## 2 Materials and Methods  
Three samples were synthesized at room temperature based on polyepoxide resin, a solidifying agent, and a reinforcing Bi\({}_{2}\)O\({}_{3}\) compound. The polyepoxides resin, as well as its solidifying agent, were bought from SlabDOC (Ivanovo, Russia) at a purity of 98%. The polyepoxide resin was mixed with the solidifying agent in a 2:1 ratio by weight for 10 min. After that, the required amount of Bi\({}_{2}\)O\({}_{3}\) was weighed using a sensitive electric balance and added to the mixture with continued stirring for another 15 min. Then, the mixture was cast in a cylindrical mold and allowed to solidify for 24 h. The final products of the synthesized composites are presented in Figure 1. A MXBAOHENG MH 300A (Guangdong, China) density meter was used to measure the density of the synthesized composites with an uncertainty of 0.01 g/cm\({}^{3}\). The measurements show that the densities of the polyepoxide-reinforced Bi\({}_{2}\)O\({}_{3}\) composites were 1.103, 1.159, and 1.20 g/cm\({}^{3}\). The composition of the fabricated composites was then determined using X-ray fluorescence (XRF) (see Table 1). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Elemental Composition (wt.\%)**} \\ \cline{2-4}  & **Bi\({}_{2}\)O\({}_{3}\) 0\%** & **Bi\({}_{2}\)O\({}_{3}\) 5\%** & **Bi\({}_{2}\)O\({}_{3}\) 10\%** \\ \hline H & 6.97 & 6.61 & 6.26 \\ \hline C & 44.01 & 41.77 & 39.54 \\ \hline O & 36.32 & 35.00 & 33.68 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Elemental composition and density of the synthesized composites. The elemental chemical composition obtained by the X-ray fluorescence and the density recorded by the MH 300A densimeter were utilized to estimate the \(\gamma\)-ray shielding properties of the samples utilizing MCNP-5 [21]. The simulation was done over a wide gamma energy (E\({}_{\gamma}\), keV) interval, which varied between 15 keV and 661 keV. The geometry used in the present work has been described elsewhere [22; 23; 24]. A radioactive source was placed at the origin of the geometry (at 0 0 0), emitting photons along the Z-direction. The photon energies, emission probability, and the photon distribution were introduced to the source card (SDEF). The radioactive source was surrounded by a lead collimator with a 1 cm slit to direct the photon flux to the fabricated samples. The sample was placed at a distance of 7 cm from the radioactive source and 5 cm from the detector. The Bi\({}_{2}\)O\({}_{3}\)-doped polyepoxide resin composites had a diameter of 3 cm and various thicknesses. The photons transmitted from the fabricated composite were collimated using a second collimator and directed to the detector. The tally used in the present work to calculate the average photon flux per unit cell of the fabricated composite was F4. The average photon flux was utilized to estimate the mean track length (MTL) of \(\gamma\)-photons inside the fabricated composites. The simulation was carried out and a new output MCNP-5 file, in the form of a txt file, was created, containing all the information about the mean track length of \(\gamma\)-photons inside the fabricated composites at the selected \(\gamma\)-ray energy interval. The relative error in the simulated data, according to the output file, was in the range of \(\pm\)1%. The obtained MTL of \(\gamma\)-photons was converted to shielding parameters through the following equations:  
\[\mu\left(\mathrm{cm^{-1}}\right)=\frac{\mathrm{I}}{\mathrm{x}}\ln\left(\frac{ \mathrm{I_{0}}}{\mathrm{I_{t}}}\right) \tag{1}\]  
The half-value thickness (\(\Delta_{0.5}\), cm) is defined as:  
\[\Delta_{0.5}\left(\mathrm{cm}\right)=\frac{\ln(2)}{\mu} \tag{2}\]  
\[\mathrm{TF}\left(\%\right)=\frac{\mathrm{I_{t}}}{\mathrm{I_{0}}}\times 100 \tag{3}\]