## 3 Results and Discussion
### Optical and Photoluminescence Characteristics  
Figure 3 presents the transmittance spectra (200-700 nm) for Lu\({}_{2.5}\)Y\({}_{0.5}\)(Al\({}_{2.5}\)Ga\({}_{2.5}\))O\({}_{12}\) samples doped with 0.5, 1, 5, and 10 mol\(\%\) Tb\({}^{3+}\). All samples exhibited transmittance of about \(\sim\)80-90\(\%\) in the visible region (400-700 nm), confirming excellent optical transparency. Notably, there is no significant absorption near 545 nm, corresponding to the prominent Tb\({}^{3+}\): \({}^{5}\)D\({}_{4}\)\(\rightarrow\)\({}^{7}\)F\({}_{5}\) green emission, hence supporting the material's effectiveness in scintillation applications. Distinct absorption bands were observed in the UV region, attributed to parity-forbidden f-f transitions of Tb\({}^{3+}\) ions, which gain intensity through crystal field mixing. The primary absorption bands include \(\sim\)220-240 nm (\({}^{7}\)F\({}_{6}\)\(\rightarrow\)\({}^{5}\)K\({}_{7}\)), \(\sim\)270-300 nm (\({}^{7}\)F\({}_{6}\)\(\rightarrow\)\({}^{5}\)K\({}_{9}\)), and \(\sim\)310-330 nm (\({}^{7}\)F\({}_{6}\)\(\rightarrow\)\({}^{5}\)H\({}_{7}\)). As expected, absorption in these regions increases with higher Tb\({}^{3+}\) concentrations due to a greater number of absorbing centers. However, the transitions remain relatively sharp, indicating a uniform crystal field environment around the Tb\({}^{3+}\) ions and minimal defect-related scattering, both of which are crucial for preserving high optical quality [3; 6; 7; 23]. High transmittance above 400 nm ensures the efficient escape of Tb\({}^{3+}\) green emission (\(\sim\)545 nm), which is crucial for optimal scintillation performance. In addition, strong absorption in the UV range enhances the material's suitability for excitation by UV or ionizing radiation, facilitating efficient energy transfer to Tb\({}^{3+}\) ions. The observed decrease in UV transmittance with increasing doping also offers a qualitative means of estimating the Tb\({}^{3+}\) concentration [13]. Figure 4a shows the PL excitation spectrum of LuYAGG doped with 5 mol\(\%\) Tb\({}^{3+}\), monitored at the characteristic green emission wavelength of 545 nm. The spectrum revealed two major excitation bands: the first, centered at \(\sim\)236 nm, corresponds to the \({}^{7}\)F\({}_{6}\)\(\rightarrow\)\({}^{5}\)K\({}_{8}\) transition of Tb\({}^{3+}\), while the second strong band appeared near \(\sim\)313 nm. These transitions arose from parity-forbidden intra-4f transitions that gained intensity through crystal field mixing, which was common in low-symmetry garnet hosts. Additional weaker bands were observed in the 320-380 nm range, attributed to higher-lying \({}^{5}\)H and \({}^{5}\)D states [24; 25; 26]. Figure 3: Diffuse light transmission spectra of Tb-doped LuYAGG single crystals. of Tb\({}^{3+}\). In particular, the dominant green emission at \(\sim\)545 nm (\({}^{5}\)D\({}_{4}\)\(\rightarrow\)\({}^{7}\)F\({}_{5}\)) was accompanied by weaker peaks at \(\sim\)490 nm (\({}^{5}\)D\({}_{4}\)\(\rightarrow\)\({}^{7}\)F\({}_{6}\)), \(\sim\)545 nm (\({}^{5}\)D\({}_{4}\)\(\rightarrow\)\({}^{7}\)F\({}_{5}\)), \(\sim\)585 nm (\({}^{5}\)D\({}_{4}\)\(\rightarrow\)\({}^{7}\)F\({}_{4}\)), and \(\sim\)620 nm (\({}^{5}\)D\({}_{4}\)\(\rightarrow\)\({}^{7}\)F\({}_{3}\)). The emission intensity increases with Tb\({}^{3+}\) concentration up to 5 mol%, beyond which it begins to saturate, suggesting the onset of concentration quenching. The spectra show no significant peak shifts or broadening, indicating that the crystal field environment remains stable across the doping range [24; 25; 26; 27; 28]. Figure 4c presents the excitation (y-axis) versus emission (x-axis) wavelength map. The color gradient ranging from blue \(\rightarrow\) green \(\rightarrow\) red indicates increasing luminescence intensity, with red areas corresponding to the strongest emission.