CALCULATION OF TOTAL MASS ATTENUATION COEFFICIENTS, EFFECTIVE ATOMIC NUMBERS AND EFFECTIVE ELECTRON DENSITIES FOR THE EARTH ATMOSPHERE

Transcription

1 International Journal of Physics and Research (IJPR) ISSN Vol. 3, Issue 3, Aug 2013, TJPRC Pvt. Ltd. CALCULATION OF TOTAL MASS ATTENUATION COEFFICIENTS, EFFECTIVE ATOMIC NUMBERS AND EFFECTIVE ELECTRON DENSITIES FOR THE EARTH ATMOSPHERE Y. ELMAHROUG 1, B. TELLILI 2 & C. SOUGA 3 1 Université De Tunis El Manar, Faculté Des Sciences De Tunis, Unité De Recherche De Physique Nucléaire Et Des Hautes Energies, 2092 Tunis, Tunisie 2 Université De Tunis El Manar, Institut Supérieur Des Technologies Médicales De Tunis, 1006 Tunis, Tunisie 3 Université De Carthage, Ecole Polytechnique De Tunisie, B.P La Marsa, Tunisie ABSTRACT The protection of astronauts and equipments from the ionizing radiation is essential for the development of manned space activities. The ionizing-radiation environment of space consists of Galactic Cosmic Radiation (GCR) and in Solar Energetic Particles (SEPs) events. Thus, the understanding of these ionizing radiations is essential for manned space activities. In this work, the physical characteristics of the atmospheric ionizing radiation environment have been investigated in terms of gamma ray attenuation. The total mass attenuation coefficients, the effective atomic numbers and the effective electron densities for Earth atmosphere have been calculated theoretically in the energy range from 1 kev to 1 GeV by using the WinXCOM program. The dependence of these parameters on incident photon energy has been examined. KEYWORDS: Attenuation Coefficients, Cross-Sections, Effective Atomic Number, Effective Electron Density, Earth Atmosphere INTRODUCTION Earth atmosphere is an important factor for the existence of life on earth, it allows to moderate the terrestrial temperature and pressure, it also allows to protect the earth from meteorites and high-energy radiation. The determination of the characteristics and properties of the atmosphere is very important. In this paper, we will examine and characterize the interaction of X and gamma-rays with the Earth atmosphere. This study is a fundamental for calculating the dose rate conversion coefficient for external exposure to photons emitters in terrestrial soil (Clouvas and Xanthos, 2000; Kocher and Sjoreen, 1985; Likar et al., 1998; Saito and Jacob, 1995), it is an important tool to evaluate the risks and effects of ionizing radiation on spacecraft equipments and especially for astronauts who are working in the International Space Station (ISS). It is also useful for ionospheric disturbances studies caused by solar flares. The total mass attenuation coefficients (μ t ), the effective atomic number (Z eff ), the effective electron density (N eff ), are the basic parameters required in determining the penetration of X and gamma-rays in the atmosphere. The total mass attenuation coefficient is a measure of the average number of interactions between incident photons and matter that occur in a given mass per unit area thickness of the substance under investigation (Hubbell, 1982; Hubbell and Seltzer, 1985; Hubbell, 1999; Jackson and Hawkes, 1981). This coefficient is not constant but depends on the incident photon energy, the material density and the atomic number for elements, but for compound and mixtures such as the atmosphere, it depends on another coefficient called effective atomic number (Z eff ). The idea of this coefficient is to assume that a compound or mixture can be considered as a simple element characterized by the atomic number (Z eff ), but it is not

