Ion energy-loss characteristics and friction in a free-electron gas at warm dense matter and nonideal dense plasma conditions

We investigate the energy-loss characteristics of an ion in warm dense matter (WDM) and dense plasmas concentrating on the influence of electronic correlations. The basis for our analysis is a recently developed ab initio quantum Monte Carlo– (QMC) based machine learning representation of the static local field correction (LFC) [Dornheim et al., J. Chem. Phys. 151, 194104 (2019)], which provides an accurate description of the dynamical density response function of the electron gas at the considered parameters. We focus on the polarization-induced stopping power due to free electrons, the friction function, and the straggling rate. In addition, we compute the friction coefficient which constitutes a key quantity for the adequate Langevin dynamics simulation of ions. Considering typical experimental WDM parameters with partially degenerate electrons, we find that the friction coefficient is of the order of $\gamma /{\omega }_{pi}=0.01$, where ${\omega }_{pi}$ is the ionic plasma frequency. This analysis is performed by comparing QMC-based data to results from the random-phase approximation (RPA), the Mermin dielectric function, and the Singwi-Tosi-Land-Sjölander (STLS) approximation. It is revealed that the widely used relaxation time approximation (Mermin dielectric function) has severe limitations regarding the description of the energy loss of ions in a correlated partially degenerate electrons gas. Moreover, by comparing QMC-based data with the results obtained using STLS, we find that the ion energy-loss properties are not sensitive to the inaccuracy of the static local field correction (LFC) at large wave numbers, $k/k_F>2$ (with $k_F$ being the Fermi wave number), but that a correct description of the static LFC at $k/k_F\lesssim 1.5$ is important.

Figure 1

(a) Stopping power and (b) friction function at $r_s=2$ and $\theta =1$. The data were obtained using QMC and STLS static local field corrections, the Mermin dielectric function (with $\nu =0.22{\omega }_p$), and RPA.

Figure 2

Stopping power for $r_s=2$ at (a) $\theta =0.5$ and (b) $\theta =2.0$. The data were obtained using QMC, STLS, and RPA.

Figure 3

Friction function at $r_s=2$ is presented for (a) $\theta =0.5$ and (b) $\theta =2.0$ and $\theta =4.0$.

Figure 4

Static local field correction at $r_s=2$ and different $\theta$. The STLS result and QMC-based machine learning representation [32] are shown.

Figure 5

Stopping power at $r_s=4$. Results are presented for (a) $\theta =0.5$, (b) $\theta =1.0$, and (c) $\theta =2.0$.

Figure 6

Friction function at $r_s=4$. Results are presented for (a) $\theta =0.5$, (b) $\theta =1.0$, and (c) $\theta =2.0$.

Figure 7

Static local field correction at $r_s=4$ and different $\theta$. The STLS result and QMC-based machine learning representation [32] are shown.

Figure 8

Stopping power at $r_s=1$. Results are presented for (a) $\theta =0.5$ and (b) $\theta =1.0$.

Figure 9

Friction function at $r_s=1$. Results are presented for $\theta =0.5$, $\theta =1.0$, and $\theta =2$. Curves of the friction function for different $\theta$ are shifted vertically for clarity.

Figure 10

Static local field correction at $r_s=1$ and different $\theta$. The STLS result and QMC-based machine learning representation [32] are shown.

Figure 11

Straggling rate at $r_s=2$. In top subplot (a), the straggling rate for $\theta =1.0$ is given. For other different values of $\theta$, the straggling rate is shown in subplot (b), where curves for different $\theta$ are shifted vertically for clarity.

Figure 12

Straggling rate for different values of the degeneracy parameter at (a) $r_s=4$ and (b) $r_s=1$. Curves for different $\theta$ are shifted vertically for clarity.