## 3 Results and Discussion
### Radiation Shielding Properties
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Element**} & **Atomic** & **Atomic Mass,** & & & & \\  & **Number, Z** & **g/mol** & **K** & **L1** & **L2** & **L3** & **Oxide Density,** \\  & & & & & & & **g/cm\({}^{3}\)** \\ \hline
**Pb** & 82 & 207.2 & 88,004.5 & 15,860.8 & 15,200 & 13,035.2 & 9.31 \\ \hline
**Si** & 14 & 28.09 & 1838.9 & 148.7 & 99.2 & 99.2 & 2.26 \\ \hline
**Ce** & 58 & 140.12 & 40,443.0 & 6548.8 & 6164.2 & 5723.4 & 6.2 \\ \hline
**Eu** & 63 & 151.97 & 48,519.0 & 8052.0 & 7617.1 & 6976.9 & 7.40 \\ \hline
**Yb** & 70 & 173.04 & 61,332.3 & 10,486.4 & 9978.2 & 8943.6 & 9.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Binding energy values (eV) of electrons in the K, L, and M shells of the constituent atoms in the studied systems. Additionally, as the content of CeO\({}_{2}\) and Eu\({}_{2}\)O\({}_{3}\) increases, an enhanced radiation attenuation effect is observed at energies between 0.05 and 0.08 MeV due to the binding energy of electrons in the K shell of Ce and Eu. Due to the photoelectric effect, \(\upmu\)m values for the PSY system show a slight increase at low energies (E = 0.01 MeV), from 91.51 to 91.77 cm\({}^{2}\)/g with an increase in Yb\({}_{2}\)O\({}_{3}\) content, associated with photon interactions with the binding energy of electrons in the L shell of Pb and Yb. As the photon energy increases, 0.02 \(\leq\) E \(\leq\) 0.06 MeV, \(\upmu\)m decreases linearly, followed by an increase at E = 0.08 MeV from 2.005 to 2.083 MeV as Yb\({}_{2}\)O\({}_{3}\) content increases due to the interaction of photons with the binding energy of electrons in the K shell of Yb. A comparative analysis of the investigated samples highlights that increasing the concentration of Yb\({}_{2}\)O\({}_{3}\) enhances the interaction between the incident photon and the material. The PSY6 sample has the highest density and \(\upmu\)m value, and the number of photons absorbed by this composition is the largest compared to the other samples. In Figure 3, the linear attenuation coefficient (\(\upmu\)) is presented on a logarithmic scale as a function of the energy of the incident photons and the compositional content of the PS, PSC, PSE, and PSY systems in the energy range of 0.015-15 MeV. The evolution of the graphs suggests that the linear attenuation coefficient decreases significantly as the PbO\({}_{2}\) content in the PS system decreases, from 654.03 to 387.73 cm  
Figure 2: Variation in mass attenuation coefficients, \(\upmu\)m, as a function of photon energy for (**a**) PS, (**b**) PSC, (**c**) PSE, and (**d**) PSY glass samples. at E = 0.01 MeV, and it increases with the rise in RE content. Specifically, \(\mu\) increases from 614.04 to 633.01 cm\({}^{-1}\) for the PSC system to 623.52 cm\({}^{-1}\) and 641.47 cm\({}^{-1}\) for the PSE and PSY systems, respectively. Furthermore, the graphical representation shows a decrease in \(\mu\) values as photon energy increases, except for energies where the photoelectric effect (due to the K level of the Pb atom, at E = 0.1 MeV) and electron-positron pair production occur (\(0.8\leq\) E \(\leq 15\) MeV). The results' analysis indicates that \(\mu\) variations depend on the density of the investigated samples, with high \(\mu\) values attributed to the large atomic number of Pb. High \(\mu\) values for a given material indicate excellent attenuation properties; thus, such a material has superior radiation shielding characteristics. The HVL (half-value layer) represents the thickness or the semi-attenuation layer that reduces gamma radiation beam exposure by 50%. Figure 4 illustrates the dependence of HVL on photon energy and the compositional content of the PS, PSC, PSE, and PSY systems. As shown in the figure, HVL values increase with photon energy up to 4 MeV, after which they decrease slightly as photon energy continues to rise.