The FLUKA (FLUktuierende KAskade in German, signifying fluctuating cascade) is a versatile Monte Carlo code widely employed in various physics research domains, including nuclear, accelerator, high energy, and particle physics (Ferrari et al., 2005; Battistoni et al., 2007; Mostafa et al., 2020b). A distinguishing feature of FLUKA compared to other Monte Carlo codes is its ability to operate in both adjustable and analogue modes. The Flair graphical interface, extensively used for radiobiological effect analysis, is incorporated in the current version (accessible at http://flair.cern), which introduces novel features such as advanced 3D visualization with photorealistic rendering and support for industry-standard volume depiction of medical phantoms.

FLUKA has been instrumental in determining radiation conditions for electronic components, assessing their reactions to diverse scenarios not covered by radiation testing regulations for space and accelerators, and beyond the scope of traditional ground-level testing. Users must provide the geometry, material, source properties, and scoring type for a specific problem using commands known as cards in a standard FLUKA input file (Mark et al., 2007; Rashad et al., 2020; Zakaly et al., 2022). The FLAIR graphical interface was employed to construct the input file necessary for calculating the mass attenuation coefficients of glass compositions in the 65TeO ₂ –(35-x)V ₂ O ₅ -xSm ₂ O ₃ system, where x ranges from 0.1 to 5 mol%, using the FLUKA algorithm (Figure 3). The DEFAULTS card in the input file is configured to EM-CASCAde, specifying FLUKA defaults for a particular problem type, and enabling electromagnetic interactions, Rayleigh scattering, and Compton scattering. Gamma energies of 0.356, 0.662, 1.332, and 2.614 MeV, commonly used in gamma shielding studies, were selected as the radiation source, oriented along the z-axis.

Table 1 presents the atomic number, mass number, and densities of the glass samples' elemental composition, determined using elemental mass fraction characteristics. Figure 3 illustrates the precise design of the geometry created for the FLUKA method, the body and region used in the simulation geometry, and a snapshot of the side, top, front, and rear views in the FLAIR geometry editor (Madbouly et al., 2022; Zhukovsky et al., 2022). The glass sample geometry was designed as a 5 cm radius circular cylinder parallel to the z-axis, segmented into various thicknesses using XYP planes (bounded by a plane perpendicular to the z-axis) (El-Taher et al., 2021).

After calculating the linear attenuation coefficient (G_LAC) by first measuring the intensities of the gamma rays that were incident (I_o) and transmitted (I), the resultant value was used to calculate the G_MAC. To get the values of the G_LAC, one must first calculate the slope of the linear graph that plots Ln (I/I_o) versus the specimen thickness. Figure 4 depicts Ln (I/I_o) vs. the sample thickness for all glasses measured at 356 keV; The patterns are almost identical for each and every photon energy. As additional Sm₂O₃ is added, the slope of the graph goes up, as can be seen in Figure 4. This happens on average. When the amount of Sm₂O₃ in the sample increases from 0.1 to 5 mol%, the slope of the graph increases from 0.506 to 0.568 at 356 keV (an example). The Glass in this specific set of glasses had the biggest gradient in the Glass with the highest concentration of Sm₂O₃, which may be interpreted as having the highest values of G_LAC in contrast to other glasses.

Take notice that the Z of Sm is 62, which is a much greater figure than the one for V (23). If a high percentage of Sm is included into the composition of the Glass, the gamma will be subjected to a more robust level of interaction with the Sm atoms that make up the Glass. Before an electron can be released from an Sm atom, a bigger quantity of photon energy must be absorbed. This is because the higher the Z, the more energy there is to absorb. It’s possible that the electron was ejected due to either the photoelectric effect (PE) or the Compton scattering (CS), but it was not both. The quantity of gamma rays that can pass through the Glass is reduced when there is a higher degree of interaction between the gamma and the target atom (Sm). This was a direct contributor to the increase in the G_MAC that occurred (Issa and Mostafa, 2017). The addition of the modulator to the Glass is another factor that led to the growth in the value of the G_MAC. It is believed that lowering the porosity nature of the Glass and generating high Glass can be accomplished by adding a high modifier (Sm₂O₃ = 8.347 g/cm³) into the glass system. This is because large modifiers have a greater surface area than low modifiers. Glass will have a stronger attenuation than other materials because it has a greater potential that gamma rays will interact with the atoms in Glass due to the fact that Glass has a lower porosity than other materials (Bagheri et al., 2017). This is because Glass has a lower porosity than other materials.

