Abstract
The WinXCom program has been used to calculate the mass attenuation coefficients (μm), effective atomic numbers (Zeff), effective electron densities (Nel), half-value layer (HVL), and mean free path (MFP) in the energy range 1 keV–100 GeV for Gd3Al2Ga3O12Ce (GAGOC) and CaMoO4 (CMO) scintillator materials. The geometrical progression (G-P) method has been used to compute the exposure buildup factors (EBF) and gamma ray energy absorption (EABF) in the photon energy range 0.015–15 MeV and up to a 40 penetration depth (mfp). In addition, the values of the removal cross section for a fast neutron have been calculated. The computed data observes that GAGOC showed excellent γ-rays and neutrons sensing a response in the broad energy range. This work could be useful for nuclear radiation sensors, detectors, nuclear medicine applications (medical imaging and mammography), nuclear engineering, and space technology.
1. Introduction
Due to the great importance of inorganic scintillator materials in the field of ionizing nuclear radiation detection, they are a very suitable to utilize in many applications such as technology of space, the design of nuclear devices, and medicinal diagnostics [1]. To develop the new scintillator materials, the knowledge of mass attenuation coefficient (μm) is very considered for scintillators because the results of μm show the probability of interaction. Furthermore, when the gamma ray interacts with the material, the half-value layer (HVL), mean free path (MFP), effective atomic number (Zeff), effective electron density (Nel), exposure buildup factors (EBF), and gamma ray energy absorption (EABF) are the fundamental quantities required to explain the penetration of nuclear radiation in matter. HVL, MFP, Zeff, Nel, EBF, and EABF parameters can be computed utilizing the values of μm [2]. Precise μm values are wanted to provide fundamental results in many nuclear radiation fields like computerized tomography, radiation shielding, nuclear radiation dosimeter, fluorescence of gamma ray, and safety inspection [3]. Various other researchers reported the properties of gamma radiation shielding for alloys, multielemental materials, soils, solutions, polyvinyl alcohol, and biological materials [4–11].
Hine [12] suggested a number of composite changes with energy called effective atomic number (Zeff) to characterize the atomic number of mixed materials with energy. Due to the high light yield, speedy decay time, high density, high Zeff, and good energy resolution of GAGOC scintillator materials, it is a great nominee for many applications like gamma spectroscopy and position emission tomography (PET) [13]; furthermore, GAGOC does not have natural radioactivity [14]. Because there is lack of knowledge of gamma ray and neutron interaction with GAGOC and CMO scintillator materials, μm, HVL, MFP, Zeff, Nel, EBF, and EABF have been investigated in a broad energy range. The values have been computed for μm, HVL, MFP, Zeff, and Nel in the energy range 1 keV–100 GeV and for EBF and EABF in the energy range 0.015–15 MeV using the WinXCom program. Also, the macroscopic fast neutron removal cross section has been calculated.
2. Theory
Photoelectric effect, Compton scattering, and pair production mechanisms can explain the interaction of photons with the GAGOC and CMO scintillator materials. If the intensity of the initial beam penetrates the sample which is I0, the intensity of the beam will be attenuated and exponentially decreased to I according to the Beer–Lambert law. where I0 is the intensity of bombarding beam, I is the intensity of transmitting beam, ρ is the density of scintillator samples (g/cm3), and d is the thickness of the samples (cm). The total photon interaction cross section (σt) of the samples has been calculated with the help of the μm according to the following equation: where the molecular weight of the sample, Ai is the atomic weight of the ith element, ni is the number of the formula units of a molecule, and NA is the Avogadro’s number. Effective atomic cross section, σa, has been calculated using the following equation:
Total electronic cross section, σe, has been calculated by where fi indicates to the fractional abundance of the element i and Zi the atomic number of the constituent element. The Zeff is related to σa and σe through the following equation:
The effective electron densities (Nel) of GAGOC and CMO have been calculated from the following:
Half-value thickness (HVL) is the thickness of any given material where 50% of the incident energy has been attenuated and has been computed utilizing the linear attenuation coefficient (μ) through the following equation:
One of the other values that are calculated in this study of GAGOC and CMO is the mean free path (MFP) which is described in [15, 16]. For the detailed knowledge on calculations of the parameters of G-P fitting, exposure buildup factor and energy absorption buildup factor, the element G-P fitting parameters have been taken from the ANSI/ANS 6.4.3 [17].
