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Photon energy absorption coefficients for nuclear track detectors using Geant4 Monte Carlo simulation
Radiation Physics and Chemistry 106 (2015) 83–87
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Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
Photon energy absorption coefficients for nuclear track detectors using Geant4 Monte Carlo simulation Vishwanath P. Singh a,b,n, M.E. Medhat c,d, N.M. Badiger a a
Department of Physics, Karnatak University, Dharwad 580003, India Health Physics Section, Kaiga Atomic Power Station-3&4, NPCIL, Karwar 581400, India c Experimental Nuclear Physics Department, Nuclear Research Centre, P.O. 13759, Cairo, Egypt d Institute of High Energy Physics, CAS, Beijing 100049, China b
H I G H L I G H T S
Geant4 code is used to calculate mass energy-absorption coefficients for elements, air and compounds. Mass energy-absorption coefficients for detectors are computed using Geant4 code. A very good agreement for simulated results and literature values is observed.
art ic l e i nf o
a b s t r a c t
Article history: Received 4 May 2014 Accepted 7 July 2014 Available online 15 July 2014
Geant4 Monte Carlo code simulations were used to solve experimental and theoretical complications for calculation of mass energy-absorption coefficients of elements, air, and compounds. The mass energyabsorption coefficients for nuclear track detectors were computed first time using Geant4 Monte Carlo code for energy 1 keV–20 MeV. Very good agreements for simulated results of mass energy-absorption coefficients for carbon, nitrogen, silicon, sodium iodide and nuclear track detectors were observed on comparison with the values reported in the literatures. Kerma relative to air for energy 1 keV–20 MeV and energy absorption buildup factors for energy 50 keV–10 MeV up to 10 mfp penetration depths of the selected nuclear track detectors were also calculated to evaluate the absorption of the gamma photons. Geant4 simulation can be utilized for estimation of mass energy-absorption coefficients in elements and composite materials. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Geant4 Mass energy-absorption coefficients Kerma Nuclear track detectors Buildup factor
1. Introduction The most important quantity characterizing the radiation interacting in extended media is the absorbed dose which represents the energy transferred to the matter. The dose quantity is one of the important parameter for radiation protection, dose measurement, radiation effect and defects in the material. The dose delivered to a medium is measured in terms of mass energyabsorption coefficient, men/ρ, which is a an essential quantity used in medical physics, radiation physics, health physics, radiation biology, radiotherapy, irradiation technology, and other practical applications. It is not possible to calculate men/ρ directly, but it is necessary to use mass energy-transfer coefficient, mtr/ρ. The amount of photon energy transferred is dependent upon interaction process namely the photoelectric effect, compton scattering
n
Corresponding author. Tel.: þ 91 8382 264225; fax: þ 91 8382 264025. E-mail address: [email protected] (V.P. Singh).
http://dx.doi.org/10.1016/j.radphyschem.2014.07.001 0969-806X/& 2014 Elsevier Ltd. All rights reserved.
and pair production. These interaction processes are dependent upon atomic numbers of the elements of compound/mixture and photon energy. Mass energy-absorption coefficient (indirectly mass energytransfer coefficeint) is a measure of average fraction of photon energy transferred to kinetic energy of the charged particle when photon interacts with a material. Photoelectric absorption, incoherent scattering and pair/triplet production exhibit these characterisitics, whereas coherent scattering transfers negligible photon energy. These events are playing a crucial role in the calculation of energy-absorption coefficients (Hubbell, 1969, 1977). The intreraction of gamma photon with the matter is a complex process where different types of events are occuring in the medium. It is found that there are various factors (average fraction of kinetic energy of secondary photon, incident photon energy, additive law for mixture, etc.) affecting the calculation of the energy absorption. Various researchers have calculated and measured the mass energy-absorption coefficietnts. The mass energy-absorption
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coefficients of the biological samples are parameterized in the photon energy range 200–1500 keV (Manjunathguru and Umesh, 2009). Rosemary (1961) has tabulated and discussed gamma photon energy absorption and transfer theoretically. Hubbell and Berger (1968) have calculated absorption coefficients for air, water and 18 elements over the photon energy range of 10 keV r E r 10 MeV. Hubbell (1977) calculated the mass energy-absorption coefficients for H, C, N, O, Ar and seven mixtures for energies from 0.1 keV to 20 MeV. Hubbell (1982) again has calculated energy-absorption coefficients theoretically for 40 elements ranging from hydrogen (Z ¼1) to uranium (Z ¼ 92) and for 45 mixtures and compounds of dosimetric interest from 1 keV to 20 MeV. Hubbell (1982) has used the fraction-by-weight of the constituents of the compounds. Higgins et al. (1992) have calculated the the mass energyabsorption coefficients theoretically for 47 media from 1 keV to 100 MeV. Gurler et al. (2000) have calculated the absorption coefficients for aluminum and water. Ban et al. (1993) have obtained mass energy-absorption coefficients for nitrogen and argon experimentally at 30 keV gamma ray. Bhandal et al. (1994) have estimated the mass energy-absorption coefficients of fatty acids for gamma rays using 662 and 1115 keV energies. Bradley et al. (1989) have determined the mass energyabsorption coefficients for paraffin experimentally. Singh et al. (1996) have mesaured the mass energy-absorption coefficients for 10 compounds experimentally for 662 keV gamma ray. Shakhreet et al. (2003) measured the mass energy-absorption coefficients of paraffin wax and gypsum at 662 keV experimentally. Oz et al. (2006) have calculated the mass energyabsorption coefficients for silicon, carbon, copper and sodium iodide theoretically. Gurler et al. (2000) have calculated mass energy-absorption coeifficients for nitrogen and mass energytransfer coefficeints for silicon, carbon copper, nirogen and sodium iodide in photon energy of 0.4–10 MeV, and showed very good agreement with earlier literature values. Other attempt is made for calculation of mass energy-absorption coeifficients of optical fiber and thermoluminiscent dosimeter in photon energy of 0.2–20 MeV using Monte Carlo N-particle code version 5 (Hossain and Wagiran, 2012). The theoretical method for calculation of the mass energyabsoprtion coefficeint is a complicated process. The experimetal values of the mass energy-absoprtion coefficeints are found for some compounds for very limited energies. After review of the literature, it has been found that this area requires investigation for finding easy ways of estimation of the mass energyabsoprtion coefficeints. This encouraged us to utilize Geant4 Monte Carlo simulation method for calculation of the mass energy-absoprtion coefficeints. Therefore, this present work aims to calculate the mass energy-absoprtion coefficeints of elements (carbon, nitrogen, silicon), air, sodium iodide, and some nuclear track detectors. The Geant4 simulation results of elements and sodium iodide were found to be in very good agreement with earlier literature data. First of all the Geant4 code simulated results of mass energy-absorption coefficients of elements, air and sodium iodide were validated with available literature data for photon energy 0.4–10 MeV, and then Geant4 was utilized for simulation for photon energy 1 keV –20 MeV. Geant4 simulation was utilized for calculation of mass energyabsoprtion coefficeints for some nuclear track detectors. The air kerma and energy absorption buildup factors were also analyzed for the nuclear track detectors. Geant4 Monte carlo simulation was used for first time for calculation of the mass energy-absoprtion coefficeints. At present Geant4 Monte carlo simulation has been used for mass attenuation coefficients of composite materials and standarized the experimental set-up (Medhat and Wang, 2013; Singh et al., 2014a, 2014b;).
