2.59 3.54 4.99 6.28 6.75 2.00 3.69 4.39 5.67
6.69 5.78 4.79 4.89 6.15 7.03 7.72 4.14 2.84 2.82 2.08 6.80 4.11 0.59 0.04
5.63 10.21 11.29 9.97 7.12 4.84 7.03 16.21 18.14 16.90 16.12 9.81 19.13 24.34 23.82
proposed support vector model for estimation of gamma-ray buildup factor for multi layer shields. Saadi (2012) parameterized the buildup factor for double layer shields by an empirical formula as a function of optical thickness of two materials. Photon buildup factor in which the quantity of interest is exposure, termed as exposure buildup factor (EBF). For computation of EBF, the use of energy response function for absorption in air is recommended (ANS 6.4.3-1991). While photon buildup factor in which the quantity of interest is the absorbed or deposited energy in the shield medium is termed as energy absorption buildup factor (EABF). The recommended energy response function used in computation is that of absorption in the shield material. The computation of buildup factors is based on the presence of infinite medium. Moreover air is available up to infinite dimensions around the shielding material. Thus, we focus our study on EBF. Various empirical formulae of DLEBF for water–iron slabs using EBF obtained by G.P. fitting method and Monte Carlo EGS4 code have been compared. The Lin and Jiang (1996) formula shows the best agreement between the two methods. It was concluded that Lin and Jiang (1996) empirical formula with EBF computed from G.P. fitting method reproduce accurately the DLEBF values for two-layered slabs up to the optical thickness of 8 mfp in the energy range (0.5–3.0 MeV). In present investigation, the effects of different atomic numbered
materials orientation on the DLEBF have been investigated at chosen optical thickness and energies.
2. Theory 2.1. EBF for individual material Five G.P. fitting function parameters (b, c, a, Xk and d) can be used to compute the values of EBF at selected energy and optical thickness, using G.P. fitting formula (Harima et al., 1986). The detailed procedure of EBF computation have been discussed in our previous publications (Mann et al., 2012; Mann and Sidhu, 2012; Mann and Korkut, 2013). 2.2. DLEBF for two-layered slabs The Kalos (1956, 1957) formula of DLEBF for two-layered slabs can be written as follows:
B (X1, X2 ) = B2 (X2 ) + [B2 (X1 + X2 ) − B2 (X2 )]. [K (X1) C (X2 )]
(1)
where B(X1, X2)¼ DLEBF for two layered slab with X1 mfp of the first material and X2 mfp of the second material; Bi(X) ¼EBF for the material of ith layer with thickness of X mfp; K(X1) ¼Ratio of scattered component transmitted through X1 mfp of the first
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K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
Table 2 Percentage deviations in DLEBF obtained by various formulae from Monte Carlo calculations in H2O-Fe slabs (low-Z followed by high-Z material) for point isotropic sources. EBF computed from G.P. fitting formula (Harima et al., 1986)
H2O
Fe
EBF-data from EGS4-code (Lin and Jiang, 1996)
X1 (mfp)
X2 (mfp)
Lin and Jiang
Burke and Beck
Kalos
Lin and Jiang
Burke and Beck
Kalos
E ¼0.5 MeV 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4
1 2 3 4 5 6 1 2 3 4 5 1 2 3 4
1.69 2.98 5.87 7.99 9.70 11.37 4.27 0.21 3.30 5.62 7.37 7.29 2.78 0.13 3.59
11.00 1.45 5.29 10.08 13.71 17.13 15.25 4.87 2.84 8.26 12.09 19.18 7.69 0.27 8.33
13.89 3.51 4.42 9.77 13.60 17.10 17.51 6.48 2.16 8.02 12.01 21.03 9.03 0.32 8.12
1.63 2.73 5.38 7.33 8.77 10.21 4.28 0.18 2.64 4.61 6.08 6.89 2.55 0.07 3.27
3.99 4.40 9.53 13.34 16.16 19.01 8.39 0.11 5.60 9.57 12.52 12.73 3.45 2.16 8.76
7.44 0.69 3.50 6.76 9.22 11.89 9.65 2.03 3.28 7.00 9.78 13.15 4.11 1.35 7.88
E ¼1.0 MeV 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4
1 2 3 4 5 6 1 2 3 4 5 1 2 3 4
0.91 1.60 2.98 4.50 5.24 6.28 2.19 0.59 0.65 1.59 3.58 3.04 1.24 0.25 1.85
5.33 0.62 4.66 8.52 10.39 12.65 5.82 0.72 3.66 6.77 11.44 6.55 0.56 3.64 9.33
8.50 1.66 3.66 8.16 10.26 12.61 8.32 2.66 2.80 6.45 11.33 8.78 2.24 2.89 9.04
2.33 0.67 1.85 3.69 4.85 4.85 2.81 1.23 0.44 1.89 2.88 3.71 1.35 0.26 1.42
4.46 1.65 4.08 7.79 10.12 10.16 4.33 0.38 3.44 6.67 8.88 5.53 0.38 4.39 7.27
7.04 2.31 0.78 2.44 4.42 4.08 5.16 1.71 1.79 4.82 6.88 5.78 0.03 3.88 6.69
Table 3 Standardization of BUF-toolkit using iron–water slabs for point isotropic sources. The percentage deviations in DLEBF values obtained by BUF-toolkit and Monte Carlo calculations using EGS4-code. H2O (water)
Fe (Iron)
For low-Z followed by high-Z material
X1 (mfp)
X2 (mfp)
0.5 MeV
1 MeV
2 MeV
2 2 2 2 2 2 3 3 3 3 3 4 4 4 4
1 2 3 4 5 6 1 2 3 4 5 1 2 3 4
0.13 0.54 1.11 1.57 2.32 3.00 0.01 0.80 1.41 2.27 3.03 0.70 0.45 0.13 0.68
2.80 1.92 2.39 1.78 0.87 3.27 1.20 1.27 0.43 0.63 1.51 1.26 0.20 1.01 0.91
3.04 2.19 1.36 0.05 1.33 2.24 4.14 3.66 2.50 1.39 0.61 4.12 2.78 1.53 0.62
Fe (Iron)
H2O (water)
For high-Z followed by low-Z material
3 MeV
X1 (mfp)
X2 (mfp)
0.5 MeV
1 MeV
2 MeV
3 MeV
6.02 5.06 5.12 5.15 5.52 4.08 4.53 3.99 3.57 3.56 1.94 4.75 4.40 4.43 2.88
2 2 2 2 2 2 3 3 3 3 3 4 4 4 4
1 2 3 4 5 6 1 2 3 4 5 1 2 3 4
0.05 1.39 1.44 2.54 3.01 4.34 0.68 1.96 2.13 2.44 3.60 0.45 1.98 1.39 2.32
0.51 2.83 3.78 4.63 4.91 6.04 1.09 2.98 4.06 4.56 5.86 0.86 2.95 3.65 5.16
1.14 0.19 0.57 1.20 1.07 0.60 0.38 1.27 1.48 1.56 1.24 0.09 1.02 0.69 0.68
0.49 0.36 0.60 0.99 0.70 0.62 1.26 0.54 0.38 0.02 0.09 0.42 0.02 0.19 0.06
material relative to that transmitted through X1 mfp of the second material:
K (X1) =
B1 (X1) − 1 B2 (X1) − 1
(2)
and C (X2)¼Correction factor. Kalos (1956, 1957) postulated that for high-Z material followed by Low-Z material, C(X2)¼1 and for Low-Z material followed by high-Z material, the correction factor is:
C (X2 ) = exp ( − 1.7X2 ) + (α/K )[1 − exp ( − X2 )]
(3)
K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
31
20 18 16
U n c e rta in tie s in D L E B F
14
Fe-H2O slabs at 0.50 MeV Using EBF computed by G.P. fitting formula
12 10 8 6 4 2 0 -2 -4 16
H2O-Fe slabs at 0.50 MeV
14
Lin and Jiang (1996) Burke and Beck(1974) Kalos (1956)
12
Uncertainties in DLEBF
Using EBF computed by G.P. fitting formula
10 8 6 4 2 0 -2 -4 3
4
5
6
7
8
----- Optical thickness(mfp) -----> Fig. 2. Uncertainties in DLEBF values at 0.5 MeV point isotropic source, obtained from various empirical formulae for water–iron slabs (in both orientations); viz. iron–water and water–iron.
where α is the ratio of Compton scattering to total cross section in the first and second material respectively:
α=
( μc /μt )1 ( μc /μt )2
(4)
Modification in the correction factor of Kalos formula was suggested by Burke and Beck (1974) called modified Kalos formula (Burke and Beck formula). The correction factor for Burke and Beck formula in high-Z material followed by low-Z material:
C (X2 ) = exp (−X2 /γ ) + 1.5 [1 − exp ( − X2 )]
(5)
and for Low-Z material followed by high-Z material:
C (X2 ) = exp ( − γX2 ) + (α/K )[1 − exp ( − X2 )]
(6)
where γ is the ratio of mass Compton cross section of first and second material:
γ=
( μc /ρ)1 ( μc /ρ)2
(7)
Lin and Jiang (1996) suggested a further modification in the correction factors of Kalos formula as explained below. The correction factors for high-Z material followed by low-Z material:
C (X2 ) = exp ( − 1.08βX2 ) + 1.13βℓ( − X2 )
(8)
and for low-Z material followed by high-Z material:
C (X2 ) = 0.8ℓ(X2 ) + (γ /K ) exp ( − X2 )
(9)
where β is the ratio of mass total cross section of second material to that of first material:
β=
and
( μt /ρ)2 ( μt /ρ)1
(10)
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K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
Total
2
-1
(cm g )
1
0.1
Total NBS Concrete Aluminium (Al) Water (H2O) Clay (CY) Lime Stone (LS)
0.1
Compton
2
-1
(cm g )
0.2 0.15
0.05
Compton Scattering (Incoherent) NBS Concrete Aluminium (Al) Water (H2O) Clay (CY) Lime Stone (LS)
0.01
Coherent
2
-1
(cm g )
0.1
1E-3 1E-4
(Photoelectric + Pair-production)
2
-1
(cm g )
1E-5
Compton Scattering (Coherent) NBS Concrete Aluminium (Al) Water (H2O) Clay (CY) Lime Stone (LS)
0.01
1E-3
1E-4
1E-5
Photoelecric + Pair-production NBS Concrete Aluminium (Al) Water (H2O) Clay (CY) Lime Stone (LS)
0.1
1 Energy (MeV)
10
Fig. 3. Combined representation of variations in total mass attenuation coefficients and partial mass attenuation coefficient values obtained from WinXCom for chosen samples.