The G_MAC values for the TVS0.1, TVS0.5, TVS1, TVS2, TVS3, TVS4, and TVS5 samples are shown in Figure 5, at 356 keV; the patterns are almost identical for each photon energy (Table 2). If you look at the graph in Figure 5, you’ll see that the values of G_MAC increase whenever the concentration of Sm₂O₃ does as well. This is a phenomenon that may be seen for oneself. The 65TeO ₂ –(35-x)V ₂ O ₅ -xSm ₂ O ₃ glass system has the highest G_MAC values, which are respectively 0.121 cm²/g. This glass system also has the highest G_MAC value. As was to be expected based on the predictions, the largest G_MAC was produced by the glass system with the maximum possible concentration of Sm₂O₃. The higher the G_MAC values are, the better a given material is in attenuating a larger number of photons. At the energies that were explored, it was discovered that increasing the quantity of Sm₂O₃ in the glass samples led to an increase in the G_MAC. The presence of Sm₂O₃ in these materials causes an increase in both their effective atomic numbers and their densities. This is the rationale for this phenomenon. Compared to other glasses, TVS5 glass (Sm2O3 = 5 mol%) had the highest density, resulting in it having the highest G_MAC value. Other glasses were unable to compete with this density. Research demonstrated that the TVS5 glass had the highest possible amount of photon interaction at the energy level that was provided. This interaction could occur as a consequence of the PE, the CS, or the creation of pairs (PP) (Kilic et al., 2020).

How well the glasses protect against G_HVL photons is also discussed. It describes the sample thickness at which 50% of the incident radiation intensity is attenuated. In Figure 6, we have a depiction of the TVS0.1, TVS0.5, TVS1, TVS2, TVS3, TVS4, and TVS5 glasses' G_HVL at 356 keV. The patterns are almost identical for each photon energy (Table 3). The G_HVL varies directly as a function of energy (Issa et al., 2020). At 15 keV, the values are at their lowest (between 0.005 and 0.004 cm), while at 15 MeV, they reach their highest (between 4.849 and 4.310 cm). This finding suggests that a very thin layer is required to significantly reduce the intensity of the low-energy photons. Figure 6 demonstrates that there is a direct correlation between a rise in the density of the glasses and a commensurate drop in the G_HVL of the samples that were investigated. Because of this pattern in the G_HVL, it can be deduced that the TVS5 glass, which is the sample with the highest Sm2O3 content and density, is the most effective in blocking photons. The second specimen, TVS0.1, on the other hand, is the one, that is, the least effective in blocking photons because it has the least value and the least quantity of Sm₂O₃ concentration. We are able to provide an explanation for the previously indicated relationship between the G_HVL and the density of the TVS0.1, TVS0.5, TVS1, TVS2, TVS3, TVS4, and TVS5 glasses on the basis of the following: The likelihood of photons interacting with atoms of Glass is very low due to the fact that there is space between the atoms inside the low-density material that gamma rays pass over. As a direct consequence of this, the passage of the photons through the Glass is made a great deal easier. Because of this, we will need to increase the thickness of the sample in order to absorb the necessary fifty percent of the initial photons. This will lead to a high G_HVL for the low-density components. In contrast, there is a good chance that photons will interact with the high-density sample because of how dense it is. Because of this, the number of photons that were able to go through the Glass was significantly decreased, which in turn resulted in a decrease in the G_HVL of the high-density Glass. In considering the fact that the TVS5 has the smallest G_HVL value of all of the glasses that were studied, it is compared with a number of typical photons shielding glasses and concretes, as shown in Figure 7, at 356, 662, 1173, and 1333 keV. The G_HVL value of the TVS5 glass material is shown to have a value, that is, lower than the G_HVL values of the various kinds of glass materials and concretes shown in these figures. It indicates that this particular glass sample has a higher capacity for absorption than S1 (Aktas et al., 2019), S2 (Yalcin et al., 2019), S3 (Mhareb et al., 2020), PCNKBi7.5 (Al-Yousef et al., 2021), Pb20 (Singh et al., 2014), PbG (Al-Harbi et al., 2021), S5 (Singh et al., 2022), (OC, HSC, ILC, BMC, IC) concretes (Bashter, 1997). It has been shown that the Glass that was generated because of the ongoing study is more effective than other glasses and concretes when subjected to a certain photon energy. When these data are taken into consideration, it is feasible to reach the conclusion that TVS5 might be an alternative worth considering for usage as a material for radiation shielding.