2. Theoretical background and computational method A few elements (nitrogen, carbon and silicon), air, sodium iodide and some soild state and plastic nuclear track detectors; quartz (SiO2), sodalime glass (73SiO2:14Na2O:9CaO:4MgO:0.15Al2O3: 0.03K2O:0.02TiO2:0.1Fe2O3), PC (C16H14O3: Makrofol, Lexan, Millar), PET (C10H8O4), CN (C6H8O9N2:Daicell, LR-115) and CR-39 (C12H18O7) have been considered for investigation of gamma photon energy absorption by mass energy-absorption coefficients and energy absorption buildup factors. The effective atomic numbers and electron densities of these nuclear track detectors are found in the literature (Medhat, 2011). 2.1. Mass energy-absorption coefficient The mass energy-absorption coefficient, men/ρ, is a measure of the average fractional amount of incident photon energy transferred to kinetic energy of charged particles as a result of gammaray interaction. This imparted charged particle kinetic energy is valid approximation for the amount of energy made available for the production of chemical, biological and other effects associated with exposure due to ionizing radiation (ICRU-33). The men/ρ is the product of mass energy-transfer coefficient, mtr/ρ (cm2/g) and (1 g), where g is the fraction of the energy of the secondary charged particle that is lost to bremsstrahlung in the material. The mass energy-absorption coefficient of a compound or composite is calculated using mixture rule (ðμen =ρÞcomposite ¼ ∑ni wi ðμen =ρÞi ) where wi is the proportion by weight and (men/ρ)i is the mass energy-absorption coefficient of the ith elements. The mass energy-absorption coefficients of elements are avaialable using differernt methods. 2.2. Geant4 simulation code Monte Carlo simulation is found to be an effective tool to calculate radiation interaction parameters in different types of compounds/mixtures for shielding, energy deposition and dosimetry. Geant4 code is based on object-oriented programming and allows user to derive classes to describe the detector geometry, primary particle generator and physics processes models along electromagnetic, hadronic, and decay physics based on theory, materials and elements, experimental data or parameterizations. Most of the physics processes models include multiple scattering, ionization, Bremsstrahlung, positron annihilation, photo-electric effect, Compton and Rayleigh scattering, pair production, synchrotron and transition radiation, Cherenkov effect, refraction, reflection, absorption, scintillation, fluorescence, and Auger electrons emission (Agostinelli et al., 2003; CERN, 2007). The Geant4 simulation toolkit covers a wide energy range starting from 250 eV to TeV. The Geant4 simulation is the modeling of the photon interaction through materials in computer environment which gives flexibility and ease of use, instead of performing an experimental determination of mass energy-attenuation coefficient of different composite materials. Mass energy-attenuation of photons is calculated by simulating all relevant physical processes and interactions before and after inserting the materials under investigation (Medhat and Wang, 2013). 2.3. Kerma The kinetic energy per unit mass (Kerma) relative to air, K a , of the detectors is derived by the following equation: Ka ¼
K Dosimeter ðμen =ρÞDosimeter ¼ K Air ðμen =ρÞAir
ð1Þ
V.P. Singh et al. / Radiation Physics and Chemistry 106 (2015) 83–87
BðE; xÞ ¼ f1 þ ðb 1Þx for K ¼ 1
ð3Þ
tanhðx=X K 2Þ tanhð 2Þ ; 1 tanhð 2Þ for penetration depth ðXÞ r 40 mfp
KðE; xÞ ¼ cxa þd
ð4Þ
The mass energy-absorption coefficients computed using Geant4 simulation for carbon, nitrogen and silicon elements, and sodium iodide are given in Table 1(a) and (b). The variation of mass energy-absorption coefficients of the nuclear track detectors with photon energy is shown in Figs. 1 and 2 using Geant4
4
10
Geant4
Quartz Sodalime PC PET CN CR-39 Air
2
2.3.1. Energy absorption buildup factor The energy absorption buildup factor (EABF) values of the selected nuclear track detectors are possible to compute using the Geometrical Progression (G-P) fitting method. The detailed description for computation of EABF can be found in the recent literatures (Singh and Badiger, 2013, 2014; Singh et al., 2014a, 2014b). The buildup factors are estimated by using G-P fitting parameters (b, c, a, Xk and d) in the photon energy range 0.015–15 MeV up to 40 mfp using the equations (Harima et al. 1986, Harima, 1993) given below: ðb 1ÞðK x 1Þ BðE; xÞ ¼ 1 þ for K a 1 ð2Þ K 1
3. Results and discussion
Mass energy absorption coefficient (cm /g)
The mass energy-absorption coefficient, men/ρ, of the nuclear track detectors and air is computed using the mixture rule explained above. The values of μen/ρ of elements are taken from literature (Hubbell and Seltzer, 1995).
85
3
10
2
10
1
10
0
10
-1
10
-2
10
where x is the distance from source (mfp) and b, the value of the buildup factor at 1 mfp and K(E,x) is the dose multiplicative factor. The variation of K (E,x) with penetration represents the change in the shape of the spectrum from that at 1 mfp which determines the value of b.
-3
-2
10
10
-1
10
0
1
10
10
E (MeV) Fig. 1. Mass energy-absorption coefficient for nuclear track detectors and air using Geant4 simulation code.
