## 3 Results and Discussions
The material thickness of LPb50 BEu and LBi50 BEu glasses for 0.015-15 MeV photon energies, which halves the incoming radiation intensity, is presented in Figure 3.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline Energy & **LPb50B** & \multicolumn{3}{c}{**LPb50 BEu0.5**} & **LPb50 BEu1** & **LPb50 BEu2** & **LBi50B** & \multicolumn{3}{c}{**LBi50 BEu0.5**} & **LBi50 BEu1** & **LBi50 BEu2** \\ \cline{2-13}
**(MeV)** & **Phy-X** & **MCNP** & **Phy-X** & **MCNP** & **Phy-X** & **MCNP** & **Phy-X** & **MCNP** & **Phy-X** & **MCNP** & **Phy-X** & **MCNP** & **Phy-X** & **MCNP** \\ \hline
0.015 & 78.429 & 81.792 & 78.587 & 81.504 & 78.742 & 80.346 & 79.045 & 81.458 & 89.281 & 90.231 & 89.322 & 90.348 & 89.363 & 90.569 & 89.442 & 90.775 \\
0.02  
Half-value layers (T\({}_{1/2}\)) of the LPb50 BEu and LBi50 BEu glasses are almost zero in the 0.015-0.1 MeV range. After 0.1 MeV, secondary scattering enhances with the effect of CS, while the T\({}_{1/2}\) values increase quickly. Beyond 3 MeV, the T\({}_{1/2}\) values reduce with the annihilation of photons in the PP process. The densities of LPb50 BEu and LBi50 BEu glasses are reduced in the range of 5.39-5.04 g/cm\({}^{3}\) and 6.81-5.94 g/cm\({}^{3}\) with the addition of Eu\({}_{2}\)O\({}_{3}\). Therefore, it is seen that the T\({}_{1/2}\) values increase with the insertion of Eu\({}_{2}\)O\({}_{3}\). The maximum T\({}_{1/2}\) values for LPb50 BEu and LBi50 BEu glasses were obtained as 3.60 cm and 2.95 cm, respectively. These results are quite satisfactory for a good shield material for gamma rays. Moreover, the mean free path values (\(\lambda\)) of proposed glasses in comparison with some commercial SCHOTT [17] glasses, RS-253-G18, RS-360, RS-520, and concrete types, barite, ferrite, chromite [18], are given in Figure 4.  
Figure 3: Variation of mass attenuation coefficient (\(\mu_{m}\)) against photon energy for (**a**) LPb50 BEu and (**b**) LBi50 BEu glasses. Figure 2: Variation of linear attenuation coefficients (\(\mu\)) against photon energy for all glasses. The \(\lambda\) values of LPb50 BEu and LBi50 BEu glasses are thinner than other shielding materials. The LBi50 BEu2 glass had the smallest \(\lambda\) values, while the RS-213-G18 glass presented the largest MFP values, as seen in Figure 5. In order to express a composite material with a single atomic number, an effective atomic number (\(Z_{\mathit{eff}}\)) is needed, which shows the shielding capacity of the shielding material well [19]. Figure 6 presents the change of \(Z_{\mathit{eff}}\) values of L (Bi/Pb)50 BEu2 glasses versus photon energy. For LPb50 BEu and LBi50 BEu glasses, the \(Z_{\mathit{eff}}\) takes values in the range of 76.72-23.15, 75.73-23.84, and 79.64-27.71, 79.38-28.18, respectively. The largest values of \(Z_{\mathit{eff}}\) are at low energies below 0.1 MeV. A few sudden peaks occur on the absorption edge of K and L shells of Pb (L:15.86 keV, K:88.00 keV) and Bi (L:16.38 keV, K: 90.52 keV), and K shell of La (38.92 keV) by the effect of PEA. Between 0.1-1 MeV, the \(Z_{\mathit{eff}}\) values rapidly decrease and, beyond 1 MeV, the \(Z_{\mathit{eff}}\) values increased due to the \(Z^{2}\)-dependent change of the PP cross section. While the addition of Eu\({}_{2}\)O\({}_{3}\) in the high energy region increased the \(Z_{\mathit{eff}}\) values of the glasses, the \(Z_{\mathit{eff}}\) values declined at medium and low energy levels. It is noted from Figure 6 that the \(Z_{\mathit{eff}}\) values of LBi50 BEu glasses prepared with Bi\({}_{2}\)O\({}_{3}\) are higher than LPb50 BEu glasses. Perfect geometry is not possible in real radiation applications. For this reason, the correction factor B (build-up factor) is needed to account for scattering in the material and in the air in the Lambert-Beer law [20]. Energy absorption and exposure build-up factors (EABF and EBF) for L(Pb/Bi)50 BEu glasses were generated using Phy-X/PSD software in photon energies of 0.015-15 MeV for several \(\lambda\) values.