# Spectroscopic Studies of Laser-Based Far-Ultraviolet Plasma Light Source
## 3 Computational Model
\begin{table}
\begin{tabular}{l l} \hline \hline
**States** & **Configurations** \\ \hline Si I & \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}\text{3s}^{2}\text{3p}^{2}\), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}\text{3s}^{1}\text{3p}^{2}\), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}\text{3s}^{2}\text{3p}^{1}\) \\  & \(nl\) (\(n=4,5\)) (\(l<n\)), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}\text{3s}^{2}\)3p\({}^{1}nl\) (\(n=6,7\)) (\(l<3\)), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}\text{3p}^{4}\) \\ \hline Si II & \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}\text{3s}^{2}\text{3p}^{1}\), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}\text{3s}^{1}\text{3p}^{2}\), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}\text{3s}^{2}nl\) (\(n=4\)) (\(l<n\)), \\  & \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}\text{3s}^{2}nl\) (\(n=5,6,7\)) (\(l<3\)), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}\text{3s}^{1}\) (\(n=4\)) (\(l<n\)), \\ \hline Si III & \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}\text{3s}^{2}\), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}\text{3s}^{1}\)3p\({}^{1}\), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}\text{3s}^{1}nl\) (\(n=4\)) (\(l<n\)), \\  & \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}\text{3s}^{1}nl\) (\(n=5,6,7\)), (\(l<3\)), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}\text{3p}^{2}\) \\ \hline Si IV & \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}\text{3s}^{1}\), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}\text{3p}^{1}\), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}\text{n}l\) (\(n=4\)) (\(l<n\)), \\  & \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}nl\) (\(n=5,6,7\)) (\(l<3\)) \\ \hline Si V & \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{6}\), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{5}nl\) (\(n=3\)) (\(l<n\)), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{5}nl\) (\(n=4,5,6,7\)) (\(l<3\)) \\ \hline Si VI & \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{5}\), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{4}nl\) (\(n=3\)) (\(l<n\)), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{4}nl\) (\(n=4,5,6,7\)) (\(l<3\)) \\ \hline Si VII & \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{4}\), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{3}nl\) (\(n=3\)) (\(l<n\)), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{3}nl\) (\(n=4,5\)) (\(l<3\)) \\ \hline Si VIII & \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{3}\), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{2}nl\) (\(n=3\)) (\(l<n\)), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{2}nl\) (\(n=4,5\)) (\(l<3\)) \\ \hline Si IX & \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{2}\), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{1}nl\) (\(n=3\)) (\(l<n\)), \(\text{1s}^{2}\text{2s}^{2}\text{2p}^{1}nl\) (\(n=4,5\)) (\(l<3\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The CR model for Si plasma includes all of the ground states from the neutral (Si I) through fully ionized charge states, and particularly, the important transitions from Si I through Si IX. Here, \(n\) and \(l\) are, respectively, the principal and orbital quantum numbers. The total levels in the CR is 1050. Figure 2a presents a typical non-LTE spectral emissivity (in units of W cm\({}^{-3}\) nm\({}^{-1}\) sr\({}^{-1}\)) and the opacity coefficients (=\(\kappa\)/\(\rho\), where \(\kappa\) is the spectral absorption coefficient in units of cm\({}^{-1}\) and \(\rho\) is the density in units of g cm\({}^{-3}\)) in the tabulated EOS Si database over the wavelength region of 120-170 nm for an artificial homogeneous plasma at \(\rho\approx 10^{-4}\) g cm\({}^{-3}\) and a temperature of kT \(\approx\) 5 eV. The CR model depends on three different temperatures for the electron (\(T_{e}\)), ion (\(T_{i}\)), and the radiation field (\(T_{r}\)). Here, it is assumed that \(T_{e}\) = \(T_{i}\) = kT \(\approx\) 5 eV and \(T_{r}\) = 0.2\(\times\)\(T_{e}\). It is found that the effect of \(T_{r}\) on the spectral emissivity and opacity coefficient (Figure 2a) is negligible at this condition. Throughout this study, the spectral emissivity and opacity coefficients include the bound-bound, bound-free and free-free processes.