Table 1 (a) Comparison of mass energy-absorption coefficients (cm2/g) of carbon, nitrogen for 0.4–10 MeV photon energy. E (MeV)
0.4 0.5 0.6 0.8 1 1.5 2 3 4 5 6 8 10
Carbon
Nitrogen
Geant4 Oz et al. (2006)
Hubbell (1982)
Higgins Hubbell and et al. (1992) Seltzer (1995)
Geant4 Guler et al., Rosemary (2009) (1961)
Hubbell and Berger (1968)
Hubbell (1982)
Higgins Hubbell and et al. (1992) Seltzer (1995)
0.026 0.027 0.028 0.027 0.026 0.024 0.022 0.019 0.017 0.016 0.015 0.014 0.013
0.0295 0.0297 0.0296 0.0288 0.0279 0.0255 0.0234 0.0204 0.0185 0.0171 0.0160 0.0147 0.0138
0.0295 0.0297 0.0295 0.0289 0.0279 0.0255 0.0234 0.0205 0.0185 0.0171 0.0160 0.0147 0.0138
0.028 0.028 0.027 0.027 0.026 0.024 0.022 0.018 0.017 0.016 0.015 0.016 0.013
– 0.0296 0.0295 0.0289 0.0279 0.0255 0.0234 0.0205 0.0186 0.0173 0.0163 0.0151 0.0143
0.0295 0.0297 0.0296 0.0289 0.0279 0.0255 0.0235 0.0205 0.0186 0.0173 0.0164 0.0151 0.0143
0.0295 0.0297 0.0296 0.0289 0.0279 0.0255 0.0235 0.0205 0.0186 0.0173 0.0164 0.0151 0.0143
0.0294 0.0296 0.0295 0.0288 0.0279 0.0254 0.0234 0.0204 0.0183 0.0169 0.0158 0.0143 0.0134
0.0295 0.0297 0.0296 0.0289 0.0279 0.0255 0.0235 0.0205 0.0185 0.0171 0.0161 0.0147 0.0138
0.0294 0.0296 0.0295 0.0288 0.0279 0.0255 0.0235 0.0208 0.0189 0.0176 0.0166 0.0152 0.0143
0.0295 0.0299 0.0296 0.0288 0.0279 0.0255 0.0235 0.0205 0.0185 0.0172 0.0162 0.0149 0.0141
(b) Comparison of mass energy absorption coefficients (cm2/g) of silicon and sodium iodide for 0.4–10 MeV photon energy E (MeV) Silicon Sodium iodide
0.4 0.5 0.6 0.8 1 1.5 2 3 4 5 6 8 10
Geant4 Oz et al. (2006)
Hubbell (1982)
Higgins Hubbell and et al. (1992) Seltzer (1995)
Geant4 Oz et al. (2006)
Hubbell (1982)
Hubbell and Seltzer (1995)
0.028 0.030 0.031 0.029 0.028 0.026 0.024 0.022 0.020 0.019 0.017 0.016 0.015
0.0297 0.0297 0.0295 0.0287 0.0278 0.0253 0.0234 0.0210 0.0196 0.0187 0.0182 0.0177 0.0175
0.0297 0.0297 0.0295 0.0288 0.0278 0.0253 0.0234 0.0210 0.0196 0.0188 0.0182 0.0177 0.0175
0.049 0.038 0.035 0.026 0.026 0.024 0.025 0.021 0.021 0.021 0.022 0.023 0.024
0.0529 0.0410 0.0351 0.0295 0.0266 0.0227 0.0211 0.0204 0.0208 0.0215 0.0223 0.0238 0.0250
0.0522 0.0405 0.0348 0.0293 0.0265 0.0242 0.0227 0.0212 0.0205 0.0210 0.0217 0.0225 0.0241
0.0297 0.0297 0.0296 0.0288 0.0278 0.0254 0.0235 0.0211 0.0197 0.0190 0.0185 0.0180 0.0178
0.0297 0.0297 0.0295 0.0288 0.0278 0.0254 0.0235 0.0210 0.0196 0.0188 0.0183 0.0177 0.0175
0.0557 0.0429 0.0361 0.0300 0.0269 0.0229 0.0212 0.0206 0.0211 0.0220 0.0229 0.0246 0.0261
0.0295 0.0297 0.0296 0.0289 0.0279 0.0255 0.0235 0.0206 0.0187 0.0173 0.0164 0.0151 0.0143
V.P. Singh et al. / Radiation Physics and Chemistry 106 (2015) 83–87
Hubbell and Seltzer, 1995
4
10
Quartz Sodalime PC PET CN CR-39 Air
2
Mass energy absorption coefficient (cm /g)
86
3
10
2
10
1
10
0
10
-1
10
-2
10
-3
10
-2
10
-1
10
0
10
1
10
Table 2 Energy absorption buildup factors for nuclear track detectors. E (MeV)
6
Quartz Sodalime PC PET CN CR-39
Geant4
5
KERMA
4
3
Energy absorption buildup factor for 0.5 mfp
Quartz 0.05 0.10 1.00 10.00
1.73 2.53 1.51 1.17
Soda lime 1.57 2.51 1.44 1.16
PC
PET 2.78 2.28 1.49 1.20
CN
CR-39
2.72 2.35 1.49 1.20
2.62 2.42 1.50 1.19
2.71 2.41 1.49 1.20
for 1 mfp 5.10 4.56 2.10 1.37
0.05 0.10 1.00 10.00
(b) Energy absorption buildup factor 2.30 1.99 5.37 4.31 4.15 4.42 2.11 1.96 2.09 1.33 1.32 1.38
4.69 4.65 2.11 1.37
5.04 4.70 2.10 1.38
0.05 0.10 1.00 10.00
(c) Energy absorption buildup factor for 5 mfp 5.30 3.90 60.93 49.27 35.81 26.00 20.86 74.40 70.41 64.12 9.67 8.36 10.05 10.02 9.98 2.46 2.45 2.60 2.59 2.57
46.41 71.34 10.02 2.59
0.05 0.10 1.00 10.00
(d) Energy absorption buildup factor for 10 mfp 8.13 5.48 273.28 193.87 117.22 72.33 51.05 487.40 423.36 342.83 24.89 21.15 26.61 26.44 26.22 3.84 3.83 3.92 3.91 3.90
174.41 418.92 26.40 3.92
E (MeV) Fig. 2. Mass energy-absorption coefficient for nuclear track detectors and air using the theoretical data by Hubbell and Seltzer (1995).
(a)
calculation by Hubbell and Seltzer (1995). The μen/ρ values of medical, biological, tissue substitutes and composite materials can also be simulated using the present standard Geant4 code. The Geant4 code produces μen/ρ values of the elements, mixtures and compounds in very good agreement with earlier reported data by solving experimental and theoretical complications. 3.2. Kerma
2
1
-3
10
-2
10
-1
10
0
10
1
10
E (MeV) Fig. 3. Kerma relative to air for nuclear track detectors using Geant4 simulation code.
simulation code and Hubbell and Seltzer (1995). The kerma relative to air using Geant4 is shown graphically in Fig. 3 and the energy absorption buildup factors are given in Table 2. 3.1. Mass energy-absorption coefficients The mass energy-absorption coefficients, μen/ρ, of carbon, nitrogen, silicon and sodium iodide using Geant4 simulation are given in Table 1(a, b) for photon energy of 0.4–10 MeV. The μen/ρ values of these elements and sodium iodide by different investigators (Rosemary, 1961; Hubbell and Berger, 1968; Hubbell, 1982; Higgins et al., 1992; Oz et al., 2006; Hubbell and Seltzer, 1995; Gurler et al., 2009) are given in Table 1(a, b). It was found that the Geant4 simulation results for the selected elements (carbon, nitrogen and silicon) and sodium iodide are in very good agreement with the earlier reported data in the literatures. The variation of μen/ρ values of the nuclear track detectors and air is shown in Figs. 1 and 2 using Geant4 simulation and theoretical (Hubbell and Seltzer, 1995) respectively. Figs. 1 and 2 show that the Geant4 simulation provides the results similar to the theoretical
Using Geant4 code simulation for μen/ρ results, the variation of Kerma of the nuclear track detectors relative to air with photon energy (1 keV–20 MeV) is shown in Fig. 3. In general the Kerma values of all the nuclear track detectors are in range of unity above 100 keV photon energy (i.e. beyond photoelectric effect). However, there is a variation in Kerma for composites containing slightly high-Z elements (quartz and soda lime). The reason for such variation in kerma is due to large photon energy transfer for high-Z elements as the photoelectric cross section is proportional to Z4–5. Similar behaviors are observed for alcohols and tissue substitutes (Singh and Badiger, 2013; Singh et al., 2014). It is easy to calculate the kerma relative to air using theoretical μen/ρ by Hubbell and Seltzer (1995) similar to Geant4 results. 3.3. Energy absorption buildup factors The energy absorption buildup factors of the nuclear track detectors for the selected photon energy (0.05, 0.1, 1 and 10 MeV) for penetration depths 0.5, 1, 5 and 10 mfps are given in Table 2. The energy absorption buildup factors of the nuclear track detectors are small for low-penetration depth whereas it is found bigger for large-penetration depths.
