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International Journal of Physics and Research (IJPR) ISSN 2250-0030 Vol. 3, Issue 3, Aug 2013, 87-96 © TJPRC Pvt. Ltd.

DETERMINATION OF TOTAL MASS ATTENUATION COEFFICIENTS, EFFECTIVE ATOMIC NUMBERS AND EFFECTIVE ELECTRON DENSITY FOR THE MARTIAN ATMOSPHERE B. TELLILI1, Y. ELMAHROUG2 & C. SOUGA3 1

Université de Tunis El Manar, Faculté des Sciences de Tunis, Unité de Recherche de Physique Nucléaire et des Hautes Energies, Tunis, Tunisie 2

Université de Tunis El Manar, Institut Supérieur des Technologies Médicales de Tunis, Tunis, Tunisie 3

Université de Carthage, Ecole Polytechnique de Tunisie, La Marsa, Tunisie

ABSTRACT Ionizing radiations on Mars have harmful effects on astronauts health and equipment functioning, they originate from three main sources: Galactic Cosmic Rays (GCR), Solar Particle Events (SPEs) and secondary particles (neutrons and gamma rays). Thus, the understanding of these ionizing radiations is essential for future Mars manned missions. In this paper, the interaction of gamma-rays with the Martian atmosphere has been studied. The total mass attenuation coefficients, the effective atomic numbers and the effective electron density for Martian atmosphere have been calculated by theoretical approach using the WinXCOM program in the energy range from 1 keV to 1 GeV. The variation of different parameters with photon energy is discussed.

KEYWORDS: Attenuation Coefficients, Cross-Sections, Effective Atomic Number, Effective Electron Density, Martian Atmosphere

INTRODUCTION In order to explore the planet Mars by manned missions in the future , the protection of astronauts and equipment from exposure to ionising radiation is one of major problems to be solved to assure the safety of human activity on the Martian surface . Therefore, the knowledge about the Martian radiation environment and the estimate of risks due to exposure to ionizing radiation is a paramount importance for future manned missions to Mars (Borggrüafe et al., 2009; Cucinotta et al., 2001; Gurtner et al., 2005; McKenna-Lawlor et al., 2012). Sources that contribute to the Martian radiation environment are generally classified into three types: Galactic Cosmic Rays (GCR), Solar Particle Events (SPEs) and secondary particles (gamma rays and neutrons) (De Angelis et al., 2007). The secondary particles are generated during interaction of GCR and SPEs with the Martian atmosphere. The determining of physical parameters which describe the interaction of these ionizing radiations with the Martian atmosphere is important to estimate in detail the risks and effects of ionizing radiation on spacecraft equipment and astronauts participating in the future Martian manned missions. In this study, the interaction of X and gamma-rays with Martian atmosphere has been investigated. The total mass attenuation coefficients (μt), the effective atomic number (Zeff ), the effective electron density (Neff), 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 ,


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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 (Zeff). 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 (Zeff), but it is not 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 (Neff) 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 (Akkurt I et al., 2009; Saim et al., 2012). 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 Martian atmosphere is given in Table 1 (Encrenaz et al.,1991 ; Krasnopolsky, 2009; Maguire, 1977; Owen et al., 1977).

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, (μlinear) 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 μt = μlinear/ ρ is the total mass attenuation coefficient (g-1cm-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 (μt,compd)i and Wi are respectively the total mass attenuation coefficient and fractional weight of ith constituent (element or compound) in the mixture, (μt)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)


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Where, (σph) is the photoelectric cross-section, (σcoh) is the coherent scattering cross-section, (σincoh) is the incoherent scattering cross section, κn 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 (σt,m) is proportional to the total mass attenuation coefficient of the mixture, (μt,mix) , through the following relation (İçelli et al., 2011);

(4) Where NA is the Avogadro’s number and nj and Aj 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 (σt,a) can be evaluated from the total molecular effective cross section of the mixture (σt,m), using the following relation (Jackson and Hawkes, 1981);

(5) Where, ntotal is the total number of atoms in the mixture chemical formula. The Total Electronic Cross-Section The total electronic effective cross-section (σt,e) is given by the following formula (Jackson and Hawkes, 1981);

(6) Where (μt)j ,fj and Zj 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 (Zeff ) 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 (Neff) (the electrons number per unit mass, electron/g) is determined by the following formula (Jackson and Hawkes, 1981);

(8)


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Where (Atotal) is the total atomic weight of the mixture. Table 1: Elemental Composition of Martian Atmosphere Constituents CO2 N2 Ar O2 CO H2O Ne He Kr O3 H2 Xe CH4 H2O2 C2H4 C2H C2H6 NO N2O PH3 OCS S02 H2S NH3 CH2O C2H2 HCl

