# X-ray Spectroscopies of High Energy Density Matter Created with X-ray Free Electron Lasers
## 5 Continuum Lowering in HED Plasmas  
The continuum lowering, also known as ionization potential depression (IPD), is a fundamental component of dense plasma studies. The electric fields of plasma compete with the atomic field, particularly for the higher-lying levels. The orbital electrons may not be bound for certain states and the effective ionization energies are reduced. It affects the ionization balance, excited state populations, electron density, as well as temperature. The opacity of emission and the absorption lines are also affected. Despite its importance, the formulation of IPD was based on crude methods. In the widely accepted classical model by [PERSON] (SP) [52], the radii for the lower bound of the continuum are estimated for two extreme cases, very dilute and dense plasmas, using the Debye radius and ion sphere radius, respectively. Then, IPD for different conditions was formulated via bridging the two cases. However, this model has been adopted without rigorous tests at various conditions owing to many obstacles in accurate measurement during the experiment.  
Given that the Al K-shell emission shown in Figure 4 originates from the absorption of LCLS XFEL photons by specific ions, which have unoccupied states and allow the transitions of electrons from the K-shell, XES in this measurement can also be considered as XAS in the fluorescence yield mode. This technique is sensitive to determine the lowest energy transition from core-level to unoccupied DOS, i.e., the absorption edge. In Figure 4, as the FEL photon energy progressively increases, the onsets of emission lines from IV to higher charge states are observed. [PERSON] et al. identified these emission thresholds as the K-edges of charge states IV\(\sim\)VII, given by the energy difference between the K-shell binding energies and IPDs [53; 54].  
As shown in Figure 5, in plasma conditions of solid-density and about 100 eV temperature, these results provided the first experimental benchmarks to test the SP model, and significant mismatches were found. Interestingly, a modified but less attentive version of continuum lowering model by [PERSON] [EK][55] provided better consistency. This test has stirred up old interests in the topic. At the Orion laser facility, IPDs in a-few-times-compressed aluminum plasmas with 500-700 eV were also measured. Here, the measured K-shell emissions were reasonably consistent with the spectrum calculation using the SP model but they were significantly more consistent with the simple ion sphere model, while the EK model was not satisfactory [56; 57]. These conflicting results have led to the resurgence of the theoretical work for IPD with modern tools for modeling. For example, [PERSON] et al. developed a two-step Hartree-Fock-Slater model, which is claimed to yield a better consistency with both the Orion and LCLS results [58]. [PERSON] et al., performed calculations using a finite-temperature density functional theory (DFT) for the electronic structure of dense aluminum, which shows good consistency with the LCLS experiment but not with the Orion experiment [59]. As shown in Figure 5, while several theoretical predictions by various groups are diverging, it is apparent that more benchmark data for various HED plasma conditions are required, and the FELs and X-ray spectroscopy techniques would be critical tools to guide future investigations.