4. Conclusions In the present paper the mass energy-absorption coefficients of carbon, nitrogen, silicon, air, sodium iodide, and some nuclear track detectors were calculated using Geant4 simulation code. There was a very good agreement between Geant4 simulation code with the data tables published earlier (Rosemary, 1961; Hubbell and Berger, 1968; Hubbell, 1982; Higgins et al., 1992;
V.P. Singh et al. / Radiation Physics and Chemistry 106 (2015) 83–87
Oz et al., 2006; Hubbell and Seltzer, 1995; Gurler et al., 2009). The present simulation code should be considered as a standard for calculation of mass energy-absorption coefficients for any elements and composite/compound materials. References Agostinelli, S., et al., 2003. G4—a simulation toolkit. Nucl. Instrum. Methods Phys. Res. A 506, 250–303. Ban, S., Hirayama, H., Namito, Y., Tanaka, S., Nakashima, H., Nakane, Y., Yoshizawa, M., Nariyama, N., 1993. Measurement of the photon energy-absorption coefficient for air, nitrogen and argon at 30 keV. Appl. Radiat. Isot. 44, 769–772. Bhandal, G.S., Singh, K., Rani, R., Kumar, V., 1994. Energy absorption coefficients for 662 and 1115 keV gamma rays in some fatty acids. Appl. Radiat. Isot. 45, 379–381. Bradley, D.A., Chong, C.S., Shukri, A., Tajuddin, A.A., Ghose, A.M., 1989. A new method for the direct measurement of the energy absorption coefficient of gamma rays. Nucl. Instrum. Methods Phys. Sect. A 280, 392–394. CERN, 2007. Geant4 Collaboration Physics Reference Manual. 〈http://geant4.cern. ch/support/userdocuments.shtml〉. Gurler, O., Oz, H., Yalcin, S., 2000. Calculation of mass energy absorption coefficients and mass radiation absorption coefficients for aluminum and water mediums. Bulg. J. Phys. Suppl. 27, 25–28. Gurler, O., Oz, H., Yalcin, S., Gundogdu, O., 2009. Mass absorption and mass energy transfer coefficients for 0.4–10 MeV gamma rays in elemental solids and gases. Appl. Radia. Isot. 67, 201–205. Harima, Y., 1993. An Historical review and current status of buildup factor calculations and application. Radiat. Phys. Chem. 41 (4/5), 631–672. Harima, Y., Sakamoto, Y., Tanka, S., Kawai, M., 1986. Validity of geometric progression formula in approximating gamma ray buildup factor. Nucl. Sci. Eng. 94, 24–35. Higgins, P.D., Attix, F.H., Hubbell, J.H., Seltzer, S.M., Berger, M.J., Sibata, C.H., 1992. Mass energy-transfer and mass energy-absorption coefficients, including inflight positron annihilation for photon energies of 1 keV–100 MeV. NISTIR 4812, 1–66. Hossain, I., Wagiran, A.H., 2012. Mass energy absorption coefficients for 0.2–20 MeV Photon in Ge-doped optical fiber and TLD-100 by Monte Carlo n-particle code version 5 (MCNP5). Optoelectron. Adv. Mater.—Rapid Commun. 6 (1–2), 162–164. Hubbell, J.H., 1969. Photon cross sections. Attenuation coefficients and energy absorption coefficients from 10 keV to 100 GeV. NSRDS-NBS 29. Hubbell, J.H., 1977. Photon mass attenuation and mass energy-absorption coefficients for H, C, N, O, Ar, and seven mixtures from 0.1 keV to 20 MeV. Radiat. Res. 70, 58–81. Hubbell, J.H., 1982. Photon mass attenuation and energy-absorption coefficients from 1 keV to 20 MeV. Int. J. Appl. Radiat. Isot. 33, 1269–1290.
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Hubbell, J.H., Berger, M.J., 1968. Shielding fundamentals and methods. In: Jaeger, R. G., Blizard, E.P., Chilton, A.B. (Eds.), Engineering Compendium on Radiation Shielding, 1. Springer, Berlin, p. 199. Hubbell J.H., Seltzer S.M., 1995. Tables of X-ray mass attenuation coefficients and mass energy absorption coefficients from 1 keV to 20 MeV for elements Z¼1 to 92 and 48 additional substances of dosimetric interest. Avaialble at: 〈http:// www.nist.gov/pml/data/xraycoef/index.cfm〉. International Commission on Radiation Units and Measurements, Report 33. 7910 Woodmont Avenue Washington, DC, 20014, USA. Manjunathguru, V., Umesh, T.K., 2009. Simple parametrization of photon mass energy absorption coefficients of H-, C-, N- and O-based samples of biological interest in the energy range 200–1500 keV. PRANAMA 72 (2), 375–387. 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. Medhat, M.E., Wang, Y., 2013. GEANT4 code for simulation attenuation of gamma rays through scintillation detectors. Ann. Nucl. Energy 62, 316–320. Oz, H., Gurler, O., Gultekin, A., Yalcin, S., Gundogdu, O., 2006. Photon mass energy absorption coefficients from 0.4 MeV to 10 MeV for silicon, carbon, copper and sodium iodide. J. Korean Phys. Soc. 49 (1), 73–76. Rosemary, B.T., 1961. The X- or gamma-ray energy absorption or transfer coefficient: tabulations and discussion. Radiat. Res. 15, 1–29. Shakhreet, B.Z., Chong, C.S., Bandyopadhyay, T., Bradley, D.A., Tajuddin, A.A., Shukri, A., 2003. Measurement of photon mass-energy absorption coefficients of paraffin wax and gypsum at 662 keV. Radiat. Phys. Chem. 68, 757–764. Singh, K., Rani, R., Kumar, V., Deep, K., 1996. Energy absorption coefficients for 662 keV g-rays in some compounds. Appl. Radiat. Isot. 47, 697–698. Singh, V.P., Badiger, N.M., 2013. Photon energy absorption buildup factors of gaseous mixtures used in radiation detectors. Int. J. Radioprot. 48 (1), 63–78. Singh, V.P., Badiger, N.M., 2013. Study of effective atomic numbers and electron densities, kerma of alcohols: phantom and human organ tissue substitutes. Nucl. Technol. Radiat. Prot. 28 (2), 137–145. Singh, V.P., Badiger, N.M., 2014. Gamma ray and neutron shielding properties of some alloy materials. Ann. Nucl. Energy 64, 301–310. Singh, V.P., Medhat, M.E., Badiger, N.M., 2014. Utilization of the Geant4 Monte Carlo simulation method for studying attenuation of photons in normal and heavy concretes at high energy values. J. Radioanal. Nucl. Chem. 300 (1), 325–331. Singh, V.P., Medhat, M.E., Badiger, N.M., 2014a. Assessment of exposure build-up factors of some oxide dispersion strengthened steels applied in modern. Nucl. Eng. Des. 270, 90–100. Singh, V.P., Badiger, N.M., Chanthima, N., Kaewkhao, J., 2014b. Evaluation of gamma-ray exposure buildup factors and neutron shielding for bismuth borosilicate glasses. Radiat. Phys. Chem. 98, 14–21. Singh, V.P., Medhat, M.E., Badiger, N.M., 2014a. Photon attenuation coefficients of thermoluminescent dosimetric materials by Geant4 toolkit, XCOM program and experimental data: a comparison study. Ann. Nucl. Energy 68, 96–100. Singh, V.P., Badiger, N.M., Kucuk, N., 2014b. Assessment of methods for estimation of effective atomic numbers of common human organs and tissue substitutes: waxes, plastics and polymers. J. Radioprot. 49, 115–121.