Table 4 Equivalent atomic numbers (Zeq ) of the selected samples. Sample's symbol
NBS Concrete Al (Aluminum) H2O Clay (CY) Lime Stone (LS)
Density(g cm 3)
2.35 2.70 1.00 1.74 1.07
Equivalent atomic numbers (Zeq ) 0.50 MeV
1.00 MeV
2.00 MeV
3.00 MeV
Source
13.63 13.00 7.51 15.01 18.23
13.64 13.00 7.51 15.03 18.23
11.65 13.00 6.93 12.56 16.69
11.55 13.00 6.94 12.41 16.48
ANSI 6.4.3. (1991) ANSI 6.4.3. (1991) ANSI 6.4.3. (1991) Mann et al., 2015 Mann et al., 2015
K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
33
Table 5 Geometric thickness (cm) of chosen samples at selected energies. Energy (MeV)
Thickness (cm) 0.5 mfp
1 mfp
2 mfp
3 mfp
4 mfp
5 mfp
6 mfp
7 mfp
0.50 1.00 2.00 3.00
Aluminum (Al) 0.11 0.08 0.06 0.05
0.23 0.17 0.12 0.10
0.45 0.33 0.23 0.19
0.68 0.50 0.35 0.29
0.91 0.66 0.47 0.38
1.13 0.83 0.58 0.48
1.36 0.99 0.70 0.57
1.59 1.16 0.82 0.67
0.50 1.00 2.00 3.00
NBS Concrete 0.10 0.07 0.05 0.04
0.20 0.15 0.11 0.09
0.41 0.30 0.21 0.17
0.61 0.45 0.32 0.26
0.82 0.60 0.42 0.34
1.02 0.75 0.53 0.43
1.23 0.90 0.63 0.51
1.43 1.05 0.74 0.60
0.50 1.00 2.00 3.00
Water (H2O) 0.05 0.04 0.02 0.02
0.10 0.07 0.05 0.04
0.19 0.14 0.10 0.08
0.29 0.21 0.15 0.12
0.39 0.28 0.20 0.16
0.48 0.35 0.25 0.20
0.58 0.42 0.30 0.24
0.68 0.49 0.35 0.28
0.50 1.00 2.00 3.00
Clay (CY) 0.08 0.05 0.02 0.02
0.15 0.11 0.05 0.05
0.30 0.22 0.10 0.09
0.45 0.33 0.14 0.14
0.60 0.44 0.19 0.18
0.75 0.55 0.24 0.23
0.90 0.66 0.29 0.28
1.05 0.77 0.34 0.32
0.50 1.00 2.00 3.00
Lime Stone (LS) 0.05 0.04 0.03 0.14
0.09 0.08 0.06 0.28
0.19 0.16 0.12 0.57
0.28 0.24 0.19 0.85
0.37 0.32 0.25 1.14
0.47 0.40 0.31 1.42
0.56 0.48 0.37 1.71
0.65 0.56 0.43 1.99
(a)
40 35 30
BUF
(b)
E=0.5 MeV
E=1.0 MeV
40
EBF (Z1=7.51)Water
EBF (Z1=7.51)Water
EBF(Z2=15.01)Clay
EBF(Z2=15.03)Clay
DLEBF (Z1Z2)
DLEBF (Z1Z2)
35 30
25
25
20
20
15
15
10
10
5
5
0
0
(c)
10
8
BUF
(d)
E=2.0 MeV
E=3.0 MeV
10
EBF (Z1=6.93)Water
EBF (Z1=6.94)Water
EBF(Z2=12.56)Clay
EBF(Z2=12.41)Clay
DLEBF (Z1Z2)
DLEBF (Z1Z2)
8
6
6
4
4
2
2
0
0 0
1
2
3
4
5
Optical Thickness (mfp)
6
7
8
0
1
2
3
4
5
6
7
8
Optical Thickness (mfp)
Fig. 4. Variation of buildup factors (EBF and DLEBF) for two layered shields made of Water and Clay with optical thickness at four energies; (a) 0.5 MeV, (b) 1.0 MeV, (c) 2.0 MeV and (d) 3.0 MeV.
34
K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
(a)
40 35 30
BUF
(b)
E=0.5 MeV
E=1.0 MeV
40
EBF (Z1=7.51)Water
EBF (Z1=7.51)Water
EBF(Z2=13.63)NBS Conc.
EBF(Z2=13.64)NBS Conc.
DLEBF (Z1Z2)
DLEBF (Z1Z2)
35 30
25
25
20
20
15
15
10
10
5
5
0
0
(c)
10
8
BUF
(d)
E=2.0 MeV
E=3.0 MeV
10
EBF (Z1=6.93)Water
EBF (Z1=6.94)Water
EBF(Z2=11.65)NBS Conc.
EBF(Z2=11.55)NBS Conc.
DLEBF (Z1Z2)
DLEBF (Z1Z2)
8
6
6
4
4
2
2
0
0 0
1
2
3
4
5
6
7
8
Optical Thickness (mfp)
0
1
2
3
4
5
6
7
8
Optical Thickness (mfp)
Fig. 5. Variation of buildup factors (EBF and DLEBF) for two layered shields made of Water and NBS Concrete with optical thickness at four energies; (a) 0.5 MeV, (b) 1.0 MeV, (c) 2.0 MeV and (d) 3.0 MeV.
⎛ B (X ) + 1 ⎞ ℓ(X2 ) = ⎜ 2 2 ⎟. [1 − exp ( − X2 )] ⎝ B1 (X2 ) + 1 ⎠
(11)
3. Computational work 3.1. BUF-toolkit-a computer program The BUF-toolkit is a computer program made in MS-Excel2007. It is capable to compute EBF values by using G.P. fitting formula (Harima et al., 1986) at desired energy and thickness for any material (compound or mixture) from its chemical composition. Thereby it computes (compare) the DLEBF values using Kalos (1956,1957), Burke and Beck (1974) and Lin and Jiang (1996) empirical formulae for the selected two materials (two layered slabs) at specified energy and optical thickness. The working of the toolkit is based on the database that consists of the available values of EBF and five G.P. fitting parameters for all the periodic table elements of arranged in
25 16 matrixes (25-energies in MeV and 16-optical thicknesses in mfp) obtained from ANS/ANSI 6.4.3. (1991) report. This matrix database is required for the execution of the BUFtoolkit. The BUF-toolkit computes the required values of EBF by G.P. fitting formula. Thereby, the toolkit compute values of DLEBF for chosen two layered slab using Lin and Jiang (1996) formula. 3.1.1. Errors and corrections Kim et al. (2013) suggested (using MCNPX 2.7.0) that existing data (ANSI/ANS-6.4.3-1991) cause about five percent (5%) overestimation in buildup factors computations. The errors caused by overestimations of EBF values by G.P. fitting method have been compensated in the BUF-toolkit. 3.2. Validation of BUF-toolkit for DLEBF computation Fig. 1 indicates that computed values of EBF using BUF-toolkit for water (H2O) and iron (Fe) at selected energies and thicknesses
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35
Fig. 6. Variation of buildup factors (EBF and DLEBF) for two layered shields made of Aluminium and Lime Stone with optical thickness at four energies; (a) 0.5 MeV, (b) 1.0 MeV, (c) 2.0 MeV and (d) 3.0 MeV.
