## 3 Results and Discussion
### Radiation Shielding Properties
Maximum values range between 2.535 and 3.434 cm for the PS system, while HVL values for the PSC, PSE, and PSY systems decrease from 2.584 to 2.495 cm, 2.541 cm, and 2.478 cm, respectively, as the RE content increases. Figure 3: Variation in linear attenuation coefficients, \(\mu\), as a function of incident photons’ energy for (**a**) PS, (**b**) PSC, (**c**) PSE, and (**d**) PSY glass samples. The TVL (tenth-value layer) represents the layer thickness required to reduce radiation by a factor of 10 or the average amount of material necessary to absorb 90% of the total radiation. Figure 5 graphically presents the TVL values as a function of photon energy for the PS, PSC, PSE, and PSY systems. The evolution of the graphs for the studied systems is similar to HVL, gradually increasing with energy, and the obtained values can be explained in terms of material density changes. The maximum TVL values are reached at E = 4 MeV and increase for the PS system from 8.421 to 11.408 cm as the PbO\({}_{2}\) content in the network decreases. For RE-doped systems, the TVL value decreases with doping, from 8.582 to 8.288 cm for the PSC system, 8.441 cm for the PSE system, and 8.245 cm for the PSY system. A comparative analysis of the systems again highlights the best performance for samples with high Yb\({}_{2}\)O\({}_{3}\) content. Figure 6 graphically represents the modifications in the MFP (mean free path) as a function of photon energy for the PS, PSC, PSE, and PSY systems. From the evolution of the graphs, it was observed that the simulated values for the mean free path gradually increase with photon energy up to 4 MeV, after which they slightly decrease. Additionally, MFP values increase with the SiO\({}_{2}\) content and decrease monotonically with RE content. The maximum values range between 3.657 and 4.954 cm for the PS system, between 3.727 and 3.600 cm for the PSC system, between 3.727 and 3.666 cm for the PSE system, and between 3.727 and 3.581 cm for the PSY system. Figure 4: Variation in HVL as a function of incident photon energy for (**a**) PS, (**b**) PSC, (**c**) PSE, and (**d**) PSY glass samples. The smaller the HVL, TVL, and MFP values for a material, the better its radiation shielding properties and absorption rate. The photon attenuation efficiency of any material also depends on its density. Therefore, the lowest values were obtained for samples with the highest density, specifically those from RE-doped systems, as follows in descending order: PSY, PSC, and PSE. The reduction in PbO\({}_{2}\) concentration in favor of SiO\({}_{2}\) decreases the material's performance; however, incorporating rare earth elements into the PbO\({}_{2}\)-SiO\({}_{2}\) matrix increases the density of the glass, leading to reduced HVL, TVL, and MFP values, enhanced interaction, and, consequently, electron release through the photoelectric effect, Compton scattering, or pair production. Comparing the obtained results with those of other similar materials, such as lead-oxide-containing glasses like lead-borate, lead-silicate, lead-germanate, and lead-tellurite [28; 29; 30], as well as other glass compositions, such as tellurite, borate, phosphate, or bismuth-based glasses [10; 11; 24; 12], shows that the investigated vitreous systems have superior attenuation efficiency. By comparing the obtained HVL values with those reported for commercial materials, such as window glass (4.73 cm), serpentine (4.07 cm), concrete (3.87 cm), SCHOTT RS253 glass (3.65 cm), and hematite serpentine (3.6 cm) [31], the investigated materials exhibit much lower values, indicating significantly higher performance. Our study demonstrated that compared to lead-based materials used as gamma radiation shielding materials, the lead dioxide glass shows superior performance in terms of toxicity, transparency, density, and significantly reduced volume. Figure 5: Variation in TVL as a function of incident photon energy for (**a**) PS, (**b**) PSC, (**c**) PSE, and (**d**) PSY glass samples.