In Figure 8; Table 4, the G_MFP was calculated based on the amount of Sm₂O₃ present in the sample. When it comes to radiation shielding technologies, a smaller G_MFP is preferred. As found in G_HVL, there is an inverse relationship between the G_MFP and the Sm₂O₃ concentration (Abouhaswa et al., 2021). A lower G_MFP is the result of increasing the Sm₂O₃ concentration. Due to the addition of 5 mol% of Sm₂O₃ to the TVS0.1, TVS0.5, TVS1, TVS2, TVS3, TVS4, and TVS5 glasses, the G_MFP has been reduced from 1.978 to 1.760 cm at an energy of 356 keV. The finding demonstrates that when there is a higher concentration of Sm₂O₃ in the glasses as well as a higher density, the G_MFP decreases, and the glasses become better at shielding radiation.

In addition, we can talk about Z_eff. This is an important quantity, that is, often used in the field of radiation shielding to understand how efficient TVS0.1, TVS0.5, TVS1, TVS2, TVS3, TVS4, and TVS5 glasses are in obstructing the path of incoming photons (Kamislioglu, 2021). Based on Z_eff, we are in a position to form an opinion about the way in which the glasses react when they are subjected to gamma radiation. If a specific attenuator has a high Z_eff value, this suggests that it is superior to other attenuators in terms of its ability to block the path of incoming photons (Lakshminarayana et al., 2020). The variation in Z_eff that takes place when the amount of energy is increased may be shown in Figure 9; Table 5 for the TVS0.1, TVS0.5, TVS1, TVS2, TVS3, TVS4, and TVS5 glasses. It is essential to take note that the Z_eff achieves its maximum value somewhere in the vicinity of 49.62 keV. Its value is 46.66 for TVS0.1, 46.93 for TVS0.5, 47.26 for TVS1, 47.88 for TVS2, 48.47 for TVS3, 49.01 for TVS4, and 49.52 for TVS5. In addition, we may infer from Figure 9; Table 5 that the incorporation of Sm₂O₃ increases the Z_eff values since these values are increased. Figure 9; Table 5 show that TVS5 has the greatest value for this parameter, while TVS0.1 has the lowest Z_eff value. We displayed the Z_eff for all TVS0.1, TVS0.5, TVS1, TVS2, TVS3, TVS4, and TVS5 glasses at 356 keV in order to demonstrate the accuracy of this discovery (Figure 9). When we go from TVS0.1 to TVS5, it is abundantly clear that the Z_eff is exhibiting an upward trend. According to these two data, the Glass with the composition of TVS5 is the most effective attenuator out of all the other glasses that were tested. Figure 10 shows the strong correlation between Z_eff and effective electron density (N_eff). This figure observed that the TVS5 has the highest N_eff value at 356 keV. In addition, Figure 11 shows the correlation between the effective atomic number (Z_eff) and the density of glasses. While Figure 12 presents the correlation between (G_MAC, G_HVL, and G_MFP) and effective atomic number (Z_eff) of glasses. As seen in these figures, the Z_eff of glasses strongly correlated to the density of glasses, which affected G_MAC, G_HVL, and G_MFP.

The nuclear photon build-up factor needs to be taken into consideration while gathering nuclear data for things like radiation shielding and dosimetry. The build-up factor is a measure of the proportion of the target, that is, contributed by photons that have collided. In this investigation, the geometry progressive (G-P) approach was used to calculate the values for the exposure build-up factor (EBF) and the energy absorption build-up factor (EABF) (Issa et al., 2017) (Supplementary Tables S1–S7). An earlier publication has all the material necessary to understand the G-P approach (Singh and Badiger, 2014). As a result, the relationship between the energy of the incoming photons and the variations in the EBF and EABF can be shown in Figure 13 for TVS0.1, TVS0.5, TVS1, TVS2, TVS3, TVS4, and TVS5 glass samples with penetration depths up to 40 mfp. The depth-dependent absorbance increases as the input energy lowers until it reaches its highest amount in the medium energy field, at which time it begins to fall. This continues till the depth-dependent absorption completely cancels out the medium energy field. Most of the gamma-ray absorption takes place in the lesser energy region, where PE predominates, and the high energy range, where PP predominates, both of which have little particle build-up. On the other hand, CS is the process, that is, seen the most often for photon-matter interaction at intermediate energies; yet it does not account for absolute photon loss. As a direct consequence of this, the EBF levels in the CS area are the highest (Sayyed et al., 2017). Apart from the fact that EBF levels might vary from area to region, it was discovered that the TVS5 sample had the lowest EBF values of all the samples that were analyzed (Figure 13C). The phrase energy absorption build-up factor (EABF) refers to the photon accumulation factor, with the quantity of interest being the energy, that is, absorbed or deposited in the material of interest. EABF values demonstrated a similar trend to EBF values. Because of this, the TVS5 sample also provided the lowest values for EABF (Figure 13D).