agreed very well with the corresponding standard values (ANSI 6.4.3, 1991). Thus the toolkit can reproduce accurate values of EBF for chosen samples in required range of energy and thickness. Table 1 show that for Fe -H2O slabs (high-Z material followed by low-Z material) the minimum percentage deviations of the DLEBF values from Monte Carlo calculations were found for Lin and Jiang formula. Similarly, Table 2 for H2O-Fe slabs (low-Z material followed by high-Z material) the minimum percentage deviations of the DLEBF values from Monte Carlo calculations were found for Lin and Jiang formula. Thereby, Lin and Jiang (1996) formula has been validated as the most accurate formula for DLEBF computation (using EBF values computed by G.P. fitting formula) for two-layered slabs for both orientations (viz. low-Z followed by high-Z material and high-Z followed by low-Z material). Table 3 validates the BUF-toolkit as the computed values of DLEBF by BUF-toolkit and Monte Carlo calculations agreed very well. Fig. 2 indicates that the uncertainties in DLEBF values for various empirical formulae (Kalos, Burke and Beck and Lin and Jiang) at 0.5 MeV and thickness up to 8 mfp, for water–iron slabs in two orientations viz. iron–water and water–iron. For computation of DLEBF, the required values of EBF for iron and water
were obtained from Monte Carlo calculations using EGS4-code (Hirayama and Shin, 1998) and computed by G.P. fitting method. Thereby, confirming that at chosen energy and thickness range the Lin and Jiang (1996) formula can reproduce DLEBF values most accurately. 3.3. Computation of mass attenuation coefficients The total and partial mass attenuation coefficients of the selected samples were computed by using WinXCom Gerward et al. (2004). Fig. 3 shows combined variations in computed total and partial mass attenuation coefficients values with energy for chosen samples. It is confirmed that the Compton scattering is dominating in the chosen energy range below 1.02 MeV. 3.4. Computation of equivalent atomic number (Zeq) The equivalent atomic number of a composite material is analogous to the atomic numbers of an element, which describes the properties of the composite material (compounds/mixture) in terms of equivalent element. The Zeq is computed from the contribution of
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25
(a)
(b)
E=0.5 MeV
20
25
E=1.0 MeV
EBF (Z 1=13.00)Aluminium
EBF (Z 1=13.00)Aluminium
EBF(Z2=15.01)Clay
EBF(Z2=15.03)Clay
DLEBF (Z1Z2)
DLEBF (Z1Z2)
20
15
10
10
5
5
BUF
15
0
0
(c)
10
8
BUF
(d)
E=2.0 MeV
E=3.0 MeV
10
EBF (Z 1=13.00)Aluminium
EBF (Z 1=13.00)Aluminium
EBF(Z2=12.56)Clay
EBF(Z2=12.41)Clay
DLEBF (Z1Z2)
DLEBF (Z1Z2)
8
6
6
4
4
2
2
0
0 0
1
2
3
4
5
6
7
Optical Thickness (mfp)
8
0
1
2
3
4
5
6
7
8
Optical Thickness (mfp)
Fig. 7. Variation of buildup factors (EBF and DLEBF) for two layered shields made of Aluminium and Clay with optical thickness at four energies; (a) 0.5 MeV, (b) 1.0 MeV, (c) 2.0 MeV and (d) 3.0 MeV.
Compton scattering only. The detailed procedure of equivalent atomic number (Zeq) computation has been discussed in our previous publications (Mann et al., 2012; Mann and Sidhu, 2012; Mann and Korkut, 2013). Table 4 enlisted the density and Zeq of the selected samples and source reference of each sample. For selected samples the variation in values of Zeq with energy of is indicated in the table. 3.5. Geometric thickness Geometric thickness (x, cm) correspond to optical thickness (mx, mfp) is the physical thickness of the sample calculated from its linear attenuation coefficient (m, cm 1) at selected energy. Geometric thicknesses of chosen samples at selected energies have been listed in Table 5.
4. Results and discussion Occasionally, at any fixed energy in the selected energy range the EBF values for low-Z materials are comparatively
higher than for high-Z material. The probability of the scattered photons (DLEBF) will reduce by using the arrangement of materials such that low-Z followed by high-Z in gamma radiation leakage protective slabs. This can be explained as follows, for a fixed energy below 1.02 MeV, the probability of Photo electric absorption is proportional to Z eq 5 and goes on increasing more rapidly than Compton scattering because the Compton cross section is proportional to Z eq . For energy above 1.02 MeV the probability of Pair production absorption is proportional to Z eq 2 starts contributing to the total absorption process. At the same time the relative contribution of Compton scattering to the total absorption goes on decreasing with increase in Z eq . The variations of computed DLEBF values at four energies, for five combinations of the chosen materials (H 2 O-CY, H 2 O-NBS Concrete, Al-LS, Al-CY and Al-NBS Concrete), in both orientations with optical thickness have been revealed in Figs. 4–8. From Figs. 4 to 6 it is observed that for high energies of the selected range of energy and optical thickness the DLEBF values for both orientations of materials are less than their
K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
37
Fig. 8. Variation of buildup factors (EBF and DLEBF) for two layered shields made of Aluminium and NBS Concrete with optical thickness at four energies; (a) 0.5 MeV, (b) 1.0 MeV, (c) 2.0 MeV and (d) 3.0 MeV.
individual EBF values (DLEBF o EBF). This type of behavior of two layered shields seems to be due to the fact that the probability of absorption of gamma-ray photons increases due to its interaction of with two layered shield of materials with different Z eq . For low-Z eq materials the Compton scattering probabilities are higher than for high-Z eq composite materials. The probabilities of photoelectric and pair-production absorptions are dominant in high-Z eq materials. For the orientation low-Z followed by high-Z, when incident gamma-ray photon of the selected energy range interacts with low-Z eq composite material it causes multiple scattering and when these scattered photons interact with high-Z eq composite material get absorbed (photoelectric or pair-production) by it, thereby reduce the DLEBF (flux of outgoing photons). Figs. 7d and 8d show a reverse trend (DLEBF 4 EBF) at 3 MeV for sample-materials with comparable Z eq such as; AlNBS Concrete and Al-CY. This seems to be due to the dominance of Compton scattering probabilities in both materials, thereby increase the outgoing flux of photons or DLEBF values. From Figs. 4–8, it is concluded that EBF values for any material depends on its equivalent atomic number. Moreover, at fixed
energy the EBF values of two materials approach each other if the difference in their equivalent atomic numbers is small and vice-versa. On the other side, the DLEBF values in both orientations remains different and no appreciable variation in DLEBF have been observed with minor change in their equivalent atomic numbers. Comparison of Figs. 9 and 10 indicates that DLEBF values are comparatively low for all chosen ten combinations low-Z followed by high-Z than their reverse combinations. It has also been observed that the same values of DLEBF for three combinations viz. LS-NBS conc., LS-CY and LS-Al in case of high-Z followed by low-Z case. Thus all these three combinations seem to provide the similar shielding behavior for gamma-rays in the energy range 0.5–3.0 MeV. Fig. 9 clearly indicated that the lowest values of DLEBF for Al-LS (low-Z followed by high-Z) combination in the chosen energy and optical thickness range. Moreover for any combination of chosen materials the DLEBF values goes on decreasing with increase in the energy of incident gamma-ray photons. Thus double layered shield with optical thickness up to 8 mfp such that Al followed by LS appears to be the best
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K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
Low-Z followed by high-Z
E=0.5 MeV 20
NBS conc.-LS Water-Al NBS Conc.-CY CY-LS Water-LS Water-CY Water-NBS Conc. Al-LS Al-CY Al-NBS Conc.
DLEBF
15
10
Low-Z followed by high-Z
E=1.0 MeV
20
NBS conc.-LS Water-Al NBS Conc.-CY CY-LS Water-LS Water-CY Water-NBS Conc. Al-LS Al-CY Al-NBS Conc.
15
10
5
5
0
0 Low-Z followed by high-Z
E=2.0 MeV 8
DLEBF
E=3.0 MeV
NBS conc.-LS Water-Al NBS Conc.-CY CY-LS Water-LS Water-CY Water-NBS Conc. Al-LS Al-CY Al-NBS Conc.
6
4
Low-Z followed by high-Z 8
NBS conc.-LS Water-Al NBS Conc.-CY CY-LS Water-LS Water-CY Water-NBS Conc. Al-LS Al-CY Al-NBS Conc.
6
4
2
2
1
2
3
4
5
6
7
8
Optical Thickness (mfp)
1
2
3
4
5
6
7
8
Optical Thickness (mfp)
Fig. 9. Variations of DLEBF for different combinations of chosen samples such that low-Z followed by high-Z material.
protective shields for gamma-rays in energy range 0.5– 3.0 MeV.
5. Conclusions It is concluded that at fixed energy, with the use of two layered shield in orientation such that low-Z followed by high-Z always reduce the value of build up factor from the individual single material of same optical thickness. Thus, in gamma-ray protection double-layered shields are more effective than a single layer shields. To account for the scattered gamma-ray photons of point isotropic source, Lin and Jiang (1996) formula has the advantage over other empirical formulae. Simultaneously, the G.P. fitting point kernel calculations accurately reproduce the EBF values for low-Z materials. Thus in medium energy range (0.5–3 MeV), for two-layered slabs of optical thickness up to 8 mfp, the Lin and Jiang formula along with G.P. fitting formula can be used to compute the double layered transmission exposure buildup factors (DLEBF) values.
It is confirmed that DLEBF values at selected energy for two layered slabs with an orientation (high-Z material followed by low-Z material) were higher than the opposite orientation. Concurrently, the difference in DLEBF values for both orientations were go on increasing with increase in the optical thickness. For the optical thickness up to 8 mfp and energy range (0.5–3.0 MeV), the Al–LS (Aluminum–Lime Stone) combination, appears to provide the best protection against the gamma-rays. The expansion of the present investigation to higher energies is planned to be conducted in the near future. The aim of this series of investigations is to devise computational tools for gamma-ray protective designs of the nuclear establishments. Above results and discussion will be useful in the construction of effectual protection against hazardous gamma-rays.