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Photon energy absorption coefficients for nuclear track detectors using Geant4 Monte Carlo simulation Vishwanath P. Singh a,b,n, M.E. Medhat c,d, N.M. Badiger a a
Department of Physics, Karnatak University, Dharwad 580003, India Health Physics Section, Kaiga Atomic Power Station-3&4, NPCIL, Karwar 581400, India c Experimental Nuclear Physics Department, Nuclear Research Centre, P.O. 13759, Cairo, Egypt d Institute of High Energy Physics, CAS, Beijing 100049, China b
H I G H L I G H T S
Geant4 code is used to calculate mass energy-absorption coefficients for elements, air and compounds. Mass energy-absorption coefficients for detectors are computed using Geant4 code. A very good agreement for simulated results and literature values is observed.
art ic l e i nf o
a b s t r a c t
Article history: Received 4 May 2014 Accepted 7 July 2014 Available online 15 July 2014
Geant4 Monte Carlo code simulations were used to solve experimental and theoretical complications for calculation of mass energy-absorption coefficients of elements, air, and compounds. The mass energyabsorption coefficients for nuclear track detectors were computed first time using Geant4 Monte Carlo code for energy 1 keV–20 MeV. Very good agreements for simulated results of mass energy-absorption coefficients for carbon, nitrogen, silicon, sodium iodide and nuclear track detectors were observed on comparison with the values reported in the literatures. Kerma relative to air for energy 1 keV–20 MeV and energy absorption buildup factors for energy 50 keV–10 MeV up to 10 mfp penetration depths of the selected nuclear track detectors were also calculated to evaluate the absorption of the gamma photons. Geant4 simulation can be utilized for estimation of mass energy-absorption coefficients in elements and composite materials. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Geant4 Mass energy-absorption coefficients Kerma Nuclear track detectors Buildup factor
1. Introduction The most important quantity characterizing the radiation interacting in extended media is the absorbed dose which represents the energy transferred to the matter. The dose quantity is one of the important parameter for radiation protection, dose measurement, radiation effect and defects in the material. The dose delivered to a medium is measured in terms of mass energyabsorption coefficient, men/ρ, which is a an essential quantity used in medical physics, radiation physics, health physics, radiation biology, radiotherapy, irradiation technology, and other practical applications. It is not possible to calculate men/ρ directly, but it is necessary to use mass energy-transfer coefficient, mtr/ρ. The amount of photon energy transferred is dependent upon interaction process namely the photoelectric effect, compton scattering
n
Corresponding author. Tel.: þ 91 8382 264225; fax: þ 91 8382 264025. E-mail address: [email protected] (V.P. Singh).
http://dx.doi.org/10.1016/j.radphyschem.2014.07.001 0969-806X/& 2014 Elsevier Ltd. All rights reserved.
and pair production. These interaction processes are dependent upon atomic numbers of the elements of compound/mixture and photon energy. Mass energy-absorption coefficient (indirectly mass energytransfer coefficeint) is a measure of average fraction of photon energy transferred to kinetic energy of the charged particle when photon interacts with a material. Photoelectric absorption, incoherent scattering and pair/triplet production exhibit these characterisitics, whereas coherent scattering transfers negligible photon energy. These events are playing a crucial role in the calculation of energy-absorption coefficients (Hubbell, 1969, 1977). The intreraction of gamma photon with the matter is a complex process where different types of events are occuring in the medium. It is found that there are various factors (average fraction of kinetic energy of secondary photon, incident photon energy, additive law for mixture, etc.) affecting the calculation of the energy absorption. Various researchers have calculated and measured the mass energy-absorption coefficietnts. The mass energy-absorption
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coefficients of the biological samples are parameterized in the photon energy range 200–1500 keV (Manjunathguru and Umesh, 2009). Rosemary (1961) has tabulated and discussed gamma photon energy absorption and transfer theoretically. Hubbell and Berger (1968) have calculated absorption coefficients for air, water and 18 elements over the photon energy range of 10 keV r E r 10 MeV. Hubbell (1977) calculated the mass energy-absorption coefficients for H, C, N, O, Ar and seven mixtures for energies from 0.1 keV to 20 MeV. Hubbell (1982) again has calculated energy-absorption coefficients theoretically for 40 elements ranging from hydrogen (Z ¼1) to uranium (Z ¼ 92) and for 45 mixtures and compounds of dosimetric interest from 1 keV to 20 MeV. Hubbell (1982) has used the fraction-by-weight of the constituents of the compounds. Higgins et al. (1992) have calculated the the mass energyabsorption coefficients theoretically for 47 media from 1 keV to 100 MeV. Gurler et al. (2000) have calculated the absorption coefficients for aluminum and water. Ban et al. (1993) have obtained mass energy-absorption coefficients for nitrogen and argon experimentally at 30 keV gamma ray. Bhandal et al. (1994) have estimated the mass energy-absorption coefficients of fatty acids for gamma rays using 662 and 1115 keV energies. Bradley et al. (1989) have determined the mass energyabsorption coefficients for paraffin experimentally. Singh et al. (1996) have mesaured the mass energy-absorption coefficients for 10 compounds experimentally for 662 keV gamma ray. Shakhreet et al. (2003) measured the mass energy-absorption coefficients of paraffin wax and gypsum at 662 keV experimentally. Oz et al. (2006) have calculated the mass energyabsorption coefficients for silicon, carbon, copper and sodium iodide theoretically. Gurler et al. (2000) have calculated mass energy-absorption coeifficients for nitrogen and mass energytransfer coefficeints for silicon, carbon copper, nirogen and sodium iodide in photon energy of 0.4–10 MeV, and showed very good agreement with earlier literature values. Other attempt is made for calculation of mass energy-absorption coeifficients of optical fiber and thermoluminiscent dosimeter in photon energy of 0.2–20 MeV using Monte Carlo N-particle code version 5 (Hossain and Wagiran, 2012). The theoretical method for calculation of the mass energyabsoprtion coefficeint is a complicated process. The experimetal values of the mass energy-absoprtion coefficeints are found for some compounds for very limited energies. After review of the literature, it has been found that this area requires investigation for finding easy ways of estimation of the mass energyabsoprtion coefficeints. This encouraged us to utilize Geant4 Monte Carlo simulation method for calculation of the mass energy-absoprtion coefficeints. Therefore, this present work aims to calculate the mass energy-absoprtion coefficeints of elements (carbon, nitrogen, silicon), air, sodium iodide, and some nuclear track detectors. The Geant4 simulation results of elements and sodium iodide were found to be in very good agreement with earlier literature data. First of all the Geant4 code simulated results of mass energy-absorption coefficients of elements, air and sodium iodide were validated with available literature data for photon energy 0.4–10 MeV, and then Geant4 was utilized for simulation for photon energy 1 keV –20 MeV. Geant4 simulation was utilized for calculation of mass energyabsoprtion coefficeints for some nuclear track detectors. The air kerma and energy absorption buildup factors were also analyzed for the nuclear track detectors. Geant4 Monte carlo simulation was used for first time for calculation of the mass energy-absoprtion coefficeints. At present Geant4 Monte carlo simulation has been used for mass attenuation coefficients of composite materials and standarized the experimental set-up (Medhat and Wang, 2013; Singh et al., 2014a, 2014b;).
