## 2 Materials and Methods  
Four chemical formulas xSiO\({}_{2}\)-(100\(-\)x)PbO\({}_{2}\), where x = 0, 10, 20, 30, 40, 53, 55, and 58; xReO\({}_{2}\)-(100\(-\)x)[80 PbO\({}_{2}\) 20 SiO\({}_{2}\)], where x = 0, 0.1, 0.2, 0.3, 0.5, 1, and 2 CeO\({}_{2}\) mol %; xReO\({}_{2}\)O\({}_{3}\)-(100\(-\)x)[80 PbO\({}_{2}\) 20 SiO\({}_{2}\)], where x = 0, 0.1, 0.2, 0.3, 0.5, 0.8, and 1 mol% ReO\({}_{2}\)O\({}_{3}\); and Re\({}_{2}\)O\({}_{3}\) = Eu\({}_{2}\)O\({}_{3}\) and Yb\({}_{2}\)O\({}_{3}\) were used to prepare through the melt quenching technique the glass systems under study, labeled numerically as PSn, PSCn, PSEn, and PSYn, where n = 0, 1, 2, 3, 4, 5, 6, and 7 as a function of the dopant and the concentration. High-analytical-grade chemicals from Sigma-Aldrich (St. Louis, MO, USA), with purity > 99.5%, of PbO\({}_{2}\), SiO\({}_{2}\), CeO\({}_{2}\), Eu\({}_{2}\)O\({}_{3}\), and Yb\({}_{2}\)O\({}_{3}\) were used for sample preparation. The mixed stoichiometric compositions were melt in a platinum crucible for 10 min at temperatures ranging between 950 and 1050 \({}^{\circ}\)C to obtain bubble-free, homogeneous, and transparent samples. All processing syntheses are amply discussed in Ref. [21]. Physical parameters were evaluated to study the compositional effect on the lead dioxide network structure. The density (\(\rho\)) of the studied samples was measured experimentally at room temperature, 25 \({}^{\circ}\)C, according to the standard Archimedes' principle, using distilled water, \(\rho\) = 0.997 g/cm\({}^{3}\), as the immersion liquid and Equation (1). The reported results represent the average value of five distinct measurements. Based on the density values, the molar volume (V\({}_{\rm m}\)), the packing density of oxygen atoms (OPD), and the molar volume of oxygen (V\({}_{\rm o}\)) were estimated according to the following formulas:  
\[\rho=\left(\frac{Wa-Wl}{Wa}\right)\rho i \tag{1}\]  
where \(\rho\) is the density, \(p_{i}\) is the density of the immersion fluid, \(\rho\) = 0.997 g/cm\({}^{3}\), \(Wl\) is the weight of the sample in immersion fluid, and \(Wa\) and is the weight of the sample in air. \[Vm=\left(\frac{\rm M}{\rho}\right) \tag{2}\]  
where \(Vm\) is the molar volume, \(\rho\) is the density, and M is the molecular weight. \[OPD=1000C\left(\frac{\rho}{\rm M}\right) \tag{3}\]  
where \(OPD\) is the oxygen packing density, \(\rho\) and M are the density and the molecular weight, and C is the number of oxygen atoms per formula unit. \[Vo=Vm\left(\frac{1}{C}\right) \tag{4}\]  
where \(Vo\) is the molar volume of oxygen, \(Vm\) is the molar volume, and \(C\) is the number of oxygen atoms per formula unit. Photon attenuation parameters, such as the mass attenuation coefficient (\(\mu\)m), the total linear attenuation coefficient (\(\mu\)), the half-value layer (HVL), the tenth-value layer (TVL), and the mean free path (MFP), were used to quantify the ability of the studied glass samples to act as safety shields required in many technological and optical fields. User-friendly online Photon Shielding and Dosimetry Phy-X/PSD software (version 1) available at [[https://phy-x.net/PSD](https://phy-x.net/PSD)]([https://phy-x.net/PSD](https://phy-x.net/PSD)), accessed on 8 November 2024 was used to calculate different shielding and dosimetry parameters. The software is fast, accurate [22], and practical, and the methodology is well-described in Ref [23]. The software was used to generate data on the aforementioned shielding parameters in the wide energy range of 0.015-15 MeV, using as data input the glass composition (mole fraction) and the density of the investigated samples. The data saved in an Excel file were graphically represented using the Origin program ([[https://www.originlab.com/](https://www.originlab.com/)]([https://www.originlab.com/](https://www.originlab.com/))). The optical absorption spectra of the studied glass samples were obtained using a Jasco V750 UV-Visible Spectrophotometer (JASCO, Inc., Easton, MD, USA) in the 200-800 nm wavelength range.