2 78 Y. Elmahroug, B. Tellili & C. Souga constant, it varies with the incident photon energy, the notion and the theoretical expression of this parameter were suggested by Hine (Hine, 1952). The effective atomic number is related to another important physical parameter called effective electron density (N eff ) and describes the interaction of x-ray and gamma photons with matter which is defined as the electron per unit mass of the target material (Gowda et al., 2005; Manohara et al., 2008). In the present work, these parameters have been determined theoretically by using WinXCom code which is a Windows version of the XCOM database (Berger and Hubbell, 1987; Gerward et al.,2001; Gerward et al.,2004), it allows to calculate the mass attenuation coefficients or photon interaction cross-sections for the chemical elements (Z = 1-100), compound and mixtures at energies from 1 kev to 100 GeV. The chemical composition of Earth atmosphere is given in Table 1 (Heicklen, 1976; Hobbs, 2000; Holland, 1978; Seinfeld and Pandis, 2004; Warneck, 2000; Wayne, 2000). METHODOLOGY The Total Mass Attenuation Coefficient During its passage through material medium, a photon undergoes several interactions such as photoelectric absorption, Coherent scattering, scattering Incoherent and Pair Production (Hubbell, 1982; Hubbell et al., 1995; Hubbell, 1999; Jackson and Hawkes, 1981). If a photon beam having an initial intensity I 0 penetrates the matter, it will be attenuated and its intensity decreases exponentially according to the exponential law; (1) This is called the Beer-Lambert law, where I is the transmitted intensity, (μ linear ) is the linear attenuation coefficient in cm -1, ρ is the material density in gcm -3, x is the thickness of the absorbing medium, d is the mass per unit area (gcm -2 ) and μ t = μ linear / ρ is the total mass attenuation coefficient (g -1 cm -2 ). For a chemical mixture composed of various elements and compounds as our case, the total mass attenuation coefficient of the mixture (μ t,mix ) is given by (Hubbell, 1982; Hubbell et al., 1995; Hubbell, 1999; Jackson et al., 1981; İçelli et al., 2011); (2) Where (μ t,compd ) i and W i are respectively the total mass attenuation coefficient and fractional weight of ith constituent (element or compound) in the mixture, (μ t ) i was obtained from WinXCOM. The Total Cross-Section The cross section is a fundamental parameter to describe the photons interaction with matter; it is defined as the probability of a photon interaction for a given reaction. The total cross section of a photon interaction is defined as the sum of the partial cross sections for each type of reaction (photoelectric absorption, Coherent scattering, scattering Incoherent and pair Production) (Hubbell, 1982; Hubbell et al., 1995; Hubbell, 1999; Jackson and Hawkes, 1981); (3)

3 Calculation of Total Mass Attenuation Coefficients, Effective Atomic 79 Numbers and Effective Electron Densities for the Earth Atmosphere Where, (σ ph ) is the photoelectric cross-section, (σ coh ) is the coherent scattering cross-section, ( σincoh) is the incoherent scattering cross section, κ n is the pair production in nuclear field cross section and κ e is the pair production in electron field cross-section. The Total Molecular Cross-Section For a chemical mixture, the total molecular effective cross section (σ t,m ) is proportional to the total mass attenuation coefficient of the mixture, (μ t,mix ), through the following relation (İçelli et al., 2011); (4) Where N A is the Avogadro s number and n j and A j are respectively the number of atoms and the molar mass of the jth element in ith compound. The Total Atomic Cross-Section The total atomic cross-section (σ t,a ) can be evaluated from the total molecular effective cross section of the mixture (σ t,m ), using the following relation (Jackson and Hawkes, 1981); (5) Where, n total is the total number of atoms in the mixture chemical formula. The Total Electronic Cross-Section The total electronic effective cross-section (σ t,e ) is given by the following formula (Jackson and Hawkes, 1981); (6) Where (μ t ) j,f j and Z j are respectively the total mass attenuation coefficient, the molar fraction and the atomic number of the jth element in ith compound. The Effective Atomic Number The effective atomic number (Z eff ) is defined as the ratio between the total atomic effective cross-section and the total electronic effective cross-section (Jackson and Hawkes, 1981); (7) The Effective Electron Density The effective electron density (N eff ) (the electrons number per unit mass, electron/g) is determined by the following formula (Jackson and Hawkes, 1981);