2. Theoretical background and computational method A few elements (nitrogen, carbon and silicon), air, sodium iodide and some soild state and plastic nuclear track detectors; quartz (SiO2), sodalime glass (73SiO2:14Na2O:9CaO:4MgO:0.15Al2O3: 0.03K2O:0.02TiO2:0.1Fe2O3), PC (C16H14O3: Makrofol, Lexan, Millar), PET (C10H8O4), CN (C6H8O9N2:Daicell, LR-115) and CR-39 (C12H18O7) have been considered for investigation of gamma photon energy absorption by mass energy-absorption coefficients and energy absorption buildup factors. The effective atomic numbers and electron densities of these nuclear track detectors are found in the literature (Medhat, 2011). 2.1. Mass energy-absorption coefficient The mass energy-absorption coefficient, men/ρ, is a measure of the average fractional amount of incident photon energy transferred to kinetic energy of charged particles as a result of gammaray interaction. This imparted charged particle kinetic energy is valid approximation for the amount of energy made available for the production of chemical, biological and other effects associated with exposure due to ionizing radiation (ICRU-33). The men/ρ is the product of mass energy-transfer coefficient, mtr/ρ (cm2/g) and (1 g), where g is the fraction of the energy of the secondary charged particle that is lost to bremsstrahlung in the material. The mass energy-absorption coefficient of a compound or composite is calculated using mixture rule (ðμen =ρÞcomposite ¼ ∑ni wi ðμen =ρÞi ) where wi is the proportion by weight and (men/ρ)i is the mass energy-absorption coefficient of the ith elements. The mass energy-absorption coefficients of elements are avaialable using differernt methods. 2.2. Geant4 simulation code Monte Carlo simulation is found to be an effective tool to calculate radiation interaction parameters in different types of compounds/mixtures for shielding, energy deposition and dosimetry. Geant4 code is based on object-oriented programming and allows user to derive classes to describe the detector geometry, primary particle generator and physics processes models along electromagnetic, hadronic, and decay physics based on theory, materials and elements, experimental data or parameterizations. Most of the physics processes models include multiple scattering, ionization, Bremsstrahlung, positron annihilation, photo-electric effect, Compton and Rayleigh scattering, pair production, synchrotron and transition radiation, Cherenkov effect, refraction, reflection, absorption, scintillation, fluorescence, and Auger electrons emission (Agostinelli et al., 2003; CERN, 2007). The Geant4 simulation toolkit covers a wide energy range starting from 250 eV to TeV. The Geant4 simulation is the modeling of the photon interaction through materials in computer environment which gives flexibility and ease of use, instead of performing an experimental determination of mass energy-attenuation coefficient of different composite materials. Mass energy-attenuation of photons is calculated by simulating all relevant physical processes and interactions before and after inserting the materials under investigation (Medhat and Wang, 2013). 2.3. Kerma The kinetic energy per unit mass (Kerma) relative to air, K a , of the detectors is derived by the following equation: Ka ¼
K Dosimeter ðμen =ρÞDosimeter ¼ K Air ðμen =ρÞAir
ð1Þ
V.P. Singh et al. / Radiation Physics and Chemistry 106 (2015) 83–87
BðE; xÞ ¼ f1 þ ðb 1Þx for K ¼ 1
ð3Þ
tanhðx=X K 2Þ tanhð 2Þ ; 1 tanhð 2Þ for penetration depth ðXÞ r 40 mfp
KðE; xÞ ¼ cxa þd
ð4Þ
The mass energy-absorption coefficients computed using Geant4 simulation for carbon, nitrogen and silicon elements, and sodium iodide are given in Table 1(a) and (b). The variation of mass energy-absorption coefficients of the nuclear track detectors with photon energy is shown in Figs. 1 and 2 using Geant4
4
10
Geant4
Quartz Sodalime PC PET CN CR-39 Air
2
2.3.1. Energy absorption buildup factor The energy absorption buildup factor (EABF) values of the selected nuclear track detectors are possible to compute using the Geometrical Progression (G-P) fitting method. The detailed description for computation of EABF can be found in the recent literatures (Singh and Badiger, 2013, 2014; Singh et al., 2014a, 2014b). The buildup factors are estimated by using G-P fitting parameters (b, c, a, Xk and d) in the photon energy range 0.015–15 MeV up to 40 mfp using the equations (Harima et al. 1986, Harima, 1993) given below: ðb 1ÞðK x 1Þ BðE; xÞ ¼ 1 þ for K a 1 ð2Þ K 1
3. Results and discussion
Mass energy absorption coefficient (cm /g)
The mass energy-absorption coefficient, men/ρ, of the nuclear track detectors and air is computed using the mixture rule explained above. The values of μen/ρ of elements are taken from literature (Hubbell and Seltzer, 1995).
85
3
10
2
10
1
10
0
10
-1
10
-2
10
where x is the distance from source (mfp) and b, the value of the buildup factor at 1 mfp and K(E,x) is the dose multiplicative factor. The variation of K (E,x) with penetration represents the change in the shape of the spectrum from that at 1 mfp which determines the value of b.
-3
-2
10
10
-1
10
0
1
10
10
E (MeV) Fig. 1. Mass energy-absorption coefficient for nuclear track detectors and air using Geant4 simulation code.
