## 2 Materials and Methods
### Studied Radiation Shielding Parameters  
Equation (1) describes the photon flux attenuation in narrow photon beam. As indicated in Equation (1), a connection exists between the radiation intensity (\(I\)) and the absorbent glass material's thickness (\(t\)), as well as the radiation intensity (\(I_{o}\)) prior to contacting the substance [14]:  
\[I=I_{o}e^{-\mu t} \tag{1}\]  
In Equation (1), \(\mu\) is the linear attenuation coefficient. The term of mass attenuation coefficient (\(\mu_{m}\)) is a measure of how likely incident photons are to interact with matter per unit density. The formula shown in Equation (2) is used to compute it:  
\[\mu_{m}=\sum_{i}w_{i}(\frac{\mu}{\rho})_{i} \tag{2}\]  
where (\(\mu_{m}\)) is the mass attenuation coefficient, (\(w_{i}\)) is the weight fraction of the \(i\)th constituent element, (\(\mu\)) is the linear attenuation coefficient, and (\(\rho\)) is the density. The mean free path (\(MFP\)) is the mean distance travelled by a photon inside a shielding material prior to encountering an interaction. It is calculated using the following Equation (3):  
\[MFP=\frac{1}{\mu} \tag{3}\]  
The half-value layer (\(HVL\)) is the absorber thickness required to reduce the radiation intensity to half of its starting value, as determined by Equation (4):  
\[HVL=\frac{ln\ (2)}{\mu} \tag{4}\]  
In composite materials, the term \"effective atomic number\" (\(Z_{eff}\)) cannot be stated as a single number; instead, it varies depending on the material and specific characteristics of the interacting radiation, and it provides information about the material. The direct method was used to compute the \(Z_{eff}\) values of the samples in this investigation:  
\[Z_{eff}=\frac{\Sigma_{i}f_{i}A_{i}\left(\frac{\mu}{\rho}\right)_{i}}{\Sigma_{j }f_{j}\left(\frac{A_{j}}{Z_{j}}\right)\left(\frac{\mu}{\rho}\right)_{j}} \tag{5}\]  
In Equation (5), \(f_{i}\) is fraction by mole, \(A_{i}\) is atomic weight, and \(Z_{j}\) is atomic number of \(i\)th constituent element. When developing gamma radiation shielding, build-up factor (BUF) considerations are crucial. The energy absorption build-up factor (EABF) is a measure of the amount of time a material is exposed to air after it has been penetrated by a particle. The exposure build-up factor (EBF) is a measurement of the amount of exposure in air after it has passed through the shielding material. BUFs are often computed using the geometric progression (G-P) fitting technique, which is described in detail below. To begin, the equivalent atomic number (\(Z_{eq}\)) of a particular energy is determined by comparing  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Sample**} & \multicolumn{4}{c}{**mol\%**} & \multicolumn{4}{c}{**wt\%**} & \multicolumn{4}{c}{\(\rho\)} \\ \multicolumn{1}{c}{**Code**} & \multicolumn{1}{c}{**La\({}_{2}\)O\({}_{3}\)**} & \multicolumn{1}{c}{**PbO**} & \multicolumn{1}{c}{**Bi\({}_{2}\)O\({}_{3}\)**} & \multicolumn{1}{c}{**Bi\({}_{2}\)O\({}_{3}\)**} & \multicolumn{1}{c}{**Eu\({}_{2}\)O\({}_{3}\)**} & \multicolumn{1}{c}{**B**} & \multicolumn{1}{c}{**O**} & \multicolumn{1}{c}{**La**} & \multicolumn{1}{c}{**Eu**} & \multicolumn{1}{c}{**Pb**} & \multicolumn{1}{c}{**Bi**} & \multicolumn{1}{c}{**(g/cm\({}^{3}\))**} \\ \hline \hline
**LPb50B** & 10 & 50 & - & 40 & 0 & 0.0503 & 0.1860 & 0.1615 & 0 & 0.6022 & - & 5.393 \\
**LPb50 Eu.5** & 10 & 50 & - & 39.5 & 0.5 & 0.0492 & 0.1845 & 0.1602 & 0.0088 & 0.5973 & - & 5.36 \\
**LPb5  
its (\(\mu_{m}\)) Compton/(\(\mu_{m}\)) total ratio to the element's convenient ratio. In this study, the \(Z_{\rm eq}\) values for the glasses were determined using the interpolation technique. The EBF and EABF values for a single-layered gamma-ray-shielding enclosure (GSE), with an OT of up to 100 mfp and an energy range of 0.015 to 15 MeV, are calculated using the following Equations (6)-(8).