Ionization potential depression model with the influence of neighboring ions in warm and dense plasmas

In warm and dense plasmas (WDP), ionization potential depression (IPD) plays a crucial role in determining the ionization balance and in understanding the resulting microscopic properties of the plasma. However, the applicability of widely used IPD models, such as the Stewart-Pyatt (SP) and Ecker-Kröll (EK) models, are found to be limited under such conditions. In WDP, the Coulomb potential of neighboring ions directly influences the screening potential around a target ion, thereby altering its ionization potential (IP). Moreover, similar to solid state systems, outer atomic orbitals expand into continuous energy bands due to the influence of neighboring ions and plasma electrons. Electrons can populate into these bands through inelastic collision processes, which will further contribute to the screening potential. Electrons in these continuous bands can migrate into neighboring ions and become delocalized. Consequently, even with total energy E < 0, electrons excited into these bands can be considered as ionized, a behavior distinct from that in isolated situations. In our previous work, using an atomic-state-dependent screening model, we incorporated the influence of band electron distributions resulting from inelastic collisions and found significant contributions to the screening potential under WDP conditions. We now extend this framework by including the effects of neighboring ions on both the screening potential and ionization conditions. This extension reveals that neighboring ions substantially affect IPD in WDP and lead to a weaker temperature dependence compared to cases where such influences are neglected. These findings suggest a potential competitive mechanism between the contributions from band electrons considered in the screening potential and those from direct Coulomb potential of neighboring ions. Furthermore, we discuss how to identify atomic shells that have expanded into bands and should be included in the screening and ionization treatments across a broader range of plasma conditions. The proposed model shows good agreement with experimental results for Al, Mg, and Si plasmas over a wide range of temperatures (18-700 eV) and densities (1-3 times solid density), including measurements of hollow Al ions. With low computational cost and broad applicability, this model offers a promising tool for studying ionization balance, atomic processes, and related radiation and particle transport properties in WDP.