## 3 Results
Similar to our results, an increasing reinforcement amount with higher atomic number resulted in an increment in the V\({}_{2}\)O\({}_{5}\)-TeO\({}_{2}\) glass system. The term HVL factor is a useful quantity to evaluate the required thickness of a shield, which can reduce the intensity of the incident gamma ray by half. Therefore, a smaller HVL can be considered as a supremacy indicator in shielding materials. In this study, HVL values of the studied glasses were determined. Figure 4 shows a variation of the half value layer (T\({}_{1/2}\)) against photon energy for all glasses. In the lower energies, HVL values were reported as small. This is an expected situation for any type of shielding material as low energy gamma rays can be attenuated in low material thicknesses. However, it can be seen from Figure 4 that HVL values are higher in the high energy zone. Figure 2: Variation of linear attenuation coefficient (\(\mu\)m) against photon energy for all glasses. It can be explained by the penetration property of gamma rays and its dependence on energy. For example, the HVL values of the VTBNd0.0, VTBNd0.5, VTBNd1.0, and VTBNd1.5 samples at different energies were found to be 0.0041 cm HVLV\({}_{\rm VTBNd0\text{-}0}\) > 0.0039 cm HVLV\({}_{\rm VTBNd0\text{-}5}\) > 0.0038 HVLV\({}_{\rm VTBNd1\text{-}0}\) > 0.0037 cm HVLV\({}_{\rm VTBNd1\text{-}5}\) at 0.015 MeV. Moreover, HVL values were reported as 0.2992 cm HVLV\({}_{\rm VTBNd0\text{-}0}\) > 0.2840 cm HVLV\({}_{\rm VTBNd0\text{-}5}\) > 0.2806 HVLV\({}_{\rm VTBNd1\text{-}0}\) > 0.2760 cm HVLV\({}_{\rm VTBNd1\text{-}5}\) at 0.15 MeV. Finally, HVL values were reported as 4.1660 cm HVLV\({}_{\rm VTBNd0\text{-}0}\) > 3.9777 cm HVLV\({}_{\rm VTBNd0\text{-}5}\) > 3.9533 HVLV\({}_{\rm VTBNd1\text{-}0}\) > 3.9106 cm HVLV\({}_{\rm VTBNd1\text{-}5}\) at 15 MeV, respectively. As shown from this ranking, the minimum HVL values were reported for the VTBNd1.5 sample, which has the highest amount of Nd\({}_{2}\)O\({}_{3}\) additive in its glass structure. Therefore, one can say that VTBNd1.5 requires the smallest thickness to reduce incident gamma rays by half (T\({}_{1/2}\)). The importance of the mean free path (\(\lambda\)) is a consideration in the gamma-protection abilities of shielding materials. The glass samples were examined, and the results are detailed in Figure 5.  
Figure 4: Variation of half value layer (T1/Z) against photon energy for all glasses. Figure 3: Variation of mass attenuation coefficient (\(\mu\)m) against photon energy for all glasses. The \(\lambda\) values will differ similarly to the evolving pattern of HVL. The minimum \(\lambda\) values were recorded for the VTBNd1.5 sample. Another important shielding parameter is the tenth value layer (TVL). The term TVL factor is another essential evaluation criterion for the required thickness of a shield, reducing the intensity of an incident gamma ray to one-tenth (1/10). TVL vales of the studied glasses were determined and the results presented in Figure 6 as a function of the incident photon energy for all glasses. In the lower energies, TVL values were reported as small. A similar variation trend of HVL was also reported for the TVL values of the VTBNd0.0, VTBNd0.5, VTBNd1.0, and VTBNd1.5 samples. For example, TVL values were reported as 0.9941 cm TVL\({}_{\text{VTBNd0-0}}>\) 0.9435 cm TVL\({}_{\text{VTBNd1-0}}>\) 0.9323 TVL\({}_{\text{VTBNd1-0}}>\) 0.9170 cm HVL\({}_{\text{VTBNd1-5}}\) at 0.15 MeV. Overall, the minimum TVL values were reported for the VTBNd1.5 sample, which has the highest amount of Nd\({}_{2}\)O\({}_{3}\) additive. The required atomic number for measuring the material's appropriateness for gamma applications is tied to the proper photon control stage. The \(Z_{\text{eff}}\) values of the glass samples measured are shown in Figure 7.  
Figure 5: Variation of mean free path (\(\lambda\)) against photon energy for all glasses. Figure 6: Variation of tenth value layer (TVL) against photon energy for all glasses.