Table 1 (a) Comparison of mass energy-absorption coefficients (cm2/g) of carbon, nitrogen for 0.4–10 MeV photon energy. E (MeV)
0.4 0.5 0.6 0.8 1 1.5 2 3 4 5 6 8 10
Carbon
Nitrogen
Geant4 Oz et al. (2006)
Hubbell (1982)
Higgins Hubbell and et al. (1992) Seltzer (1995)
Geant4 Guler et al., Rosemary (2009) (1961)
Hubbell and Berger (1968)
Hubbell (1982)
Higgins Hubbell and et al. (1992) Seltzer (1995)
0.026 0.027 0.028 0.027 0.026 0.024 0.022 0.019 0.017 0.016 0.015 0.014 0.013
0.0295 0.0297 0.0296 0.0288 0.0279 0.0255 0.0234 0.0204 0.0185 0.0171 0.0160 0.0147 0.0138
0.0295 0.0297 0.0295 0.0289 0.0279 0.0255 0.0234 0.0205 0.0185 0.0171 0.0160 0.0147 0.0138
0.028 0.028 0.027 0.027 0.026 0.024 0.022 0.018 0.017 0.016 0.015 0.016 0.013
– 0.0296 0.0295 0.0289 0.0279 0.0255 0.0234 0.0205 0.0186 0.0173 0.0163 0.0151 0.0143
0.0295 0.0297 0.0296 0.0289 0.0279 0.0255 0.0235 0.0205 0.0186 0.0173 0.0164 0.0151 0.0143
0.0295 0.0297 0.0296 0.0289 0.0279 0.0255 0.0235 0.0205 0.0186 0.0173 0.0164 0.0151 0.0143
0.0294 0.0296 0.0295 0.0288 0.0279 0.0254 0.0234 0.0204 0.0183 0.0169 0.0158 0.0143 0.0134
0.0295 0.0297 0.0296 0.0289 0.0279 0.0255 0.0235 0.0205 0.0185 0.0171 0.0161 0.0147 0.0138
0.0294 0.0296 0.0295 0.0288 0.0279 0.0255 0.0235 0.0208 0.0189 0.0176 0.0166 0.0152 0.0143
0.0295 0.0299 0.0296 0.0288 0.0279 0.0255 0.0235 0.0205 0.0185 0.0172 0.0162 0.0149 0.0141
(b) Comparison of mass energy absorption coefficients (cm2/g) of silicon and sodium iodide for 0.4–10 MeV photon energy E (MeV) Silicon Sodium iodide
0.4 0.5 0.6 0.8 1 1.5 2 3 4 5 6 8 10
Geant4 Oz et al. (2006)
Hubbell (1982)
Higgins Hubbell and et al. (1992) Seltzer (1995)
Geant4 Oz et al. (2006)
Hubbell (1982)
Hubbell and Seltzer (1995)
0.028 0.030 0.031 0.029 0.028 0.026 0.024 0.022 0.020 0.019 0.017 0.016 0.015
0.0297 0.0297 0.0295 0.0287 0.0278 0.0253 0.0234 0.0210 0.0196 0.0187 0.0182 0.0177 0.0175
0.0297 0.0297 0.0295 0.0288 0.0278 0.0253 0.0234 0.0210 0.0196 0.0188 0.0182 0.0177 0.0175
0.049 0.038 0.035 0.026 0.026 0.024 0.025 0.021 0.021 0.021 0.022 0.023 0.024
0.0529 0.0410 0.0351 0.0295 0.0266 0.0227 0.0211 0.0204 0.0208 0.0215 0.0223 0.0238 0.0250
0.0522 0.0405 0.0348 0.0293 0.0265 0.0242 0.0227 0.0212 0.0205 0.0210 0.0217 0.0225 0.0241
0.0297 0.0297 0.0296 0.0288 0.0278 0.0254 0.0235 0.0211 0.0197 0.0190 0.0185 0.0180 0.0178
0.0297 0.0297 0.0295 0.0288 0.0278 0.0254 0.0235 0.0210 0.0196 0.0188 0.0183 0.0177 0.0175
0.0557 0.0429 0.0361 0.0300 0.0269 0.0229 0.0212 0.0206 0.0211 0.0220 0.0229 0.0246 0.0261
0.0295 0.0297 0.0296 0.0289 0.0279 0.0255 0.0235 0.0206 0.0187 0.0173 0.0164 0.0151 0.0143
V.P. Singh et al. / Radiation Physics and Chemistry 106 (2015) 83–87
Hubbell and Seltzer, 1995
4
10
Quartz Sodalime PC PET CN CR-39 Air
2
Mass energy absorption coefficient (cm /g)
86
3
10
2
10
1
10
0
10
-1
10
-2
10
-3
10
-2
10
-1
10
0
10
1
10
Table 2 Energy absorption buildup factors for nuclear track detectors. E (MeV)
6
Quartz Sodalime PC PET CN CR-39
Geant4
5
KERMA
4
3
Energy absorption buildup factor for 0.5 mfp
Quartz 0.05 0.10 1.00 10.00
1.73 2.53 1.51 1.17
Soda lime 1.57 2.51 1.44 1.16
PC
PET 2.78 2.28 1.49 1.20
CN
CR-39
2.72 2.35 1.49 1.20
2.62 2.42 1.50 1.19
2.71 2.41 1.49 1.20
for 1 mfp 5.10 4.56 2.10 1.37
0.05 0.10 1.00 10.00
(b) Energy absorption buildup factor 2.30 1.99 5.37 4.31 4.15 4.42 2.11 1.96 2.09 1.33 1.32 1.38
4.69 4.65 2.11 1.37
5.04 4.70 2.10 1.38
0.05 0.10 1.00 10.00
(c) Energy absorption buildup factor for 5 mfp 5.30 3.90 60.93 49.27 35.81 26.00 20.86 74.40 70.41 64.12 9.67 8.36 10.05 10.02 9.98 2.46 2.45 2.60 2.59 2.57
46.41 71.34 10.02 2.59
0.05 0.10 1.00 10.00
(d) Energy absorption buildup factor for 10 mfp 8.13 5.48 273.28 193.87 117.22 72.33 51.05 487.40 423.36 342.83 24.89 21.15 26.61 26.44 26.22 3.84 3.83 3.92 3.91 3.90
174.41 418.92 26.40 3.92
E (MeV) Fig. 2. Mass energy-absorption coefficient for nuclear track detectors and air using the theoretical data by Hubbell and Seltzer (1995).
(a)
calculation by Hubbell and Seltzer (1995). The μen/ρ values of medical, biological, tissue substitutes and composite materials can also be simulated using the present standard Geant4 code. The Geant4 code produces μen/ρ values of the elements, mixtures and compounds in very good agreement with earlier reported data by solving experimental and theoretical complications. 3.2. Kerma
2
1
-3
10
-2
10
-1
10
0
10
1
10
E (MeV) Fig. 3. Kerma relative to air for nuclear track detectors using Geant4 simulation code.
simulation code and Hubbell and Seltzer (1995). The kerma relative to air using Geant4 is shown graphically in Fig. 3 and the energy absorption buildup factors are given in Table 2. 3.1. Mass energy-absorption coefficients The mass energy-absorption coefficients, μen/ρ, of carbon, nitrogen, silicon and sodium iodide using Geant4 simulation are given in Table 1(a, b) for photon energy of 0.4–10 MeV. The μen/ρ values of these elements and sodium iodide by different investigators (Rosemary, 1961; Hubbell and Berger, 1968; Hubbell, 1982; Higgins et al., 1992; Oz et al., 2006; Hubbell and Seltzer, 1995; Gurler et al., 2009) are given in Table 1(a, b). It was found that the Geant4 simulation results for the selected elements (carbon, nitrogen and silicon) and sodium iodide are in very good agreement with the earlier reported data in the literatures. The variation of μen/ρ values of the nuclear track detectors and air is shown in Figs. 1 and 2 using Geant4 simulation and theoretical (Hubbell and Seltzer, 1995) respectively. Figs. 1 and 2 show that the Geant4 simulation provides the results similar to the theoretical
Using Geant4 code simulation for μen/ρ results, the variation of Kerma of the nuclear track detectors relative to air with photon energy (1 keV–20 MeV) is shown in Fig. 3. In general the Kerma values of all the nuclear track detectors are in range of unity above 100 keV photon energy (i.e. beyond photoelectric effect). However, there is a variation in Kerma for composites containing slightly high-Z elements (quartz and soda lime). The reason for such variation in kerma is due to large photon energy transfer for high-Z elements as the photoelectric cross section is proportional to Z4–5. Similar behaviors are observed for alcohols and tissue substitutes (Singh and Badiger, 2013; Singh et al., 2014). It is easy to calculate the kerma relative to air using theoretical μen/ρ by Hubbell and Seltzer (1995) similar to Geant4 results. 3.3. Energy absorption buildup factors The energy absorption buildup factors of the nuclear track detectors for the selected photon energy (0.05, 0.1, 1 and 10 MeV) for penetration depths 0.5, 1, 5 and 10 mfps are given in Table 2. The energy absorption buildup factors of the nuclear track detectors are small for low-penetration depth whereas it is found bigger for large-penetration depths.
