## 3 Calculations
\begin{table}
\begin{tabular}{c c c c c c c c} \hline  & & & & & & **Experiment** & **Theory** & \\ \hline
**Charge** & **Label** & **Upper Level** & **Lower Level** & \(\lambda_{\text{measured}}\) & \(\lambda_{\text{other}}\) & \(\lambda_{\text{FAC}}\) & \(\Delta\) & **Intensity** \\ \hline
44 & 3D & \((2p_{3}^{5}\)3/23d\({}_{3}))\)\({}_{-1}\) & \((2p_{3}^{6})\)\({}_{-0}\) & 2.7203 (1) & 2.7203 (1) \({}^{\text{\text{\tiny{a}}}}\)\({}^{\text{\text{\tiny{b}}}}\) & 2.72057 & 0.010\% & 23.98 \\
43 & Na1 & \((2p_{3}^{5}\)3/23d\({}_{3}))\)\({}_{-1/2}\) & \((2p_{3}^{6})\)\({}_{-1/2}\) & 2.7240 (2) & 2.7240 (4) \({}^{\text{\text{\tiny{d}}}}\) & 2.72385 & \(-\)0.006\% & 2.96 \\
44 & 3F & \((2p_{1}^{5}\)1/2 36/12)\({}_{-1}\) & \((2p_{3}^{6})\)\({}_{-0}\) & 2.7288 (1) & 2.7288 (1) \({}^{\text{\text{\tiny{a}}}}\)\({}^{\text{\text{\tiny{b}}}}\) & 2.72945 & 0.023\% & 12.20 \\
43 & 3 DNa & \((2p_{3}^{5}\)3/23d\({}_{3}))\)\({}_{-3/2}\) & \((2p_{3}^{6})\)\({}_{-1/2}\) & 2.7358 (2) & 2.7358 (2) \({}^{\text{\text{\tiny{a}}}}\)\({}^{\text{\text{\tiny{c}}}}\) & 2.73595 & 0.006\% & 18.41 \\
43 & Na2 & \((2p_{3}^{5}\)3/23d\({}_{3}))\)\({}_{-1/2}\) & \((2p_{3}^{6}\)3/23d\({}_{3}))\)\({}_{-1/2}\) & 2.7408 (2) & 2.7403 & 0.009\% & 1.99 \\
42 & 3 DMo & \((2p_{3}^{5}\)3/23d\({}_{3}^{5}\)3/23)\)\({}_{-1/2}\) & \((2p_{3}^{6}\)3/23)\)\({}_{-1/2}\) & 2.7460 (2) & 2.7460 (2) \({}^{\text{\text{\tiny{a}}}}\)\({}^{\text{\text{\tiny{c}}}}\) & 2.74505 & \(-\)0.035\% & 11.94 \\
44 & 3E & \((2p_{3}^{5}\)3/23d\({}_{3}))\)\({}_{-1/2}\) & \((2p_{3}^{6})\)\({}_{-0}\) & 2.7534 (2) & 2.7535 (2) \({}^{\text{\text{\tiny{c}}}}\) & 2.75425 & 0.030\% & 1.33 \\
42 & Mg1 & \((2p_{3}^{5}\)3/23d\({}_{3}\)2/3p\({}^{2}\))\({}_{-1/2}\) & \((2p_{3}^{6}\)3/23)\({}_{-0}\) & 2.7595 (2) & 2.7596 (2) \({}^{\text{\text{\tiny{c}}}}\) & 2.75975 & 0.010\% & 3.62 \\ \hline \end{tabular}
\end{table} 
Table 2: Summary of measured L-shell transition lines from highly charged Xenon and comparison with theoretical values calculated by FAC. All wavelengths are in Å. The line-intensity, given in photons/(ion-s), was calculated using CRM based on FAC at an electron-beam energy of 5.5 keV and an electron density of 1.6 \(\times\) 10\({}^{12}\) cm\({}^{-3}\). \(\Delta\) is the relative difference between present EBIT measured and calculated wavelength, where \(\Delta=(\lambda_{\text{FAC}}-\lambda_{\text{measured}})/\lambda_{\text{measured}}\). density, \(v\) is impact electron velocity, \(\sigma\) is collision cross-section. The deexcitation rate \(C^{d}\) can be obtained from \(C^{c}\) by the detailed balance principle. These rate equations for all levels can be solved under the quasi-steady-state approximation \(dN_{i}/dt=0\), and the normalized condition \(\Sigma_{i}N_{i}=1\). The line-intensity of transition can be calculated after the population of its upper level is determined. Figure 1a illustrates the calculated spectra for Xe ions from 42+ to 44+. For comparison, plasma parameters in this simulation were set according to experimental conditions, with the electron-beam energy of 5.5 keV and the electron density of 1.6 \(\times\) 10\({}^{12}\) cm\({}^{-3}\). The intensity results from each individual charge state were normalized to the brightest lines. In the simulated spectra, all transition lines were assumed to have the Gaussian profile with the linewidth of 0.8 mA, which corresponds to the experimental resolution. The theoretical wavelengths and emission intensities under the given plasma parameters are also presented in Table 2. The discrepancies between theoretical and experimental wavelengths for all lines in three ions are within 0.04%.