Acknowledgments We are grateful to SAIF, Punjab University, Chandigarh for providing WD-XRF-facility. We are thankful to Punjab technical
K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
35
High-Z followed by low-Z
E=0.5 MeV
DLEBF
25 20 15 10
High-Z followed by low-Z
E=1.0 MeV
LS-NBS conc. Al-Water CY-NBS Conc. LS-CY LS-Water CY-Water NBS Conc.-Water LS-Al CY-Al NBS Conc.-Al
30
39
LS-NBS conc. Al-Water CY-NBS Conc. LS-CY LS-Water CY-Water NBS Conc.-Water LS-Al CY-Al NBS Conc.-Al
30 25 20 15 10
5
5
0 10
0 High-Z followed by low-Z
E=2.0 MeV
6
High-Z followed by low-Z
E=3.0 MeV
LS-NBS conc. Al-Water CY-NBS Conc. LS-CY LS-Water CY-Water NBS Conc.-Water LS-Al CY-Al NBS Conc.-Al
8
DLEBF
35
LS-NBS conc. Al-Water CY-NBS Conc. LS-CY LS-Water CY-Water NBS Conc.-Water LS-Al CY-Al NBS Conc.-Al
10
8
6
4
4
2
2 1
2
3
4
5
6
7
8
Optical Thickness (mfp)
1
2
3
4
5
6
7
8
Optical Thickness (mfp)
Fig. 10. Variations of DLEBF for different combinations of chosen samples such that high-Z followed by low-Z material.
University (PTU), Kapurthala for providing necessary research related literature and infrastructure. The present work is devoted to the Ph.D.-thesis under Reg. number:1311025, Punjab Technical University, Kapurthala.
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.radphyschem. 2016.03.001.
References ANSI/ANS-6.4.3, 1991. Gamma ray attenuation coefficient and buildup factors for engineering materials american nuclear society. La. Grange Park., IL. Burke, G. de P., Beck, H.L., 1974. Calculated and measured dose buildup factors for gamma rays penetrating multilayered slabs. Nucl. Sci. Eng. 53, 109. Eisenhauer, C.M., Simmons, G.L., 1975. Point isotropic gamma ray buildup factors in concrete. Nucl. Sci. Eng., 56. 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. Goldstein, H., Wilkins Jr., J.E., 1954. Calculations of penetrations of gamma rays. NDA/AEC report NYO- 3075. US Government printing office, Washington.
Gopinath, D.V., Samthanam, K., 1971. Radiation transport in one dimensional finite technique. Nucl. Sci. Eng. 43, 186. Guvendik, M., Nicholas, T., 2000. Formulas giving buildup factor for double layered shields. Nucl. Tech. 131, 332–3360. Hirayama, H., Shin, K., 1998. Application of the EGS4 Monte Carlo Code to a study of multilayer gamma-ray exposure buildup factors of up to 40 mfp. J. Nucl. Sci. Technol. 35, 816–829. Harima, Y., 1986. An approximation of gamma ray buildup factors by modified geometric progression. Nucl. Sci. Eng. 83, 299–309. Harima, Y., 1993. An historical review and current status of buildup factor calculations and applications. Radiat. Phys. Chem. 41, 631–672. Harima, Y., Sakamoto, Y., Tonaka, S., Kawai, M., 1986. Validity of geometric progression gamma ray buildup factors. Nucl. Sci. Eng. 94, 24–25. Icelli, O., Mann, K.S., Yalcın, Z., Orak, S., Karakaya, V., 2013. Investigation of shielding properties of some boron compounds. Ann. Nucl. Energy 55, 341–350. Kalos, M.H., 1956. Nuclear Development Associates (NDA), 56–57. Kalos, M.H., 1957. A Monte Carlo calculation of the transport of gamma rays, NDA 56-10. Kalos, M.H., 1959. Quoted in Goldstein H., Fundamental Aspects of Reactor Shielding, 225. Addison-Wesley, Reading, Mass. Kavanoz, H.B., Yagci, O., Yalçın, Z., Içelli, O., Altındal, A., Okutan, M., Mann, K.S., 2014. Photon parameters for γ-rays sensing properties of some thick oxide films. Vacuum 101, 238–245. Kazuo, S., Hirayama, H., 2001. Calculation of gamma ray buildup factors for two layered shields made of water, concrete and iron and application of approximating formula. Radiat. Phys. Chem. 64, 583–584. Kim, Kyung-O., ROH, G., Park, C.J., Kim, H., Lee, B., 2013. Evaluation of geometric progression (GP) buildup factors using MCNPX 2.7.0. Trans. of Korean Nucl. Scoci. Autumn Meeting Gyeongju, Korea. Kurudirek, M., Sardari, D., Khaledi, N., Cakır, C., Mann, K.S., 2013. Investigation of X-
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and gamma ray photons buildup in some neutron shielding materials using GP fitting approximation. Ann. Nucl. Energy 53, 485–491. Lin, Uei-Tyng, Jiang, Shiang-Huei, 1996. A dedicated empirical formula for gammaray buildup factors for a point isotropic source in stratified shields. Radiat. Phys. Chem. 48 (4), 389–401. Mann, K.S., Kurudirek, M., Sidhu, G.S., 2012. Verification of dosimetric materials to be used as tissue-substitutes in radiological diagnosis. Appl. Radiat. Isot. 70, 681–691. Mann, K.S., Rani, A., Heer, M.S., 2015. Shielding behaviours of some polymer and plastic materials for gamma-rays. Radiat. Phys. Chem. 106, 247–254. Mann, K.S., Sidhu, G.S., 2012. Verification of some low-Z silicates as gamma-ray shielding materials. Ann. Nucl. Energy 40, 241–252. Mann, K.S., Korkut, T., 2013. Gamma-ray buildup factors study for deep penetration in some silicates. Ann. Nucl. Energy 51, 81–93. Manohara, S.R., Hanagodimath, S.M., Gerward, L., 2010. Energy absorption buildup factors for thermoluminescent dosimetric materials and their tissue equivalence. Radiat. Phys. Chem. 79, 575–582. Medhat, M.E., 2011. Studies on effective atomic numbers and electron densities in different solid state track detectors in the energy range 1 keV–100 GeV. Ann. Nucl. Energy 38, 1252–1263. Nelson, W.R., Hirayama, H., Rogers, D., 1985. The EGS4 code system-SLAC-265, Stanford Linear Accelerator Center. Stanford, California. Saadi, Abbas J. Al., 2012. Calculation of buildup factor for gamma-ray exposure in two layered shields made of water and lead. J. KUFA- Phy. 4 (1), 1–10. Sakamoto, Y., Tanaka, S., Harima, Y., 1988. Interpolation of gamma-ray buildup
factors for isotropic source with respect to atomic number. Nucl. Sci. Eng. 100, 33–42. Sardari, D., Abbaspour, A., Baradaran, S., Babapour, F., 2009. Estimation of gamma and X-ray photons buildup factor in soft tissue with Monte Carlo method. Appl. Radiat. Isot. 67, 1438–1440. Schirmers, F.G., 2006. Improvement of photon buildup factors for radiological assessment. North Carolina State University. Shimizu, A., 2002. Calculations of gamma-ray buildup factors up to depths of 100 mfp by the method of invariant embedding, (I) analysis of accuracy and comparison with other data. J. Nucl. Sci. Technol. 39, 477–486. Shimizu, A., Onda, T., Sakamoto, Y., 2004. Calculations of gamma-ray buildup factors up to depths of 100 mfp by the method of invariant embedding, (III) generation of an improved data set. J. Nucl. Sci. Technol. 41, 413–424. Shin, K., Hirayama, H., 1995. Approximation model for multilayer gamma-ray buildup factors by transmission matrix methods: application to point isotropic source geometry. Nucl. Sci. Eng. 120, 211. Suteau, C., Chiron, M., 2005. An iterative method for calculating gamma ray buildup factors in multi-layer shields. Radiat. Prot. Dosim. 116 (1–4), 489–492. Takeuchi, K., Tanaka, S., 1984. PALLAS-ID(VII), a code for direct integration of transport equation in one dimensional plane and spherical geometries. JAERIM84, 214. Trontl, K., Smuc, T., Pevec, D., 2007. Support vector regression model for the estimation of γ-ray buildup factors for multi-layer shields. Ann. Nucl. Energy 34, 939–952.