4 80 Y. Elmahroug, B. Tellili & C. Souga Where (A total) is the total atomic weight of the mixture. RESULTS AND DISCUSSIONS Table 1: Elemental Composition of Earth Atmosphere Constituents Percentage by Volume N O Ar CO Ne E-03 He 5.24E-04 H 2 O 2.875E-04 Kr 1.14E-04 CH 4 1.5E-04 H 2 5E-05 N 2 O 2.7E-05 CO 1.9E-05 Xe 8.9E-06 O 3 1E-06 NH 4 4E-07 S0 2 1E-07 NO 2 1E-07 We have calculated the total attenuation coefficients (μ t ), the total effective molecular (σ t,m ), the atomic (σ t;a ) and electronic cross-sections (σ t,e ), the effective atomic number (Z eff ), and the effective electron density (N eff ) for Earth atmosphere, for energies ranging from 1 kev to 1 GeV, using the WinXCOM program. The values of these parameters are listed in Table 2. Total Mass Attenuation Coefficients The mass attenuation coefficient (μ t ) for Earth atmosphere, has been shown graphically in Figure1, it is clear that the (μ t ) is not constant but varies as a function of the incident photon energy, in the low incident photon energies (1-30keV), it decreases rapidly (3.58 x 10 3 at 1 kev to 3.44 x 10-1 at 30 kev) when the incident photons energy increases. In the intermediate energy (30 kev-20 MeV), it decreases slowly. Finally, in high energy regions (20MeV < E), it increases slowly and is almost constant. This behavior can be explained by the fact that the dominance of different interaction processes of photon with the matter (photoelectric absorption, Compton scattering and pair production in nuclear field and in electronic field) is not the same for different photon energies. Figure 2 shows the partial mass attenuation coefficients of different photon interaction processes for the Earth atmosphere. It is clear that in the low energy region, the photoelectric absorption is the dominant process and the contribution of other processes is negligible. Also, we note that the partial mass attenuation coefficients of the photoelectric absorption decreases rapidly and its contribution becomes negligible starting from 30keV, because its effective cross section is inversely proportional to the incident photon energy as (E 3.5 ) (Hubbell, 1999). Therefore, the fast decrease of the total mass attenuation coefficient in the low energy range is caused by this effect. We also note, when the incident photon energy is between 30 kev and 22 MeV, the Compton scattering process (especially incoherent) becomes the dominant mechanism, indeed its partial mass attenuation coefficients increases when the energy is between 1 kev and 30 kev but is smaller than the partial mass attenuation coefficients of the photoelectric absorption. (8)

5 Calculation of Total Mass Attenuation Coefficients, Effective Atomic 81 Numbers and Effective Electron Densities for the Earth Atmosphere Then, it becomes almost constant up to 150 kev and from this value it decreases slowly. The behavior of this coefficient is due to the fact that the cross section of Compton scattering process is inversely proportional to the incident photons energy (E -1 ) (Hubbell, 1999). Therefore, the slow decrease in (μ t ) values in the intermediate energy can be explained by the dominance of the Compton scattering process. Finally, in the high energy region, the pair-production process becomes dominant. The partial mass attenuation coefficient of this process is zero for an energy between 1 kev and 1.02 MeV. Then, it increases linearly with the increasing of energy and when the energy is 24 MeV it becomes equivalent to the partial mass attenuation coefficients of the Compton scattering process and from 100 MeV it becomes almost constant. So, this may explain why (μ t ) remains almost constant in the high photon energy region. Figure 1: Variation of Total Mass Attenuation Coefficients versus Incident Photon Energy for the Earth Atmosphere Figure 2: Variation of the Partial Mass Attenuation Coefficients of the Different Photon Interaction Processes versus Incident Photon Energy for the Earth Atmosphere Effective Atomic Numbers and Effective Electron Density By using the total mass attenuation coefficient (μ t ), the total atomic cross-sections (σ t,a ), and the electronic crosssections, (σ t,e ), the effective atomic numbers (Z eff ) and the effective electron density (N eff ) for Earth atmosphere were calculated from Eqs.(7,8).

6 82 Y. Elmahroug, B. Tellili & C. Souga Effective Atomic Numbers The variation of (Z eff) values versus photon energy is presented in Figure 3, it is clearly seen that the (Z eff) are not constant but depends on the photon energy. The (Z eff) values of the atmosphere decreases rapidly with increasing of photon energy from 1 to 10 kev. Thereafter, (Z eff) values increases up to the incident photon energy of about 200 kev. Beyond this energy, (Z eff) value becomes almost constant. The minimum and maximum values of (Z eff) are respectively 8.03 and The variation of (Z eff) is due to the fact that the interaction processes of photons with the matter is different for various photon energies. Effective Electron Density The variation of effective electron density with incident photon energy for the atmosphere is displayed in Figure 4. It is seen that the (N eff) varies between 5.60x10 23 and 5.67x10 23, and this figure shows that the variation of the effective electron number (N eff), with the incident photon energy dependence, is similar to the variation of the effective atomic numbers (Z eff), this is normal since this two parameters are related through Eq(8). Figure 3: Variation of Effective Atomic Numbers versus Incident Photon Energy for the Earth Atmosphere Figure 4: Variation of Effective Electron Density versus Incident Photon Energy for the Earth Atmosphere