Finally, the removal cross sections for fast neutrons for GAGOC and CMO materials can be calculated using the following equations: where ρi is the partial density and is the mass removal cross section of the ith element which is taken from Kaplan and Chilten [18, 19].
3. Results and Discussion
3.1. Mass Attenuation Coefficient (μm)
Coherent scattering, incoherent scattering, photoelectric absorption, nuclear pair production, and electron pair production are the interaction processes of photon energy with matter. These interaction processes can explain the dependency of total mass attenuation coefficient (μm) on the photon energy, as shown in Figure 1 for GAGOC. This figure shows that the low photon energy range (E < 0.3 MeV), intermediate photon energy range (0.3 < E < 5 MeV), and high photon energy range (E > 5 MeV) are the three photon energy ranges in interaction processes. Figure 2 shows the calculated μm values of GAGOC and CMO scintillator materials. As shown in Figure 2, the μm values of the samples decrease quickly, from 3.50 × 103 to 1.68 × 10−1cm2/g and 4.81 × 103 to 1.17 × 10−1cm2/g for GAGOC and CMO, respectively, as the photon energy increases up to 0.3 MeV. In this photon energy range, the K-, L-, and M-absorption edges have been observed of Al, Ca, Ga, Mo, Ce, and Gd as shown in Table 1 due to the photoelectric effect. This behavior of μm with photon energy may be attributed to the photoelectric absorption cross section which is relative to E3.5. In the photon energy range 0.3 < E < 5 MeV, the μm values of GAGOC and CMO scintillator materials change slowly, form 0.01179 to 0.0345 cm2/g and 0.0971 to 0.0317 cm2/g for GAGOC and CMO, respectively. The difference of the μm values becomes approximately equal to zero as shown in Figure 2. This is because the process of Compton scattering is a predominant mechanism [20]. Since, the Compton scattering cross-section process is relative to E−1 and linearly changes with the Z number. Figure 2 shows that, as the photon energy increases from 5 MeV to 100 GeV, the values of μm increase slowly, becoming constant and highly dependent on the composition of samples. This may be attributed to the fact that the pair production process is a predominant mechanism. The results show that the GAGOC scintillator material has higher μm than CMO.
3.2. HVL and MFP
The HVL and MFP results are the most suitable quantities describing the radiation attenuation. For a best radiation shielding mixture, lower HVL and MFP values are required. The values of the half-value layer as a function of photon energy are plotted in Figure 3. In the photon energy range 1–100 keV, the values of the half-value layer are photon energy and sample composition independent. The half-value layer values increase when the photon energy increases up to 6 and 10 MeV for GAGOC and CMO, respectively. Above 2000 MeV, the HVL values are dependent on the composition of GAGOC and CMO. The values of HVL for GAGOC are lower than those for CMO [21].
As shown in Figure 4, the values of the mean free path (MFP) increase with increasing photon energy. In the photon energy range 1–300 keV and 1–150 keV, the MFP values are <1 for GAGOC and CMO. Above 5 MeV, the values of MFP are dependent on the composition of the GAGOC and CMO samples. The values of MFP for GAGOC are lower than those for CMO. The results of HVL and MFP indicate that the GAGOC compound is the excellent γ-ray sensing a response in the broad energy range.
3.3. Effective Atomic Numbers () and Electron Densities ()
Figure 5 shows Zeff as a function of photon energy for GAGCO and CMO scintillator materials. In the photon energy range 1 keV–100 GeV, the values of Zeff are dependent on the composition of GAGCO and CMO scintillator materials. As shown in Figure 5, there are two peaks at 10 and 60 keV for GAGCO due to the K-absorption edges of Ga and Gd, respectively. The other two peaks for CMO at 4 and 20 keV are due to the K-absorption edges of Ca and Mo, respectively. In the photon energy range 0.03–1 MeV, the values of Zeff decrease rapidly as the photon energy increases and then increase slowly up to 200 MeV. As the photon energy increases up to 100 GeV, the values of Zeff become nearly constant for both scintillator materials. It is worth noting that different values of Zeff occur due to their corresponding K-absorption edges. We have calculated the Zeff values at K-edge energies of the constituent elements of the scintillators and obtained two possible Zeff values, one corresponding to the lower side and the other to the upper side of the same energy (Table 2) [22].