Contents lists available at ScienceDirect
Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
Gamma-ray double-layered transmission exposure buildup factors of some engineering materials, a comparative study Kulwinder Singh Mann a,b,n, Manmohan Singh Heer c, Asha Rani d a
Department of Applied Sciences, Punjab Technical University, Kapurthala 144601, India Department of Physics, D.A.V. College, Bathinda 151001, Punjab, India c Department of Physics, Kanya Maha Vidyalaya, Jalandhar 144001, India d Department of Applied Sciences, Ferozpur College of Engineering and Technology, Ferozshah, Ferozpur 142052, India b
H I G H L I G H T S
G.P. fitting formula accurately reproduces the EBF values for low-Z materials. Lin and Jiang empirical formula computes DLEBF with minimum differences. For low-Z followed by high-Z, DLEBF values are smaller than the reverse order. Two-materials protect γ-rays effectively than a single material of same thickness. Al-LS seem to be the best γ-ray protective shield in energy range 0.5–3.0 MeV.
art ic l e i nf o
a b s t r a c t
Article history: Received 22 July 2015 Received in revised form 28 February 2016 Accepted 1 March 2016 Available online 3 March 2016
Comparative study on various deterministic methods and formulae of double layered transmission exposure buildup factors (DLEBF) for point isotropic gamma-ray sources has been performed and the results are provided here. This investigation has been performed on some commonly available engineering materials for the purpose of gamma-ray shielding. In reality, the presence of air around the gamma-ray shield motivated to focus this study on exposure buildup factor (EBF). DLEBF have been computed at four energies viz. 0.5, 1.0, 2.0 and 3.0 MeV for various combinations of the chosen five samples taken two at a time with combined optical thickness up to 8 mean free path (mfp). For the necessary computations for DLEBF, a computer program (BUF-toolkit) has been designed. Comparison of Monte Carlo (EGS4-code) and Geometric Progression (G.P.) fitting point kernel methods were done for DLEBF computation. It is concluded that empirical formula given by Lin and Jiang using EBF computed by G.P. fitting formula is the most accurate and easiest method for DLEBF computations. It was observed that DLEBF values at selected energies for two layered slabs with an orientation (low-Z material followed by high-Z material) were lower than the opposite orientation. For optical thickness up to 8 mfp and chosen energy range (0.5–3.0 MeV), Aluminum-Lime Stone shield, appears to provide the best protection against the gamma-rays. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Buildup factors Empirical formulae Lin and Jiang formula BUF-toolkit
1. Introduction Buildup factor of a material for gamma-rays exposure is an important parameter in the investigation of material’s radiation protection ability. The exposure buildup factor (EBF) for gammarays at a point is the ratio of the correct value of photon flux after
n Corresponding author at: Department of Physics, D.A.V. College, Bathinda 151001, Punjab, India. E-mail address: [email protected] (K.S. Mann).
http://dx.doi.org/10.1016/j.radphyschem.2016.03.001 0969-806X/& 2016 Elsevier Ltd. All rights reserved.
transmission through a material-slab to the uncollided photon flux (without the slab) measured at that point. The value of EBF depends on the atomic number (Z) of the attenuating material, energy of gamma-ray photon (E), optical thickness (number of mean free paths penetrated by the photon) and geometrical form of the radiation source. One mean free path (mfp) is the average distance that a photon traveled between two successive scattering points inside the material. Goldstein and Wilkins (1954) firstly reported data of photon buildup factors. The significance of EBF is indicated by the available literature on it (Harima, 1986; Harima et al., 1986;
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K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
50
(a)
40
EBF
30
Water G.P. fitting formula 0.5 MeV 1.0 MeV 2.0 MeV 3.0 MeV
ANSI 6.4.3. (1991) 0.5 MeV 1.0 MeV 2.0 MeV 3.0 MeV
G.P. fitting formula 0.5 MeV 1.0 MeV 2.0 MeV 3.0 MeV
ANSI 6.4.3. (1991) 0.5 MeV 1.0 MeV 2.0 MeV 3.0 MeV
20 10 15
(b)
EBF
10
Iron
5
0
1
2
3
4
5
6
7
8
Optical Thickness (mfp) Fig. 1. Standardization of BUF-toolkit for EBF calculations using corresponding standard values of EBF (a) for water and (b) for iron.
Guvendik and Nicholas, 2000; Kazuo and Hirayama, 2001; Saadi, 2012). To compute the buildup factors for a material, there are numerous methodologies available such as: Moments method by Eisenhauer and Simmons (1975); G.P. fitting method by Harima et al. (1986); Invariant embedding method by Sakamoto et al. (1988) and Shimizu (2002); Iterative method by Suteau and Chiron (2005) and Monte Carlo method by Sardari et al. (2009). Various codes exist for computation of the buildup factors such as: ASFIT (Anisotropic Source-Flux Iteration Technique) (Gopinath and Samthanam, 1971), PALLAS (Takeuchi and Tanaka, 1984) and Monte Carlo Code EGS4 (Nelson et al. 1985). Harima et al. (1986) reported that G.P. (Geometric Progression) fitting method using five fitting parameters for point kernel calculations reproduce the basic buildup factor data over the whole range of energy, atomic number and shield thickness within a few percent errors. He further reported that G.P. fitting method can reproduce the EBF with better accuracy. Sakamoto et al. (1988), Harima (1993) and Shimizu et al. (2004) confirmed that for EBF calculations, G. P. fitting method agreed well with simple differences for low-Z materials to other methods (invariant embedding and Monte Carlo calculation). Thus the G.P. fitting method can be used for precise computations of EBF for shield made from low-Z material.
American National Standards report (ANSI/ANS-6.4.3-1991) provided database of gamma-ray buildup factors and G.P. fitting parameters for 23 elements (4Be, 5B, 6C, 7N, 8O, 11Na, 12Mg, 13Al, 14Si, 15P,16S, 18Ar, 19K, 20Ca, 26Fe, 29Cu, 42Mo, 50Sn, 57La, 64Gd, 74W, 82Pb and 92U), one compound (H2O), two mixtures (i.e. air and concrete) at 25 energies among 0.015–15 MeV and 16 optical thicknesses between 0.5 and 40 mfp. Numerous attempts have been made to determine EBF of different materials (single slab) using G.P. fitting method (Manohara et al., 2010; Medhat, 2011; Icelli et al., 2013; Kurudirek et al., 2013; Kavanoz et al., 2014). In selection of suitable materials for manufacturing of an efficient gamma-rays protective shield, double layered transmission exposure buildup factors (DLEBF) for two-layered slabs is required. Kalos (1956, 1957) for the first time proposed an empirical formula for double layer buildup factors from those of single layered slabs; Kalos and Goldstein (1959) explained fundamental aspects of reactor shielding; Burke and Beck (1974) using results of transport calculations made some modifications to Kalos formula; Shin and Hariyama (1995) validated the formula using Monte Carlo method; Lin and Jiang (1996) confirmed the empirical method used for double layer shields in point isotropic source. Suteau and Chiron (2005 , ) proposed an iterative method for calculating gamma-ray build-up factors in multi-layer shields. Schirmers (2006) proposed an improvement of photon buildup factors formula using optical thickness of materials. Trontl et al. (2007)
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29
Table 1 Percentage deviations in DLEBF obtained by various formulae from Monte Carlo calculations in Fe-H2O slabs (High-Z followed by low-Z material) for point isotropic sources. EBF computed from G.P. fitting formula (Harima et al., 1986)
Fe
H2O
EBF-data from EGS4-code (Lin and Jiang, 1996)
X1 (mfp)
X2 (mfp)
Lin and Jiang
Burke and Beck
Kalos
Lin and Jiang
Burke and Beck
Kalos
E ¼0.5 MeV 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4
1 2 3 4 5 6 1 2 3 4 5 1 2 3 4
4.02 2.83 3.65 3.04 3.87 3.43 1.79 0.12 0.88 0.83 0.60 1.05 2.13 1.56 2.57
10.93 3.72 3.52 10.69 13.13 16.55 7.05 2.57 11.31 18.92 24.67 5.93 6.88 18.34 29.48
1.78 15.63 24.39 31.23 32.51 34.64 8.38 26.55 37.65 45.64 50.07 11.32 34.57 50.23 62.45
4.08 4.80 5.65 6.62 8.03 9.49 2.77 2.83 4.02 4.43 5.93 1.71 0.96 0.58 1.09
13.40 10.76 7.80 5.93 6.03 7.11 11.81 7.09 3.68 0.48 1.07 10.40 3.59 4.08 9.10
1.45 5.05 8.44 9.39 7.84 5.29 2.67 13.07 17.48 21.14 20.05 5.87 20.06 30.30 35.06
E ¼1.0 MeV 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4
1 2 3 4 5 6 1 2 3 4 5 1 2 3 4
1.52 0.17 0.43 0.69 0.17 1.01 1.00 1.03 1.24 0.65 2.47 0.72 0.80 1.23 2.44
6.50 1.22 2.23 4.42 3.76 6.90 6.05 0.16 4.17 5.05 10.16 5.92 0.49 4.36 9.25
6.19 16.17 20.22 21.81 19.75 21.26 9.12 21.99 27.33 27.68 31.44 11.03 24.20 31.49 36.32
2.27 4.10 5.29 6.35 7.51 8.24 2.59 3.54 4.99 6.28 6.75 2.00 3.69 4.39 5.67
6.69 5.78 4.79 4.89 6.15 7.03 7.72 4.14 2.84 2.82 2.08 6.80 4.11 0.59 0.04
5.63 10.21 11.29 9.97 7.12 4.84 7.03 16.21 18.14 16.90 16.12 9.81 19.13 24.34 23.82
proposed support vector model for estimation of gamma-ray buildup factor for multi layer shields. Saadi (2012) parameterized the buildup factor for double layer shields by an empirical formula as a function of optical thickness of two materials. Photon buildup factor in which the quantity of interest is exposure, termed as exposure buildup factor (EBF). For computation of EBF, the use of energy response function for absorption in air is recommended (ANS 6.4.3-1991). While photon buildup factor in which the quantity of interest is the absorbed or deposited energy in the shield medium is termed as energy absorption buildup factor (EABF). The recommended energy response function used in computation is that of absorption in the shield material. The computation of buildup factors is based on the presence of infinite medium. Moreover air is available up to infinite dimensions around the shielding material. Thus, we focus our study on EBF. Various empirical formulae of DLEBF for water–iron slabs using EBF obtained by G.P. fitting method and Monte Carlo EGS4 code have been compared. The Lin and Jiang (1996) formula shows the best agreement between the two methods. It was concluded that Lin and Jiang (1996) empirical formula with EBF computed from G.P. fitting method reproduce accurately the DLEBF values for two-layered slabs up to the optical thickness of 8 mfp in the energy range (0.5–3.0 MeV). In present investigation, the effects of different atomic numbered
materials orientation on the DLEBF have been investigated at chosen optical thickness and energies.