Percentage by Volume 9.53E+01 2.70E+00 1.60E+00 2.00E-01 8.00E-02 5.00E-02 2.50E-02 1.70E-02 3.00E-03 2.00E-03 1.84E-03 8.00E-04 1.00E-04 1.00E-04 5.00E-05 4.00E-05 4.00E-05 1.70E-05 1.00E-05 1.00E-05 7.00E-06 3.00E-06 2.00E-06 5.00E-07 3.00E-07 2.00E-07 1.00E-07

RESULTS AND DISCUSSIONS We have determined the partial mass attenuation coefficients for different photon interaction processes (coherent scattering, incoherent scattering, photoelectric absorption and pair production), the mass attenuation coefficients for each chemical element of the Martian atmosphere and the total mass attenuation coefficient (μt) for Martian atmosphere, for energies ranging from1 keV to 1 GeV, using the WinXCOM program. From these results, we have calculated the total effective molecular (σt,m), the atomic (σt;a) and electronic cross-sections (σt,e), the effective atomic number (Zeff ), and the effective electron density (Neff ) for Martian atmosphere. The values of these parameters are listed in Table 2. Total Mass Attenuation Coefficients The mass attenuation coefficient (μt) for Martian atmosphere, has been shown graphically in Figure1, it is clear that the (μt) is not constant but varies as a function of the incident photon energy, in the low incident photon energies (130keV), it decreases rapidly (3.91 x 103 at 1 keV to 3.82 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 photon interaction processes 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 Martian atmosphere. It is clear that in the low energy region, the photoelectric absorption is the dominant process and the contribution


Determination of Total Mass Attenuation Coefficients, Effective Atomic Numbers and Effective Electron Density for the Martian Atmosphere

91

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. Then, it becomes almost constant up to 150 keV and from this value it decreases slowly. The behaviour 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 (Îźt) 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 (Îźt) remains almost constant in the high photon energy region.

Figure 1: Variation of Total Mass Attenuation Coefficients versus Incident Photon Energy for the Martian Atmosphere

Figure 2: Variation of the Partial Mass Attenuation Coefficients of the Different Photon Interaction Processes versus Incident Photon Energy for the Martian Atmosphere


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Effective Atomic Numbers and Effective Electron Density Effective Atomic Numbers The variation of (Zeff ) values versus photon energy is presented in Figure 3, it is clearly seen that the (Zeff ) are not constant but depends on the photon energy. Initially, the (Z eff) values of the atmosphere increase with increasing of photon energy, and at 3 keV it reaches its maximum which is 17.32, and from this value it decreases rapidly and at 30 keV it find its minimum which is 12.75 up to the incident photon energy 30 keV . After, it increases slowly up to the photon energy of about 10 MeV. Beyond this energy, (Z eff) values become almost constant. The variation of (Z eff) is due to the fact that the photons interaction processes with the matter is different for different 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 2x1024 and 1.47 x 1024, 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 Martian Atmosphere

Figure 4: Variation of Effective Electron Density versus Incident Photon Energy for the Martian Atmosphere

CONCLUSIONS In this work, the values of the total mass attenuation coefficient (Îźt), the photon interaction cross section for


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Determination of Total Mass Attenuation Coefficients, Effective Atomic Numbers and Effective Electron Density for the Martian Atmosphere

Martian atmosphere, have been calculated in the energy region from 1 keV to 100 GeV using WinXCom. Whereas the effective atomic numbers and the effective electron density were determined theoretically using the obtained (μt) values. 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 predominance of photoelectric absorption process. In this region, the total mass attenuation coefficient and photon interaction cross sections decrease rapidly with the increasing of the incident photon energy and we also note that the maximum values of the total mass attenuation coefficient (μt), the photon interaction cross section, the effective atomic numbers and the effective electron densities are obtained in this region.Therefore, the photon absorption by the atmosphere in the lower energy region is maximum. 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 the electron density is identical to 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 Martian Atmosphere Energy(MeV) 1.00E-03 2.00E-03 3.00E-03 4.00E-03 5.00E-03 6.00E-03 8.00E-03 1.00E-02 2.00E-02 3.00E-02 4.00E-02 5.00E-02 6.00E-02 8.00E-02 1.00E-01 2.00E-01 3.00E-01 4.00E-01 5.00E-01 6.00E-01 8.00E-01 1.00E+00 2.00E+00 3.00E+00 4.00E+00 5.00E+00 6.00E+00 7.00E+00 8.00E+00 9.00E+00 1.00E+01 2.00E+01 3.00E+01 4.00E+01 5.00E+01 6.00E+01 8.00E+01 1.00E+02 2.00E+02 3.00E+02 4.00E+02