7 Calculation of Total Mass Attenuation Coefficients, Effective Atomic 83 Numbers and Effective Electron Densities for the Earth Atmosphere CONCLUSIONS In this paper, the values of the total mass attenuation coefficient (μ t ), the photon interaction cross section, the effective atomic numbers and the effective electron density for Earth atmosphere, have been calculated in the energy region from 1 kev to 1 GeV using WinXCom. From this study, we can conclude that all these parameters are dependent on the incident photon energy. This dependence is remarkable in the low incident photon energies (1-30keV) due to predominant photoelectric absorption process and in the intermediate and high energies. All these parameters are nearly constant due to predominance of the Compton scattering and pair production. Also, it can be concluded that the energy dependence of photon interaction cross section is identical to the total mass attenuation coefficient, and it is the same thing for the electron density and the effective atomic number. Table 2: The Values of the Total Mass Attenuation, the Photon Interaction Cross Section, the Effective Atomic Numbers and the Effective Electron Density for Earth Atmosphere Energy(MeV) (μ t ) (σ t,m ) (σ t,a ) (σ t,e ) (Z eff ) (N eff ) 1.00E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+23

8 84 Y. Elmahroug, B. Tellili & C. Souga Table 2 :Contd., 3.00E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E+23 REFERENCES 1. Clouvas A, Xanthos S, Antonopoulos-Domis M, Silva J (2000). Monte Carlo calculation of dose rate conversion factors for external exposure to photon emitters in soil. Health Phys 78, Berger MJ, Hubbell JH (1987). Report. NBSIR 87, XCOM, Photon cross sections on a personal computer. 3597, 3. Gerward L, Guilbert N, Jensen K.B, Levring H (2001). X-ray absorption in matter. Reengineering XCOM. Radiat. Phys.Chem. 60: Gerward L, Guilbert N, Jensen K.B, Levring H (2004). WinXCom a program for calculating X-ray attenuation coefficients. Radiat. Phys.Chem. 71: Gowda S, Krishnaveni S, Gowda R (2005).Studies on effective atomic numbers and electron densities in amino acids and sugars in the energy range kev. Nucl. Instrum. Meth. B. 239: Heicklen J (1976). Atmospheric Chemistry. New York, Academic Press. 7. Hobbs P.V (2000). Introduction to Atmospheric Chemistry. Cambridge University Press. 8. Holland H.D (1978). The Chemistry of the Atmosphere and Oceans. New York, John Wiley & Sons. 9. Hubbell J.H (1982). Photon mass attenuation and energy-absorption coefficients. Int. J. Appl. Radiat. Isot. 33: Hubbell J.H, Seltzer S.M (1995). Tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients from 1 kev 20 MeV for elements Z = 1 to 92 and 48 additional substances of dosimetric interest. NISTIR Hubbell J.H (1999). Review of photon interaction cross section data in the medical and biological context. Phys. Med. Biol. 44(1). 12. İçelli O, Yalçın Z, Okutan M, Boncukçuoğlu R, Şen A (2011). The determination of the total mass attenuation coefficients and the effective atomic numbers for concentrated colemanite and Emet colemanite clay. Ann. Nucl. Energy 38: Jackson D.F, Hawkes D.J (1981). X-ray attenuation coefficients of elements and mixtures. Physics Reports. 70: Kocher D.C, Sjoreen A.L (1985). Dose rate conversion factors for external exposure to photon emitters in soil. Health Phys 48: Likar A, Vidmar T, Pucelj B (1998). Monte Carlo determination of gamma-ray dose rate with the Geant system, Health Phys 75,

9 Calculation of Total Mass Attenuation Coefficients, Effective Atomic 85 Numbers and Effective Electron Densities for the Earth Atmosphere 16. Manohara SR, Hanagodimath SM, Thind KS, Gerward L (2008). On the effective atomic number and electron density, a comprehensive set of formulas for all types of materials and energies above 1 kev. Nucl. Instr. Meth. B, 266: McEwan M.J, Phillips L.F (1975). Chemistry of the Atmosphere. New York, John Wiley & Sons. 18. Saito K, Jacob P (1995). Gamma ray fields in air due to sources in ground. Radiat. Protect. Dosim. 58: Seinfeld J.H, Pandis S.N (2006). Atmospheric Chemistry and Physics: From Air Pollution to Climate Change (2nd Ed.). John Wiley and Sons. 20. Warneck P (2000). Chemistry of the Natural Atmosphere (2nd Ed.). Academic Press. 21. Wayne R.P (2000). Chemistry of Atmospheres (3rd Ed.). Oxford University Press.

10