Local field correction to ionization potential depression of ions in warm or hot dense matter

An analytical self-consistent approach was recently established to predict the ionization potential depression (IPD) in multicomponent dense plasmas, which is achieved by considering the self-energy of ions and electrons within the quantum statistical theory. In order to explicitly account for the exchange-correlation effect of electrons, we incorporate the effective static approximation of local field correction (LFC) within our IPD framework through the connection of dynamical structure factor. The effective static approximation poses an accurate description for the asymptotic large wave number behavior with the recently developed machine learning representation of static LFC induced from the path-integral Monte Carlo data. Our calculation shows that the introduction of static LFC through dynamical structure factor brings a nontrivial influence on IPD at warm/hot dense matter conditions. The correlation effect within static LFC could provide up to 20% correction to free-electron contribution of IPD in the strong coupling and degeneracy regime. Furthermore, a new screening factor is obtained from the density distribution of free electrons calculated within the average-atom model, with which excellent agreements are observed with other methods and experiments at warm/hot dense matter conditions.

Figure 1

Screening factor ${[1-q_{\text{scr}}\left(k\right)]}^2$ for ${\text{Al}}^{3+}$ plasma at $\rho =2.7\text{g}{\text{cm}}^{-3}$ and $t=10\text{eV}$. Dash-dotted green line: average-atom model; solid red line: random phase approximation; dashed black line: effective static approximation; and dotted blue line: long-wavelength formula.

Figure 2

Corrections to the free-electron part of IPD [Eq. (7)] at WDM conditions ($0.5\le \mathrm{\Theta }\le 4.0$, $1.0\le r_s\le 10.0$) by introducing different effects: (a) the consideration of dynamical SF under RPA instead of the Debye-Hückel formula [Eq. (9)]; (b) the introduction of static LFC in calculating dynamical SF; (c) a combination of these two effects.

Figure 3

Different approximations of static SFs at $r_s=1.0$ and $\mathrm{\Theta }=0.5$ (upper panel) and $\mathrm{\Theta }=4.0$ (lower panel). Dotted blue line: Debye-Hückel formula (Eq. (9)); solid red line: dynamical SF approach [Eq. (10)] under RPA; dashed black line: dynamical SF approach under ESA.

Figure 4

Different approximations of static SFs at $r_s=10.0$ and $\mathrm{\Theta }=0.5$ (upper panel) and $\mathrm{\Theta }=4.0$ (lower panel).

Figure 5

IPD (upper panel) and its components (lower panel) as a function of different charge state ${\text{Fe}}^{n+}$ at a fixed free-electron density of $3.1\times {10}^{22}{\mathrm{cm}}^{-3}$ and temperature of $181.834\mathrm{eV}$. The averaged ionic SF and free-electron density distribution are obtained from MIMD simulation, and the corresponding screening function is calculated via Eq. (17). The SF of free electrons is computed via Eqs. (10, 11, 12) with RPA.

Figure 6

IPD (upper panel) and its component (lower panel) as a function of different charge states ${\text{Fe}}^{n+}$ at a fixed free-electron density $n_e=1.6\times {10}^{24}{\mathrm{cm}}^{-3}$ and temperature $t=100.2\mathrm{eV}$. The corresponding IPs in the isolated condition are also included in the upper panel as a green dashed line. The averaged ionic SF and free-electron density distribution are obtained from MIMD simulation, and the corresponding screening function is calculated via Eq. (17). The SF of free electrons is computed via Eqs. (10, 11, 12) with ESA.

Figure 7

IPD for aluminum plasma as a function of different charge state $A{l}^{n+}$ at solid density and electron temperature $T_e=100\mathrm{eV}$. Shown are experimental results taken from Ref. [19, 20] with an error bar $\pm 5\mathrm{eV}$, in comparison to our predictions (previous work and this work) and other theoretical models.