## 3 Results and Discussion
### Radiation Shielding Properties  
The radiation attenuation parameters, such as the mass attenuation coefficient (\(\upmu\)m), the total linear attenuation coefficient (\(\upmu\)), the half-value layer (HVL), the tenth-value layer (MVL), and the mean free path (MFP), were used to quantify the interaction of photons with the material. The values of these parameters were estimated using the Phy-X/PSD  
Figure 1: Variation of density and molar volume as a function of glasses’ composition for (**a**) PS, (**b**) PSC, (**c**) PSE, and (**d**) PSY systems. program in the energy range of 0.015-15 MeV [23]. For this energy range, the main photon interaction processes with matter are photoelectric absorption, Compton scattering, and pair production. The photoelectric effect predominates at low photon energies, E \(<\) 0.1 MeV, and always occurs during interactions with bound electrons. The probability of this mechanism is higher for materials with a large atomic number (Z) and increases as the photon energy approaches the binding energy of electrons in the atomic K, L, and M shells, after which it decreases abruptly because the electrons are too tightly bound to be displaced from the atom [4]. Table 1 presents the binding energy values of electrons in the K, L, and M shells of the constituent atoms in the studied systems. Through the photoelectric effect, the target atom fully absorbs the energy of the incident photon. Compton scattering predominates at intermediate energies, E\(\sim\)1 MeV, and involves the scattering of photons by free electrons, with the photons altering only their direction and energy, which is transferred to the electron. The pair production process occurs when a photon interacts with the electric field of a charged particle, resulting in the annihilation of the photon, while its energy is used to generate electron-positron pairs. This effect occurs at high energies, E \(>\) 1.02 MeV, but the changes become significant at even higher energies, specifically E \(>\) 10 MeV. The likelihood of photons interacting with a barrier is known as the material's mass attenuation coefficient (\(\upmu\)m). Higher MAC of a material at a particular radiation energy indicates its higher protection ability. In Figure 2, the logarithmic-scale dependence of the energy and the compositional content on the mass attenuation coefficient, \(\upmu\)m, for the PS, PSC, PSE, and PSY systems in the energy range of 0.015-15 MeV is presented. The evolution of the graphs for the four systems indicates a discontinuous decrease in the values of \(\upmu\)m as the energy of the incident photons increases; therefore, attenuation decreases with the increase in photon energy. As shown in Figure 3, the interaction of photons with the binding energy of electrons in the K shell of Pb, consistent with the values summarized in Table 1, leads to a sudden increase in \(\upmu\)m when E = 0.1 MeV. The pair production effect can be observed in the same figure at high energies, specifically when E \(\geq\) 0.8 MeV. Here, \(\upmu\)m increases with photon energy from 0.044 to 0.052 MeV (at 15 MeV), and the values are significantly similar for all systems. It was also found that the reduction of PbO\({}_{2}\) content in the network in favor of SiO\({}_{2}\) significantly affects \(\upmu\)m. The drastic decrease in \(\upmu\)m values from 96.89 to 73.43 cm\({}^{2}\)/g is associated with a decrease in the total molecular mass of the components, from 239.19 to 135.31 g/mol, as well as a decrease in the density as the SiO\({}_{2}\) content in the network increases. For the PSC and PSE systems, \(\upmu\)m shows an insignificant decrease at low energies, from 91.51 to 90.95 cm\({}^{2}\)/g with an increase in CeO\({}_{2}\) concentration and from 91.51 to 91.30 cm\({}^{2}\)/g with an increase in Eu\({}_{2}\)O\({}_{3}\) content.