2. Theory 2.1. EBF for individual material Five G.P. fitting function parameters (b, c, a, Xk and d) can be used to compute the values of EBF at selected energy and optical thickness, using G.P. fitting formula (Harima et al., 1986). The detailed procedure of EBF computation have been discussed in our previous publications (Mann et al., 2012; Mann and Sidhu, 2012; Mann and Korkut, 2013). 2.2. DLEBF for two-layered slabs The Kalos (1956, 1957) formula of DLEBF for two-layered slabs can be written as follows:
B (X1, X2 ) = B2 (X2 ) + [B2 (X1 + X2 ) − B2 (X2 )]. [K (X1) C (X2 )]
(1)
where B(X1, X2)¼ DLEBF for two layered slab with X1 mfp of the first material and X2 mfp of the second material; Bi(X) ¼EBF for the material of ith layer with thickness of X mfp; K(X1) ¼Ratio of scattered component transmitted through X1 mfp of the first
30
K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
Table 2 Percentage deviations in DLEBF obtained by various formulae from Monte Carlo calculations in H2O-Fe slabs (low-Z followed by high-Z material) for point isotropic sources. EBF computed from G.P. fitting formula (Harima et al., 1986)
H2O
Fe
EBF-data from EGS4-code (Lin and Jiang, 1996)
X1 (mfp)
X2 (mfp)
Lin and Jiang
Burke and Beck
Kalos
Lin and Jiang
Burke and Beck
Kalos
E ¼0.5 MeV 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4
1 2 3 4 5 6 1 2 3 4 5 1 2 3 4
1.69 2.98 5.87 7.99 9.70 11.37 4.27 0.21 3.30 5.62 7.37 7.29 2.78 0.13 3.59
11.00 1.45 5.29 10.08 13.71 17.13 15.25 4.87 2.84 8.26 12.09 19.18 7.69 0.27 8.33
13.89 3.51 4.42 9.77 13.60 17.10 17.51 6.48 2.16 8.02 12.01 21.03 9.03 0.32 8.12
1.63 2.73 5.38 7.33 8.77 10.21 4.28 0.18 2.64 4.61 6.08 6.89 2.55 0.07 3.27
3.99 4.40 9.53 13.34 16.16 19.01 8.39 0.11 5.60 9.57 12.52 12.73 3.45 2.16 8.76
7.44 0.69 3.50 6.76 9.22 11.89 9.65 2.03 3.28 7.00 9.78 13.15 4.11 1.35 7.88
E ¼1.0 MeV 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4
1 2 3 4 5 6 1 2 3 4 5 1 2 3 4
0.91 1.60 2.98 4.50 5.24 6.28 2.19 0.59 0.65 1.59 3.58 3.04 1.24 0.25 1.85
5.33 0.62 4.66 8.52 10.39 12.65 5.82 0.72 3.66 6.77 11.44 6.55 0.56 3.64 9.33
8.50 1.66 3.66 8.16 10.26 12.61 8.32 2.66 2.80 6.45 11.33 8.78 2.24 2.89 9.04
2.33 0.67 1.85 3.69 4.85 4.85 2.81 1.23 0.44 1.89 2.88 3.71 1.35 0.26 1.42
4.46 1.65 4.08 7.79 10.12 10.16 4.33 0.38 3.44 6.67 8.88 5.53 0.38 4.39 7.27
7.04 2.31 0.78 2.44 4.42 4.08 5.16 1.71 1.79 4.82 6.88 5.78 0.03 3.88 6.69
Table 3 Standardization of BUF-toolkit using iron–water slabs for point isotropic sources. The percentage deviations in DLEBF values obtained by BUF-toolkit and Monte Carlo calculations using EGS4-code. H2O (water)
Fe (Iron)
For low-Z followed by high-Z material
X1 (mfp)
X2 (mfp)
0.5 MeV
1 MeV
2 MeV
2 2 2 2 2 2 3 3 3 3 3 4 4 4 4
1 2 3 4 5 6 1 2 3 4 5 1 2 3 4
0.13 0.54 1.11 1.57 2.32 3.00 0.01 0.80 1.41 2.27 3.03 0.70 0.45 0.13 0.68
2.80 1.92 2.39 1.78 0.87 3.27 1.20 1.27 0.43 0.63 1.51 1.26 0.20 1.01 0.91
3.04 2.19 1.36 0.05 1.33 2.24 4.14 3.66 2.50 1.39 0.61 4.12 2.78 1.53 0.62
Fe (Iron)
H2O (water)
For high-Z followed by low-Z material
3 MeV
X1 (mfp)
X2 (mfp)
0.5 MeV
1 MeV
2 MeV
3 MeV
6.02 5.06 5.12 5.15 5.52 4.08 4.53 3.99 3.57 3.56 1.94 4.75 4.40 4.43 2.88
2 2 2 2 2 2 3 3 3 3 3 4 4 4 4
1 2 3 4 5 6 1 2 3 4 5 1 2 3 4
0.05 1.39 1.44 2.54 3.01 4.34 0.68 1.96 2.13 2.44 3.60 0.45 1.98 1.39 2.32
0.51 2.83 3.78 4.63 4.91 6.04 1.09 2.98 4.06 4.56 5.86 0.86 2.95 3.65 5.16
1.14 0.19 0.57 1.20 1.07 0.60 0.38 1.27 1.48 1.56 1.24 0.09 1.02 0.69 0.68
0.49 0.36 0.60 0.99 0.70 0.62 1.26 0.54 0.38 0.02 0.09 0.42 0.02 0.19 0.06
material relative to that transmitted through X1 mfp of the second material:
K (X1) =
B1 (X1) − 1 B2 (X1) − 1
(2)
and C (X2)¼Correction factor. Kalos (1956, 1957) postulated that for high-Z material followed by Low-Z material, C(X2)¼1 and for Low-Z material followed by high-Z material, the correction factor is:
C (X2 ) = exp ( − 1.7X2 ) + (α/K )[1 − exp ( − X2 )]
(3)
K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
31
20 18 16
U n c e rta in tie s in D L E B F
14
Fe-H2O slabs at 0.50 MeV Using EBF computed by G.P. fitting formula
12 10 8 6 4 2 0 -2 -4 16
H2O-Fe slabs at 0.50 MeV
14
Lin and Jiang (1996) Burke and Beck(1974) Kalos (1956)
12
Uncertainties in DLEBF
Using EBF computed by G.P. fitting formula
10 8 6 4 2 0 -2 -4 3
4
5
6
7
8
----- Optical thickness(mfp) -----> Fig. 2. Uncertainties in DLEBF values at 0.5 MeV point isotropic source, obtained from various empirical formulae for water–iron slabs (in both orientations); viz. iron–water and water–iron.
where α is the ratio of Compton scattering to total cross section in the first and second material respectively:
α=
( μc /μt )1 ( μc /μt )2
(4)
Modification in the correction factor of Kalos formula was suggested by Burke and Beck (1974) called modified Kalos formula (Burke and Beck formula). The correction factor for Burke and Beck formula in high-Z material followed by low-Z material:
C (X2 ) = exp (−X2 /γ ) + 1.5 [1 − exp ( − X2 )]
(5)
and for Low-Z material followed by high-Z material:
C (X2 ) = exp ( − γX2 ) + (α/K )[1 − exp ( − X2 )]
(6)
where γ is the ratio of mass Compton cross section of first and second material:
γ=
( μc /ρ)1 ( μc /ρ)2
(7)
Lin and Jiang (1996) suggested a further modification in the correction factors of Kalos formula as explained below. The correction factors for high-Z material followed by low-Z material:
C (X2 ) = exp ( − 1.08βX2 ) + 1.13βℓ( − X2 )
(8)
and for low-Z material followed by high-Z material:
C (X2 ) = 0.8ℓ(X2 ) + (γ /K ) exp ( − X2 )
(9)
where β is the ratio of mass total cross section of second material to that of first material:
β=
and
( μt /ρ)2 ( μt /ρ)1
(10)
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K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
Total
2
-1
(cm g )
1
0.1
Total NBS Concrete Aluminium (Al) Water (H2O) Clay (CY) Lime Stone (LS)
0.1
Compton
2
-1
(cm g )
0.2 0.15
0.05
Compton Scattering (Incoherent) NBS Concrete Aluminium (Al) Water (H2O) Clay (CY) Lime Stone (LS)
0.01
Coherent
2
-1
(cm g )
0.1
1E-3 1E-4
(Photoelectric + Pair-production)
2
-1
(cm g )
1E-5
Compton Scattering (Coherent) NBS Concrete Aluminium (Al) Water (H2O) Clay (CY) Lime Stone (LS)
0.01
1E-3
1E-4
1E-5
Photoelecric + Pair-production NBS Concrete Aluminium (Al) Water (H2O) Clay (CY) Lime Stone (LS)
0.1
1 Energy (MeV)
10
Fig. 3. Combined representation of variations in total mass attenuation coefficients and partial mass attenuation coefficient values obtained from WinXCom for chosen samples.
