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Abstract: In the present study, various photon interaction parameters such as mass attenuation coefficient, effective atomic number, electron density, mean free path, half value layer and tenth value layer have been computed for different compositions of Pb-Cu alloy systems in the wide energy region of 1 keV to 100 GeV. Further, the variation of these parameters with incident photon energy for different composition of alloys has been analyzed. The results obtained from the present computations are helpful for finding optimum thickness of these alloys and performing experimental verifications.
Keywords: Photon Interaction Parameters, Alloys
INTRODUCTION
The interaction of high energy photons with matter is important in various branches of science and technology such as physics, radiation, medicine, biology, nuclear engineering and space technology. An interaction of radiation leads to the partial or complete transfer of photon energy to electron energy either electron disappears or scattered by some angle. There are many possible interaction mechanisms by which gamma rays can interact with matter. However, three processes are more significant viz. photoelectric effect, Compton scattering and pair production.
The knowledge of photon interaction parameters such as mass attenuation coefficient (μm), effective atomic number (Zeff), electron density (Neff), mean free path (mfp), half value layer (HVL) and tenth value layer (TVL) plays an important role in understanding the properties of radiation shielding alloys. Mass attenuation coefficient measures that how strongly a substance absorbs or scatters radiation at different energy. Most of the researchers focused on studying the photon interaction parameters with the different types of matter. There are great number of experimental and theoretical investigations to determine (μm) values in various elements and compound/mixtures. Hubbel1 calculated μm values for 40 elements, 45 mixtures and compounds over the energy range from 1keV to 200MeV. The work was extended by Hubbel and Seltzer2 for all elements (Z=1-92) and 48 additional substances of dosimetric interest. Berger and Hubbell3 developed a program XCom for calculating mass attenuation coefficient for any element, compound or mixture in the wide energy region from 1 keV to 100 GeV. This program was transformed to the windows platform by Gerward et.al4 and the Windows version has been named as WinXCom.
Scattering and absorption of X-rays and γ rays are related to the density and atomic numbers of an element. However for compounds and mixtures, a single number cannot represent the atomic number uniquely across entire energy range, as the partial interaction cross section have different atomic number, Z, dependence5. This number is called the effective atomic number (Zeff). It a very useful parameter for the interpretation of attenuation of radiation by a compound/mixture and describes the properties of the compound/mixture and also plays a vital role in determining the effectiveness of shielding material. Hine5 reported it for the first time and suggested that effective atomic number (Zeff) of any compound/mixture may not be expressed by a single number for each process of interaction of gamma rays with matter. El-Kateb6 measured atomic cross section and effective atomic numbers for some alloys like brass, bronze, lead antimony in the energy region 81- 1332 KeV.
Unlike pure elements, the electron density (Ne) also varies with energy for compounds and mixtures. It is expressed in the units of e/g. It provides the average number of electrons per unit mass of the interacting material. T. Singh7 reported photon interaction parameter (mass attenuation coefficients, effective atomic number and electron density) for some commonly used solvents in the energy region of 1 keV-100 GeV.
Penetration depth/thickness of an interacting material is measured in the units of mean free path (mfp), where one mean free path (mfp) represents the average distance between two successive interactions of photons which results in decreasing the intensity of incident photon beam by the factor of 1/e. It is equal to the reciprocal of linear attenuation coefficient. Since, the linear attenuation coefficient is an energy dependent parameter; therefore the value of mean free path also varies with the variation in incident photon energy.
Further, other parameters which help in visualizing the shielding effectiveness of interacting materials are HVL and TVL. Half value layer8 (HVL) is the density of an absorber that will reduce the gamma radiation to half of its intensity. Tenth value layer (TVL) is the density of an absorber that will reduce the gamma radiation to tenth of its intensity. The units of HVL and TVL are g/cm2.
COMPUTATIONAL WORK
The computational work has been divided into three sub categories. The first category deals with generating mass attenuation coefficients values for the selected alloys as shown in Table 1. The Pb-Cu alloys will be prepared by pellet machine. Pellets of different composition are made by KBr press. Fixed pressure will be put on the uniformly mixed powder sample. The Second category deals with computational methodology for effective atomic numbers and finally third category deals with computations of electron density, half value layer and tenth value layer. Following samples are prepared in lab.
Results and Discussions
The variation of mass attenuation coefficient with photon energy for the selected alloys has been shown in Fig 1. The mass attenuation coefficient values decreases rapidly with the increase in energy in the lower energy region (below 300 keV). In the intermediate energy region (300 keV – 3.0 MeV), the mass attenuation coefficients decrease slowly with the energy and moreover same values were observed for different compositions of Pb-Cu alloys. Beyond 3.0 MeV, the mass attenuation coefficients increase slowly with the energy. This variation in mass attenuation coefficient can be explained on the basis of different photon interaction processes in different energy regions viz. photoelectric effect (lower energy region), Compton scattering (intermediate energy region) and pair production (high energy region). Further, it has been also found that the total mass attenuation coefficient values increases with the increasing in the concentration of the Pb in prepared alloy samples.
Fig. 2 shows the variation of effective atomic number with the energy for the prepared alloys. The variation in concentration of elements in the alloy samples results in an appreciable change in effective atomic number of the alloys. In the lower energy region, the drastic change in the effective atomic number of alloys can be explained on the basis of absorption edges of Cu and Pb elements. In the entire energy region, Zeff values lies between low atomic number constituent element i.e. 29Cu and high atomic number constituent element i.e. 82Pb. Fig. 3 shows the variation of electron density with energy for the selected alloy samples. Similar to the effective atomic number, the electron density also depends on photon energy. Higher is the value of electron density, more is the probability of photon interaction with electrons.
The variation of mean free path with the energy for the selected alloys has been shown in the Fig. 4. It has been found that mean free path (mfp) values were low in lower energy region; gradually increases with the increase in energy and becomes independent of photon energy in the higher energy region. The variation of mean free path of the alloys is dependent upon Z of elemental composition and densities.
Figs. 5 - 6 show the variation of half value layer (HVL) and tenth value layer (TVL) with energy respectively. The probability of interaction decreases with increase in energy. Hence, the thickness required to reduce the gamma ray intensity to one-half/one-tenth of its value is lower at lower energy and it increases with the energy.
Almost similar variation in mfp, HVL and TVL values of all the selected alloys with energy has been observed, which can be explained on the basis of mathematical expressions for these parameters.
Conclusion
Among the selected alloys, Pb80Cu20 offer maximum values for µm, Zeff, Ne; minimum values for mfp, HVL and TVL. Hence, it will offer better shielding from gamma rays than other selected alloys