## 4 Results and Discussion
The theoretical ratios (red short dash dot) are calculated using CRM based on the FAC package, with a fixed electron density of 1.6 \(\times\) 10\({}^{12}\) cm\({}^{-3}\). Both experimental measurements (black square) by Tokyo-EBIT and theoretical predictions (black short dot) by the HULLAC code for the line-intensity ratios are from Ref. [16]. the magnitude of this surge is much smaller. To explain this surge and discrepancy, we analyzed the feeding and decay fluxes in population equilibriums of the upper levels of 3F and 3D at 6000 eV and 6350 eV, as shown in Figure 5. Here the population flux refers to the rate of change in the population of a specific energy level due to electron impact excitation (EIE) and/or radiative transitions (flux = population \(\times\) rate, given in cm\({}^{-3}\).s\({}^{-1}\)). Due to the lower density in EBIT plasma, all collisional coupling processes among excited levels can be neglected, which is called corona approximation [87]. For the upper levels of 3D and 3F, the branching ratio of rapid transition to ground level is almost 100%, implying that cascade transitions to lower levels can be ignored in the decay path. Thus, the complex CRM for a certain level can be simplified to a balance among several main processes: EIE from the ground level and cascade transitions from higher levels and radiative transition, as shown in Figure 5. Particularly for feeding paths, branching ratios of EIE and cascade channel are also shown. It can be observed from Figure 5 that for level 18 of 3D, EIE from ground level dominates the feeding path (>90%). However, for level 16 of 3F, radiative cascades from higher levels 20-60 are significant, accounting for 38% of the branching ratio at 6000 eV. As the electron-beam energy increases, the activation of new cascade channels becomes the primary factor leading to the growth of 3F intensity, as collision cross-sections exhibit less drastic changes with increasing incident electron energy. While the energy increases from 6000 eV to 6350 eV, EIE contributes only 9% to the total growth in feeding path, while cascades from new excited levels originating from 2p\({}^{5}\)\({}_{1/2}\)4p (levels 63-66, averaging 6170 eV above ground level) contribute 53% through rapid 4p-3s cascade channel. The rest of the growth comes from secondary cascades mediated by levels 20-60. It is noteworthy that level 64 (2p\({}^{5}\)\({}_{1/2}\)4p\({}_{1/2}\))\({}_{\gamma=0}\) contributes the most to the growth, as its transitions back to the ground state are strictly forbidden. This indicates that the intensity of 3F is highly sensitive to changes in radiative cascade channel, unlike the idealized low-density limit where the radiative cascade is usually ignored [14, 48]. In contrast, 3D is primarily influenced by the EIE from ground. Each rising edge in the theoretical curves in Figure 4 reflects the growth in cascade channels, while the declining edges reflect that the collision cross-section of  
Figure 5: Grotrian diagram of the main levels concerned about 3D and 3F transitions in Ne-like Xe\({}^{44+}\). The italic numbers are the indexes of levels in FAC calculations, especially level 16 for 3F and level 18 for 3D. The gray rectangle refers to a series of energy levels 20–60 below 6000 eV. Levels 63–66 are from configuration 2p\({}^{5}\)\({}_{1/2}\)4p. The fluxes (in cm\({}^{-3}\).s\({}^{-1}\)) of feeding paths (red arrows) and radiative decay paths (blue arrows) are shown in the electron-beam energy of 6000 eV (**a**) and 6350 eV (**b**), with the excitation limit on it respectively. The branching ratios of feeding paths for level 18 and level 16 are shown in parentheses behind the flux values, including electron-impact excitation (EIE, short dot arrows) and cascade transition (solid arrows). the upper level of 3D rises more than that of 3F, resulting in the entire theoretical curve showing a jagged pattern. Unlike the actual EBIT plasma environment, the current CRM discussed above only involves the population equilibrium among the levels in the single Xe44+.