Table 4 Equivalent atomic numbers (Zeq ) of the selected samples. Sample's symbol
NBS Concrete Al (Aluminum) H2O Clay (CY) Lime Stone (LS)
Density(g cm 3)
2.35 2.70 1.00 1.74 1.07
Equivalent atomic numbers (Zeq ) 0.50 MeV
1.00 MeV
2.00 MeV
3.00 MeV
Source
13.63 13.00 7.51 15.01 18.23
13.64 13.00 7.51 15.03 18.23
11.65 13.00 6.93 12.56 16.69
11.55 13.00 6.94 12.41 16.48
ANSI 6.4.3. (1991) ANSI 6.4.3. (1991) ANSI 6.4.3. (1991) Mann et al., 2015 Mann et al., 2015
K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
33
Table 5 Geometric thickness (cm) of chosen samples at selected energies. Energy (MeV)
Thickness (cm) 0.5 mfp
1 mfp
2 mfp
3 mfp
4 mfp
5 mfp
6 mfp
7 mfp
0.50 1.00 2.00 3.00
Aluminum (Al) 0.11 0.08 0.06 0.05
0.23 0.17 0.12 0.10
0.45 0.33 0.23 0.19
0.68 0.50 0.35 0.29
0.91 0.66 0.47 0.38
1.13 0.83 0.58 0.48
1.36 0.99 0.70 0.57
1.59 1.16 0.82 0.67
0.50 1.00 2.00 3.00
NBS Concrete 0.10 0.07 0.05 0.04
0.20 0.15 0.11 0.09
0.41 0.30 0.21 0.17
0.61 0.45 0.32 0.26
0.82 0.60 0.42 0.34
1.02 0.75 0.53 0.43
1.23 0.90 0.63 0.51
1.43 1.05 0.74 0.60
0.50 1.00 2.00 3.00
Water (H2O) 0.05 0.04 0.02 0.02
0.10 0.07 0.05 0.04
0.19 0.14 0.10 0.08
0.29 0.21 0.15 0.12
0.39 0.28 0.20 0.16
0.48 0.35 0.25 0.20
0.58 0.42 0.30 0.24
0.68 0.49 0.35 0.28
0.50 1.00 2.00 3.00
Clay (CY) 0.08 0.05 0.02 0.02
0.15 0.11 0.05 0.05
0.30 0.22 0.10 0.09
0.45 0.33 0.14 0.14
0.60 0.44 0.19 0.18
0.75 0.55 0.24 0.23
0.90 0.66 0.29 0.28
1.05 0.77 0.34 0.32
0.50 1.00 2.00 3.00
Lime Stone (LS) 0.05 0.04 0.03 0.14
0.09 0.08 0.06 0.28
0.19 0.16 0.12 0.57
0.28 0.24 0.19 0.85
0.37 0.32 0.25 1.14
0.47 0.40 0.31 1.42
0.56 0.48 0.37 1.71
0.65 0.56 0.43 1.99
(a)
40 35 30
BUF
(b)
E=0.5 MeV
E=1.0 MeV
40
EBF (Z1=7.51)Water
EBF (Z1=7.51)Water
EBF(Z2=15.01)Clay
EBF(Z2=15.03)Clay
DLEBF (Z1
DLEBF (Z1
35 30
25
25
20
20
15
15
10
10
5
5
0
0
(c)
10
8
BUF
(d)
E=2.0 MeV
E=3.0 MeV
10
EBF (Z1=6.93)Water
EBF (Z1=6.94)Water
EBF(Z2=12.56)Clay
EBF(Z2=12.41)Clay
DLEBF (Z1
DLEBF (Z1
8
6
6
4
4
2
2
0
0 0
1
2
3
4
5
Optical Thickness (mfp)
6
7
8
0
1
2
3
4
5
6
7
8
Optical Thickness (mfp)
Fig. 4. Variation of buildup factors (EBF and DLEBF) for two layered shields made of Water and Clay with optical thickness at four energies; (a) 0.5 MeV, (b) 1.0 MeV, (c) 2.0 MeV and (d) 3.0 MeV.
34
K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
(a)
40 35 30
BUF
(b)
E=0.5 MeV
E=1.0 MeV
40
EBF (Z1=7.51)Water
EBF (Z1=7.51)Water
EBF(Z2=13.63)NBS Conc.
EBF(Z2=13.64)NBS Conc.
DLEBF (Z1
DLEBF (Z1
35 30
25
25
20
20
15
15
10
10
5
5
0
0
(c)
10
8
BUF
(d)
E=2.0 MeV
E=3.0 MeV
10
EBF (Z1=6.93)Water
EBF (Z1=6.94)Water
EBF(Z2=11.65)NBS Conc.
EBF(Z2=11.55)NBS Conc.
DLEBF (Z1
DLEBF (Z1
8
6
6
4
4
2
2
0
0 0
1
2
3
4
5
6
7
8
Optical Thickness (mfp)
0
1
2
3
4
5
6
7
8
Optical Thickness (mfp)
Fig. 5. Variation of buildup factors (EBF and DLEBF) for two layered shields made of Water and NBS Concrete with optical thickness at four energies; (a) 0.5 MeV, (b) 1.0 MeV, (c) 2.0 MeV and (d) 3.0 MeV.
⎛ B (X ) + 1 ⎞ ℓ(X2 ) = ⎜ 2 2 ⎟. [1 − exp ( − X2 )] ⎝ B1 (X2 ) + 1 ⎠
(11)
3. Computational work 3.1. BUF-toolkit-a computer program The BUF-toolkit is a computer program made in MS-Excel2007. It is capable to compute EBF values by using G.P. fitting formula (Harima et al., 1986) at desired energy and thickness for any material (compound or mixture) from its chemical composition. Thereby it computes (compare) the DLEBF values using Kalos (1956,1957), Burke and Beck (1974) and Lin and Jiang (1996) empirical formulae for the selected two materials (two layered slabs) at specified energy and optical thickness. The working of the toolkit is based on the database that consists of the available values of EBF and five G.P. fitting parameters for all the periodic table elements of arranged in
25 16 matrixes (25-energies in MeV and 16-optical thicknesses in mfp) obtained from ANS/ANSI 6.4.3. (1991) report. This matrix database is required for the execution of the BUFtoolkit. The BUF-toolkit computes the required values of EBF by G.P. fitting formula. Thereby, the toolkit compute values of DLEBF for chosen two layered slab using Lin and Jiang (1996) formula. 3.1.1. Errors and corrections Kim et al. (2013) suggested (using MCNPX 2.7.0) that existing data (ANSI/ANS-6.4.3-1991) cause about five percent (5%) overestimation in buildup factors computations. The errors caused by overestimations of EBF values by G.P. fitting method have been compensated in the BUF-toolkit. 3.2. Validation of BUF-toolkit for DLEBF computation Fig. 1 indicates that computed values of EBF using BUF-toolkit for water (H2O) and iron (Fe) at selected energies and thicknesses
K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
35
Fig. 6. Variation of buildup factors (EBF and DLEBF) for two layered shields made of Aluminium and Lime Stone with optical thickness at four energies; (a) 0.5 MeV, (b) 1.0 MeV, (c) 2.0 MeV and (d) 3.0 MeV.
agreed very well with the corresponding standard values (ANSI 6.4.3, 1991). Thus the toolkit can reproduce accurate values of EBF for chosen samples in required range of energy and thickness. Table 1 show that for Fe -H2O slabs (high-Z material followed by low-Z material) the minimum percentage deviations of the DLEBF values from Monte Carlo calculations were found for Lin and Jiang formula. Similarly, Table 2 for H2O-Fe slabs (low-Z material followed by high-Z material) the minimum percentage deviations of the DLEBF values from Monte Carlo calculations were found for Lin and Jiang formula. Thereby, Lin and Jiang (1996) formula has been validated as the most accurate formula for DLEBF computation (using EBF values computed by G.P. fitting formula) for two-layered slabs for both orientations (viz. low-Z followed by high-Z material and high-Z followed by low-Z material). Table 3 validates the BUF-toolkit as the computed values of DLEBF by BUF-toolkit and Monte Carlo calculations agreed very well. Fig. 2 indicates that the uncertainties in DLEBF values for various empirical formulae (Kalos, Burke and Beck and Lin and Jiang) at 0.5 MeV and thickness up to 8 mfp, for water–iron slabs in two orientations viz. iron–water and water–iron. For computation of DLEBF, the required values of EBF for iron and water
were obtained from Monte Carlo calculations using EGS4-code (Hirayama and Shin, 1998) and computed by G.P. fitting method. Thereby, confirming that at chosen energy and thickness range the Lin and Jiang (1996) formula can reproduce DLEBF values most accurately. 3.3. Computation of mass attenuation coefficients The total and partial mass attenuation coefficients of the selected samples were computed by using WinXCom Gerward et al. (2004). Fig. 3 shows combined variations in computed total and partial mass attenuation coefficients values with energy for chosen samples. It is confirmed that the Compton scattering is dominating in the chosen energy range below 1.02 MeV. 3.4. Computation of equivalent atomic number (Zeq) The equivalent atomic number of a composite material is analogous to the atomic numbers of an element, which describes the properties of the composite material (compounds/mixture) in terms of equivalent element. The Zeq is computed from the contribution of
36
K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
25
(a)
(b)
E=0.5 MeV
20
25
E=1.0 MeV
EBF (Z 1=13.00)Aluminium
EBF (Z 1=13.00)Aluminium
EBF(Z2=15.01)Clay
EBF(Z2=15.03)Clay
DLEBF (Z1
DLEBF (Z1
20
15
10
10
5
5
BUF
15
0
0
(c)
10
8
BUF
(d)
E=2.0 MeV
E=3.0 MeV
10
EBF (Z 1=13.00)Aluminium
EBF (Z 1=13.00)Aluminium
EBF(Z2=12.56)Clay
EBF(Z2=12.41)Clay
DLEBF (Z1
DLEBF (Z1
8
6
6
4
4
2
2
0
0 0
1
2
3
4
5
6
7
Optical Thickness (mfp)
8
0
1
2
3
4
5
6
7
8
Optical Thickness (mfp)
Fig. 7. Variation of buildup factors (EBF and DLEBF) for two layered shields made of Aluminium and Clay with optical thickness at four energies; (a) 0.5 MeV, (b) 1.0 MeV, (c) 2.0 MeV and (d) 3.0 MeV.
