## 3 Results and Discussion
### Photoluminescence Measurements
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Temperature**} \\ \hline
**18 K** & **25 K** & **50 K** & **75 K** & **100 K** & **150 K** & **200 K** & **250 K** & **Band** \\ \hline  & & \multicolumn{6}{c}{\(\lambda\) **(nm)**} \\ \hline
613.5 & 612.7 & 612.5 & 612.4 & 612.3 & 612.3 & 612.3 & & B \\
625.2 & 624.5 & 624.0 & 623.7 & 623.4 & 623.1 & 623.0 & 622.1 & A \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Temperature dependence of the bands for ZnSe:Eu\({}^{3+}\). Figure 7: Photoluminescence spectrum of ZnSe co-doped with Eu\({}^{3+}\)/Yb\({}^{3+}\) at 20 K. a is the emission line of pure ZnSe and b, c, d are the new emission lines due to dopants. It is clear from the figures and Table 5 that the position of the bands remained fixed with temperature; however, their intensity was a function of temperature. The spectra exhibited narrow emission bands assigned according to Table 5. It can be seen from the results presented in this table that co-doping of the ZnSe semiconductor led to an enrichment of the photoluminescence spectrum. Moreover, the spectrum at low temperature clearly showed more emission peaks and at 20 K, was shifted to longer wavelengths (peak d in Figure 8). The peak b intensity increased with temperature, while in contrast, the peak c intensity decreased with temperature, as can be noted from Figures 8 and 9. Figure 8: Photoluminescence spectrum of ZnSe co-doped with Eu\({}^{3+}\)/Yb\({}^{3+}\) at 20 K without the ZnSe contribution. a is the emission line of pure ZnSe and b, c, d are the new emission lines due to dopants. Figure 9: Photoluminescence spectrum of ZnSe co-doped with Eu\({}^{3+}\)/Yb\({}^{3+}\) at 200 K after eliminating the ZnSe bands. a is the emission line of pure ZnSe and b, C are the new emission lines due to dopants. The energy value for the theoretical transitions shown in the photoluminescence spectrum can be described by the Hamiltonian equation for electrons with the 4\({}^{\text{fN}}\) configuration. Two important assumptions were made: first, the electronic states were well separated from the other electronic states of the matrix; and second, the non-spherical crystal field contribution due to the matrix that surrounds the rare earth ion can be treated as a perturbation of the 4\({}^{\text{fN}}\) ion configuration. Then, we can use the following Hamiltonian [20]:  
\[ \begin{split} H=H_{\text{F}}+H_{\text{CF}}=\sum\limits_{i=2,4,6}F^{ i}f_{i}+\xi_{i}A_{so}+\eta L(L+1)+\beta G(G_{2})+\gamma G(G_{7})\\ +\sum\limits_{i=2,3,4,6,8}T^{i}i^{i}+\sum\limits_{i=0,2,4}M^{i}m^ {i}+\sum\limits_{i=2,4,6}P^{i}p^{i}+H_{\text{CF}}\end{split}  \tag{4}\]  
The first part of the Hamiltonian \(H_{\text{F}}\) contains the contribution of the electrostatic repulsion between the 4\({}^{\text{fN}}\) electrons in the trivalent ion configuration and the spin orbit couplings. This term represents the atomic (or free ion) contribution and \(H_{\text{CF}}\) the crystal field interactions. \(F^{i}\) and \(\xi_{i}\) are the electrostatic and spin-orbit integrals; \(f_{i}\) and \(A_{SO}\) are the angular parts of the electrostatic and spin-orbit interactions. \(\eta\), \(\beta\), and \(\gamma\) are parameters associated with the two body correction terms. \(G(G_{2})\) and \(G(G_{7})\) are [PERSON]'s operators for the \(G_{2}\) and \(G_{7}\) groups, and \(L\) is the total orbital angular momentum [20]. [PERSON] proposed the three particle configuration interaction terms [21], which arose from the perturbation effects of those configurations that differed from \({}^{\text{fN}}\) in the quantum numbers of a simple electron. These terms can be represented as \(t_{i}T^{i}\), where \(T^{i}\) are the parameters and \(t_{i}\) are three particle operators, and \(M^{i}\) represents the spin-spin and spin-other-orbit relativistic corrections. The parameters \(P^{i}\) represent electrostatically correlated spin-orbit perturbation, which involves the excitation of an f electron into a higher-lying f shell.