The Nel results of the investigated GAGCO and CMO scintillator materials in the photon energy 1 keV–100 GeV have been computed according to (6). There are slight variations in Nel results for various GAGCO and CMO scintillator materials where a higher result of Nel would indicate an increased probability of photon–electron energy transfer and energy deposition into the material. The results of Nel present identical photon energy dependence to what was observed for Zeff [23]. This behavior has been confirmed in Figure 6 which showing a correlation of Zeff and Nel.
Besides, the calculated μm and Zeff values of GAGOC and CMO scintillators were compared with the experimental values at different energies for the two scintillator materials taken from [1] and the results were shown in Table 3. In general, it can be seen that the experimental μm and Zeff values show good agreement with the theoretical values.
3.4. Exposure Buildup Factors (EBF) and Gamma Ray Energy Absorption (EABF)
Equivalent atomic number (Zeq) and G-P exposure (EBF) and energy absorption (EABF) buildup factor coefficients of GAGOC and CMO are listed in Tables 4 and 5. The variation of EBF and EABF values with photon energy at 1, 10, 20, 30, and 40 mfp of GAGCO and CMO scintillator materials has been presented in Figure 7. This figure shows that the maximum values of EBF and EABF are dependent on the composition of scintillator materials and penetration depth and shifted to higher energy. Also, it is clear that the EBF and EABF values increase up to the maximum value with increase in photon energy and then decrease with further increase in photon energy. In the low-photon energy region, the EBF and EABF values are smallest because a great number of photons were absorbed because the predominant interaction process is the photoelectric effect. In the intermediate photon energy region, the EBF and EABF values are highest because the predominant interaction process is the Compton scattering. In the high-energy region, the photons have been absorbed again because the predominant interaction process is the pair production. The EBF and EABF results of GAGCO and CMO observe sharp peaks at 20 and 60 keV which may be attributed to K-absorption edges of Mo and Gd, respectively. Due to the occurrence of multiple scatterings at high penetration depths, the highest values of EBF and EABF were observed at a penetration depth of 40 mfp while the lowest values were observed at 1 mfp. Figures 8 and 9 show the variation of buildup factors (EBF and EABF) with incident photon energy for GAGCO and CMO at different penetration depths (1, 10, 20, and 40 mfp). It is clear that at the selected penetration depths, the GAGCO in general has the lowest EBF and EABF values which emphasize that the GAGCO compound is superior as a gamma ray sensor material.
3.5. Fast Neutron Removal Cross Section
The removal cross section for fast neutron of GAGCO and CMO scintillator materials is listed in Table 6. The values of are 0.121 and 0.048 cm−1 for GAGCO and CMO, respectively. The height value of was found for GAGCO—this may be attributed to the fact that the elements that have a high Z number are greatly accountable to the removal of fast neutrons as the elements that have a low Z number do [23].
4. Conclusions
The gamma ray mass attenuation coefficient, half-value layer, mean free path, effective atomic number, and effective electron densities have been calculated using the WinXCom program in the energy range 1 keV–100 GeV of GAGCO and CMO scintillator materials. The EBF and EABF values in the energy range 0.015–15 MeV and penetration depth of up to 40 mfp have been computed using the G-P fitting parameter method for GAGCO and CMO scintillator materials. In addition, the values of removal cross section for fast neutrons have been calculated. The calculated values present that the GAGCO showed excellent γ-rays and neutrons sensing a response in the broad energy range due to higher values for mass attenuation coefficient and effective atomic number and lower values for the half-value layer, mean free path, and buildup factors.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
The authors gratefully acknowledge the financial support for this study which is from the Malaysian Ministry of Higher Education (MOHE) through the Fundamental Research Grant Scheme, and also, the financial support from the University of Tabuk and Al-Azhar University is gratefully acknowledged.