Compton scattering only. The detailed procedure of equivalent atomic number (Zeq) computation has been discussed in our previous publications (Mann et al., 2012; Mann and Sidhu, 2012; Mann and Korkut, 2013). Table 4 enlisted the density and Zeq of the selected samples and source reference of each sample. For selected samples the variation in values of Zeq with energy of is indicated in the table. 3.5. Geometric thickness Geometric thickness (x, cm) correspond to optical thickness (mx, mfp) is the physical thickness of the sample calculated from its linear attenuation coefficient (m, cm 1) at selected energy. Geometric thicknesses of chosen samples at selected energies have been listed in Table 5.
4. Results and discussion Occasionally, at any fixed energy in the selected energy range the EBF values for low-Z materials are comparatively
higher than for high-Z material. The probability of the scattered photons (DLEBF) will reduce by using the arrangement of materials such that low-Z followed by high-Z in gamma radiation leakage protective slabs. This can be explained as follows, for a fixed energy below 1.02 MeV, the probability of Photo electric absorption is proportional to Z eq 5 and goes on increasing more rapidly than Compton scattering because the Compton cross section is proportional to Z eq . For energy above 1.02 MeV the probability of Pair production absorption is proportional to Z eq 2 starts contributing to the total absorption process. At the same time the relative contribution of Compton scattering to the total absorption goes on decreasing with increase in Z eq . The variations of computed DLEBF values at four energies, for five combinations of the chosen materials (H 2 O-CY, H 2 O-NBS Concrete, Al-LS, Al-CY and Al-NBS Concrete), in both orientations with optical thickness have been revealed in Figs. 4–8. From Figs. 4 to 6 it is observed that for high energies of the selected range of energy and optical thickness the DLEBF values for both orientations of materials are less than their
K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
37
Fig. 8. Variation of buildup factors (EBF and DLEBF) for two layered shields made of Aluminium and NBS Concrete with optical thickness at four energies; (a) 0.5 MeV, (b) 1.0 MeV, (c) 2.0 MeV and (d) 3.0 MeV.
individual EBF values (DLEBF o EBF). This type of behavior of two layered shields seems to be due to the fact that the probability of absorption of gamma-ray photons increases due to its interaction of with two layered shield of materials with different Z eq . For low-Z eq materials the Compton scattering probabilities are higher than for high-Z eq composite materials. The probabilities of photoelectric and pair-production absorptions are dominant in high-Z eq materials. For the orientation low-Z followed by high-Z, when incident gamma-ray photon of the selected energy range interacts with low-Z eq composite material it causes multiple scattering and when these scattered photons interact with high-Z eq composite material get absorbed (photoelectric or pair-production) by it, thereby reduce the DLEBF (flux of outgoing photons). Figs. 7d and 8d show a reverse trend (DLEBF 4 EBF) at 3 MeV for sample-materials with comparable Z eq such as; AlNBS Concrete and Al-CY. This seems to be due to the dominance of Compton scattering probabilities in both materials, thereby increase the outgoing flux of photons or DLEBF values. From Figs. 4–8, it is concluded that EBF values for any material depends on its equivalent atomic number. Moreover, at fixed
energy the EBF values of two materials approach each other if the difference in their equivalent atomic numbers is small and vice-versa. On the other side, the DLEBF values in both orientations remains different and no appreciable variation in DLEBF have been observed with minor change in their equivalent atomic numbers. Comparison of Figs. 9 and 10 indicates that DLEBF values are comparatively low for all chosen ten combinations low-Z followed by high-Z than their reverse combinations. It has also been observed that the same values of DLEBF for three combinations viz. LS-NBS conc., LS-CY and LS-Al in case of high-Z followed by low-Z case. Thus all these three combinations seem to provide the similar shielding behavior for gamma-rays in the energy range 0.5–3.0 MeV. Fig. 9 clearly indicated that the lowest values of DLEBF for Al-LS (low-Z followed by high-Z) combination in the chosen energy and optical thickness range. Moreover for any combination of chosen materials the DLEBF values goes on decreasing with increase in the energy of incident gamma-ray photons. Thus double layered shield with optical thickness up to 8 mfp such that Al followed by LS appears to be the best
38
K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
Low-Z followed by high-Z
E=0.5 MeV 20
NBS conc.-LS Water-Al NBS Conc.-CY CY-LS Water-LS Water-CY Water-NBS Conc. Al-LS Al-CY Al-NBS Conc.
DLEBF
15
10
Low-Z followed by high-Z
E=1.0 MeV
20
NBS conc.-LS Water-Al NBS Conc.-CY CY-LS Water-LS Water-CY Water-NBS Conc. Al-LS Al-CY Al-NBS Conc.
15
10
5
5
0
0 Low-Z followed by high-Z
E=2.0 MeV 8
DLEBF
E=3.0 MeV
NBS conc.-LS Water-Al NBS Conc.-CY CY-LS Water-LS Water-CY Water-NBS Conc. Al-LS Al-CY Al-NBS Conc.
6
4
Low-Z followed by high-Z 8
NBS conc.-LS Water-Al NBS Conc.-CY CY-LS Water-LS Water-CY Water-NBS Conc. Al-LS Al-CY Al-NBS Conc.
6
4
2
2
1
2
3
4
5
6
7
8
Optical Thickness (mfp)
1
2
3
4
5
6
7
8
Optical Thickness (mfp)
Fig. 9. Variations of DLEBF for different combinations of chosen samples such that low-Z followed by high-Z material.
protective shields for gamma-rays in energy range 0.5– 3.0 MeV.
5. Conclusions It is concluded that at fixed energy, with the use of two layered shield in orientation such that low-Z followed by high-Z always reduce the value of build up factor from the individual single material of same optical thickness. Thus, in gamma-ray protection double-layered shields are more effective than a single layer shields. To account for the scattered gamma-ray photons of point isotropic source, Lin and Jiang (1996) formula has the advantage over other empirical formulae. Simultaneously, the G.P. fitting point kernel calculations accurately reproduce the EBF values for low-Z materials. Thus in medium energy range (0.5–3 MeV), for two-layered slabs of optical thickness up to 8 mfp, the Lin and Jiang formula along with G.P. fitting formula can be used to compute the double layered transmission exposure buildup factors (DLEBF) values.
It is confirmed that DLEBF values at selected energy for two layered slabs with an orientation (high-Z material followed by low-Z material) were higher than the opposite orientation. Concurrently, the difference in DLEBF values for both orientations were go on increasing with increase in the optical thickness. For the optical thickness up to 8 mfp and energy range (0.5–3.0 MeV), the Al–LS (Aluminum–Lime Stone) combination, appears to provide the best protection against the gamma-rays. The expansion of the present investigation to higher energies is planned to be conducted in the near future. The aim of this series of investigations is to devise computational tools for gamma-ray protective designs of the nuclear establishments. Above results and discussion will be useful in the construction of effectual protection against hazardous gamma-rays.
Acknowledgments We are grateful to SAIF, Punjab University, Chandigarh for providing WD-XRF-facility. We are thankful to Punjab technical
K.S. Mann et al. / Radiation Physics and Chemistry 125 (2016) 27–40
35
High-Z followed by low-Z
E=0.5 MeV
DLEBF
25 20 15 10
High-Z followed by low-Z
E=1.0 MeV
LS-NBS conc. Al-Water CY-NBS Conc. LS-CY LS-Water CY-Water NBS Conc.-Water LS-Al CY-Al NBS Conc.-Al
30
39
LS-NBS conc. Al-Water CY-NBS Conc. LS-CY LS-Water CY-Water NBS Conc.-Water LS-Al CY-Al NBS Conc.-Al
30 25 20 15 10
5
5
0 10
0 High-Z followed by low-Z
E=2.0 MeV
6
High-Z followed by low-Z
E=3.0 MeV
LS-NBS conc. Al-Water CY-NBS Conc. LS-CY LS-Water CY-Water NBS Conc.-Water LS-Al CY-Al NBS Conc.-Al
8
DLEBF
35
LS-NBS conc. Al-Water CY-NBS Conc. LS-CY LS-Water CY-Water NBS Conc.-Water LS-Al CY-Al NBS Conc.-Al
10
8
6
4
4
2
2 1
2
3
4
5
6
7
8
Optical Thickness (mfp)
1
2
3
4
5
6
7
8
Optical Thickness (mfp)
Fig. 10. Variations of DLEBF for different combinations of chosen samples such that high-Z followed by low-Z material.
University (PTU), Kapurthala for providing necessary research related literature and infrastructure. The present work is devoted to the Ph.D.-thesis under Reg. number:1311025, Punjab Technical University, Kapurthala.
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.radphyschem. 2016.03.001.
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