4. Conclusions In the present paper the mass energy-absorption coefficients of carbon, nitrogen, silicon, air, sodium iodide, and some nuclear track detectors were calculated using Geant4 simulation code. There was a very good agreement between Geant4 simulation code with the data tables published earlier (Rosemary, 1961; Hubbell and Berger, 1968; Hubbell, 1982; Higgins et al., 1992;
V.P. Singh et al. / Radiation Physics and Chemistry 106 (2015) 83–87
Oz et al., 2006; Hubbell and Seltzer, 1995; Gurler et al., 2009). The present simulation code should be considered as a standard for calculation of mass energy-absorption coefficients for any elements and composite/compound materials. References Agostinelli, S., et al., 2003. G4—a simulation toolkit. Nucl. Instrum. Methods Phys. Res. A 506, 250–303. Ban, S., Hirayama, H., Namito, Y., Tanaka, S., Nakashima, H., Nakane, Y., Yoshizawa, M., Nariyama, N., 1993. Measurement of the photon energy-absorption coefficient for air, nitrogen and argon at 30 keV. Appl. Radiat. Isot. 44, 769–772. Bhandal, G.S., Singh, K., Rani, R., Kumar, V., 1994. Energy absorption coefficients for 662 and 1115 keV gamma rays in some fatty acids. Appl. Radiat. Isot. 45, 379–381. Bradley, D.A., Chong, C.S., Shukri, A., Tajuddin, A.A., Ghose, A.M., 1989. A new method for the direct measurement of the energy absorption coefficient of gamma rays. Nucl. Instrum. Methods Phys. Sect. A 280, 392–394. CERN, 2007. Geant4 Collaboration Physics Reference Manual. 〈http://geant4.cern. ch/support/userdocuments.shtml〉. Gurler, O., Oz, H., Yalcin, S., 2000. Calculation of mass energy absorption coefficients and mass radiation absorption coefficients for aluminum and water mediums. Bulg. J. Phys. Suppl. 27, 25–28. Gurler, O., Oz, H., Yalcin, S., Gundogdu, O., 2009. Mass absorption and mass energy transfer coefficients for 0.4–10 MeV gamma rays in elemental solids and gases. Appl. Radia. Isot. 67, 201–205. Harima, Y., 1993. An Historical review and current status of buildup factor calculations and application. Radiat. Phys. Chem. 41 (4/5), 631–672. Harima, Y., Sakamoto, Y., Tanka, S., Kawai, M., 1986. Validity of geometric progression formula in approximating gamma ray buildup factor. Nucl. Sci. Eng. 94, 24–35. Higgins, P.D., Attix, F.H., Hubbell, J.H., Seltzer, S.M., Berger, M.J., Sibata, C.H., 1992. Mass energy-transfer and mass energy-absorption coefficients, including inflight positron annihilation for photon energies of 1 keV–100 MeV. NISTIR 4812, 1–66. Hossain, I., Wagiran, A.H., 2012. Mass energy absorption coefficients for 0.2–20 MeV Photon in Ge-doped optical fiber and TLD-100 by Monte Carlo n-particle code version 5 (MCNP5). Optoelectron. Adv. Mater.—Rapid Commun. 6 (1–2), 162–164. Hubbell, J.H., 1969. Photon cross sections. Attenuation coefficients and energy absorption coefficients from 10 keV to 100 GeV. NSRDS-NBS 29. Hubbell, J.H., 1977. Photon mass attenuation and mass energy-absorption coefficients for H, C, N, O, Ar, and seven mixtures from 0.1 keV to 20 MeV. Radiat. Res. 70, 58–81. Hubbell, J.H., 1982. Photon mass attenuation and energy-absorption coefficients from 1 keV to 20 MeV. Int. J. Appl. Radiat. Isot. 33, 1269–1290.
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Hubbell, J.H., Berger, M.J., 1968. Shielding fundamentals and methods. In: Jaeger, R. G., Blizard, E.P., Chilton, A.B. (Eds.), Engineering Compendium on Radiation Shielding, 1. Springer, Berlin, p. 199. Hubbell J.H., Seltzer S.M., 1995. Tables of X-ray mass attenuation coefficients and mass energy absorption coefficients from 1 keV to 20 MeV for elements Z¼1 to 92 and 48 additional substances of dosimetric interest. Avaialble at: 〈http:// www.nist.gov/pml/data/xraycoef/index.cfm〉. International Commission on Radiation Units and Measurements, Report 33. 7910 Woodmont Avenue Washington, DC, 20014, USA. Manjunathguru, V., Umesh, T.K., 2009. Simple parametrization of photon mass energy absorption coefficients of H-, C-, N- and O-based samples of biological interest in the energy range 200–1500 keV. PRANAMA 72 (2), 375–387. 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. Medhat, M.E., Wang, Y., 2013. GEANT4 code for simulation attenuation of gamma rays through scintillation detectors. Ann. Nucl. Energy 62, 316–320. Oz, H., Gurler, O., Gultekin, A., Yalcin, S., Gundogdu, O., 2006. Photon mass energy absorption coefficients from 0.4 MeV to 10 MeV for silicon, carbon, copper and sodium iodide. J. Korean Phys. Soc. 49 (1), 73–76. Rosemary, B.T., 1961. The X- or gamma-ray energy absorption or transfer coefficient: tabulations and discussion. Radiat. Res. 15, 1–29. Shakhreet, B.Z., Chong, C.S., Bandyopadhyay, T., Bradley, D.A., Tajuddin, A.A., Shukri, A., 2003. Measurement of photon mass-energy absorption coefficients of paraffin wax and gypsum at 662 keV. Radiat. Phys. Chem. 68, 757–764. Singh, K., Rani, R., Kumar, V., Deep, K., 1996. Energy absorption coefficients for 662 keV g-rays in some compounds. Appl. Radiat. Isot. 47, 697–698. Singh, V.P., Badiger, N.M., 2013. Photon energy absorption buildup factors of gaseous mixtures used in radiation detectors. Int. J. Radioprot. 48 (1), 63–78. Singh, V.P., Badiger, N.M., 2013. Study of effective atomic numbers and electron densities, kerma of alcohols: phantom and human organ tissue substitutes. Nucl. Technol. Radiat. Prot. 28 (2), 137–145. Singh, V.P., Badiger, N.M., 2014. Gamma ray and neutron shielding properties of some alloy materials. Ann. Nucl. Energy 64, 301–310. Singh, V.P., Medhat, M.E., Badiger, N.M., 2014. Utilization of the Geant4 Monte Carlo simulation method for studying attenuation of photons in normal and heavy concretes at high energy values. J. Radioanal. Nucl. Chem. 300 (1), 325–331. Singh, V.P., Medhat, M.E., Badiger, N.M., 2014a. Assessment of exposure build-up factors of some oxide dispersion strengthened steels applied in modern. Nucl. Eng. Des. 270, 90–100. Singh, V.P., Badiger, N.M., Chanthima, N., Kaewkhao, J., 2014b. Evaluation of gamma-ray exposure buildup factors and neutron shielding for bismuth borosilicate glasses. Radiat. Phys. Chem. 98, 14–21. Singh, V.P., Medhat, M.E., Badiger, N.M., 2014a. Photon attenuation coefficients of thermoluminescent dosimetric materials by Geant4 toolkit, XCOM program and experimental data: a comparison study. Ann. Nucl. Energy 68, 96–100. Singh, V.P., Badiger, N.M., Kucuk, N., 2014b. Assessment of methods for estimation of effective atomic numbers of common human organs and tissue substitutes: waxes, plastics and polymers. J. Radioprot. 49, 115–121.