VB-BFC model for calculation of the IPDs in dense finite temperature plasmas

The disparity between the theoretical and experimental ionization potential depression (IPDs) has long been a significant issue besetting atomic physics in dense plasmas. Despite more than a decade of intensive research after the first X-ray free-electron laser (XFEL) experiments, the methods and principles underlying the theoretical calculations of IPDs remain highly contentious. Ever since the introduction of the VB-BFC model, it has been recognized that the valence state of each ionic species within a dense plasma exhibits the properties of continuum (or pseudo-continuum) and bound-free mixing. The transition of an inner-shell bound electron to the continuous state does not necessarily signify ionization. As a result, significant challenges emerge when employing ionization models to calculate so-called experimental IPDs. In contrast, the excitation model based on the VB-BFC framework has successfully addressed all IPD-related issues in aluminum plasmas without relying on empirical parameters or calibration procedures. Furthermore, it has elucidated the physical insight of the measurements obtained in XFEL IPD experiments. To further validate and demonstrate the reliability and accuracy of the VB-BFC model, the IPDs of Mg, Si, and SiO₂ have been computed using this framework and compared with experimental data. This comparison not only highlights the model's versatility but also reaffirms that the measurements from XFEL IPD experiments are associated with the excitation of inner-shell electrons rather than ionization.