(μt) 3.92E+03 5.85E+02 1.82E+02 8.78E+01 4.56E+01 2.66E+01 1.13E+01 5.82E+00 8.67E-01 3.80E-01 2.60E-01 2.14E-01 1.91E-01 1.68E-01 1.55E-01 1.23E-01 1.07E-01 9.55E-02 8.71E-02 8.06E-02 7.07E-02 6.36E-02 4.45E-02 3.58E-02 3.09E-02 2.76E-02 2.53E-02 2.37E-02 2.24E-02 2.14E-02 2.06E-02 1.73E-02 1.66E-02 1.64E-02 1.65E-02 1.66E-02 1.69E-02 1.72E-02 1.84E-02 1.90E-02 1.94E-02

(σt,m) 6.75E-18 1.01E-18 3.13E-19 1.51E-19 7.84E-20 4.57E-20 1.94E-20 1.00E-20 1.49E-21 6.54E-22 4.47E-22 3.68E-22 3.28E-22 2.89E-22 2.67E-22 2.12E-22 1.84E-22 1.64E-22 1.50E-22 1.39E-22 1.22E-22 1.09E-22 7.66E-23 6.17E-23 5.31E-23 4.75E-23 4.36E-23 4.07E-23 3.85E-23 3.68E-23 3.54E-23 2.97E-23 2.85E-23 2.82E-23 2.83E-23 2.85E-23 2.91E-23 2.96E-23 3.16E-23 3.27E-23 3.34E-23

(σt,a) 8.33E-20 1.24E-20 3.86E-21 1.87E-21 9.68E-22 5.64E-22 2.40E-22 1.24E-22 1.84E-23 8.07E-24 5.52E-24 4.54E-24 4.06E-24 3.56E-24 3.29E-24 2.62E-24 2.27E-24 2.03E-24 1.85E-24 1.71E-24 1.50E-24 1.35E-24 9.45E-25 7.61E-25 6.55E-25 5.86E-25 5.38E-25 5.02E-25 4.75E-25 4.54E-25 4.37E-25 3.67E-25 3.52E-25 3.48E-25 3.50E-25 3.52E-25 3.59E-25 3.66E-25 3.90E-25 4.03E-25 4.12E-25

(σt,e) 5.03E-21 7.29E-22 2.24E-22 1.32E-22 6.95E-23 4.09E-23 1.77E-23 9.24E-24 1.45E-24 6.51E-25 4.53E-25 3.75E-25 3.36E-25 2.97E-25 2.75E-25 2.19E-25 1.90E-25 1.70E-25 1.55E-25 1.43E-25 1.26E-25 1.13E-25 7.90E-26 6.35E-26 5.44E-26 4.85E-26 4.43E-26 4.12E-26 3.89E-26 3.70E-26 3.55E-26 2.90E-26 2.74E-26 2.69E-26 2.68E-26 2.69E-26 2.73E-26 2.77E-26 2.93E-26 3.03E-26 3.09E-26

(Zeff) 1.657E+01 1.705E+01 1.725E+01 1.412E+01 1.393E+01 1.378E+01 1.356E+01 1.339E+01 1.274E+01 1.240E+01 1.219E+01 1.210E+01 1.205E+01 1.200E+01 1.199E+01 1.196E+01 1.196E+01 1.195E+01 1.195E+01 1.195E+01 1.195E+01 1.195E+01 1.196E+01 1.199E+01 1.204E+01 1.209E+01 1.213E+01 1.219E+01 1.223E+01 1.227E+01 1.232E+01 1.264E+01 1.283E+01 1.294E+01 1.303E+01 1.308E+01 1.316E+01 1.321E+01 1.330E+01 1.332E+01 1.332E+01

(Neff) 1.921E+24 1.977E+24 2.000E+24 1.637E+24 1.615E+24 1.598E+24 1.572E+24 1.552E+24 1.477E+24 1.438E+24 1.414E+24 1.402E+24 1.397E+24 1.392E+24 1.390E+24 1.386E+24 1.386E+24 1.385E+24 1.385E+24 1.385E+24 1.385E+24 1.385E+24 1.387E+24 1.391E+24 1.396E+24 1.402E+24 1.407E+24 1.413E+24 1.418E+24 1.423E+24 1.428E+24 1.465E+24 1.487E+24 1.500E+24 1.511E+24 1.517E+24 1.526E+24 1.531E+24 1.542E+24 1.544E+24 1.545E+24


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5.00E+02 6.00E+02 8.00E+02 1.00E+03

1.97E-02 1.99E-02 2.02E-02 2.04E-02

Table 2: Contd., 3.39E-23 4.18E-25 3.14E-26 3.42E-23 4.22E-25 3.17E-26 3.47E-23 4.28E-25 3.22E-26 3.50E-23 4.33E-25 3.25E-26

1.333E+01 1.332E+01 1.333E+01 1.332E+01

1.545E+24 1.544E+24 1.545E+24 1.544E+24

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