## 4 Results and Discussion
By contrast, the peak area of the 3D line under Gaussian fitting profile is approximately reduced by 13.05%; while for 3F, it is reduced by 5.75%. This discrepancy in peak area loss can introduce a systematic overestimation in ratio 3F/3D if using Gaussian profile. As shown in Figure 3, relative deviations from calculations in line-intensity ratios 3F/3D under Gaussian fitting are uniformly 9.1% higher compared to Voigt fitting. This may explain the discrepancy between experimental ratios of 3F/3D and synthetic calculations reported in Ref. [16], although the fitting profile used for line-intensity ratio measurements in their work has not been described. Figure 4 illustrates the variation of the experimental 3F/3D line-intensity ratio with electron-beam energy for all conditions, accompanied by corresponding error bars, with an average relative uncertainty of 2.1%. Total uncertainty contains statistical errors from  
Figure 3: Relative differences between experimental and theoretical line-intensity ratios of 3F/3D fitted with Gaussian (blue square) and Voigt (red circle) profiles. Figure 2: The 3D peak from Ne-like Xe fitted with Gaussian (blue dash) and Voigt (red solid) profiles at an electron-beam energy of 7.2 keV. Voigt fitting was conducted with a fixed Lorentz width of 0.187 mÅ, as inferred from Ref. [65]. fitting profile and reproducibility at the same energy conditions, and systematic error from threshold selection. Figure 4 also shows the theoretical curves obtained from CRM simulations based on FAC, which depicts the variation of 3F/3D line-intensity ratio with electron energy in the range 5000-8000 eV. The electron density was fixed at 1.6 \(\times\) 10\({}^{12}\) cm\({}^{-3}\), because the impact of various electron density on the line-intensity ratios can be neglected according to another simulation with different density. The theoretical predictions of 3F/3D intensity ratio exhibit good agreement with the experimental results for electron-beam energy higher than approximately 6000 eV. Not only do they share the same trend, but the theoretical ratios also fall within the experimental error bars, with relative deviations less than 1.4%. For the results at about 6.0 keV and 5.5 keV, theoretical ratios are still lower than experimental measurements, with relative deviations of 7.0% and 7.4%, respectively. In previous study from Ref. [16], there is a larger significant discrepancy (\(\approx\)13.7%) of 3F/3D between measured spectrum from Tokyo-EBIT and theoretical predictions calculated by the HULLAC code. These results are also presented in Figure 4. Our measured ratios fall within the error bars of their measured values and exhibit significantly better agreement with our calculated values, even for the results in the low-energy region. Their theoretical curves from HULLAC exhibit similar jagged changing patterns as the FAC results but differ in positions of peaks and valleys, averaging about 5% lower overall. This reflects the differences between these two theoretical methods in describing atomic structure and population equilibrium. As previously mentioned and clearly illustrated in Figure 3, there persist notable discrepancies between experimental and theoretical results in the low electron-beam energy region. Notably, the deviations at different electron-beam energies exhibit remarkable similarity, specifically 7.0% and 7.4% for energies at 5.5 keV and 6.0 keV, respectively. This indicates that the remaining discrepancies are likely attributed to systematic shortcomings in the current CRM simulation. In the theoretical curves shown in Figure 4, there is a significant surge in the line-intensity ratio from 6000 eV to 6350 eV, whereas experimentally,  
Figure 4: The measured and calculated intensity ratio of 3F/3D as a function of electron-beam energy. The measured ratios (red circle) with errors are derived from Voigt fitting results of peaks in the spectra obtained from Shanghai-EBIT.