Dynamical structure factor of strongly coupled ions in a dense quantum plasma

The dynamical structure factor (DSF) of strongly coupled ions in dense plasmas with partially and strongly degenerate electrons is investigated. The main focus is on the impact of electronic correlations (nonideality) on the ionic DSF. The latter is computed by carrying out molecular dynamics (MD) simulations with a screened ion-ion interaction potential. The electronic screening is taken into account by invoking the Singwi-Tosi-Land-Sjölander approximation, and it is compared to the MD simulation data obtained considering the electronic screening in the random phase approximation and using the Yukawa potential. We find that electronic correlations lead to lower values of the ion-acoustic mode frequencies and to an extension of the applicability limit with respect to the wave-number of a hydrodynamic description. Moreover, we show that even in the limit of weak electronic coupling, electronic correlations have a nonnegligible impact on the ionic longitudinal sound speed. Additionally, the applicability of the Yukawa potential with an adjustable screening parameter is discussed, which will be of interest, e.g., for the interpretation of experimental results for the ionic DSF of dense plasmas.

Figure 1

Dynamical structure factor of ions at $\theta =0.1$ and at three values of the density parameter. The data obtained using STLS and RPA potentials are denoted as STLS and RPA, respectively. The DSF curves for $r_s=1.5,1.0$ and $r_s=0.5$ are shifted vertically for clarity.

Figure 2

Dynamical structure factor of ions at $r_s=1.5$ and at different values of the degeneracy parameter. The data obtained using the STLS and RPA potential are denoted as STLS and RPA, respectively. The DSF curves for $\theta =1$ and $\theta =2$ are shifted for clarity.

Figure 3

Ion-acoustic peak positions at $r_s=1.5$ and different values of degeneracy parameter. Solid and dashed lines correspond to the linear dispersion at small wave numbers.

Figure 4

Ion-acoustic peak height (a) and width (b) at $r_s=1.5$ and two values of the degeneracy parameter. The width is measured at the half height of the ion-acoustic peak. The width values at $\theta =2.0$ are shifted by $-0.4$ for a better illustration. The sharp increase of the ion-acoustic peak width (indicated by a dashed vertical line) takes place when the half of ion-acoustic peak height becomes lower than $S(k,0)$. In panel (c), the ratio of the ion-acoustic peak height to the Rayleigh peak height is shown, and the ratio of heights is described by a dependence of the form ${10}^{\alpha \left(ka\right)}$ at $0.5<ka<2.2 [\alpha$ is indicated in the legend of panel (c)].

Figure 5

(a) Ion-acoustic peak positions and width at $r_s=0.5$ and $\theta =0.1$, with solid lines corresponding to the linear dispersion at small wave-numbers. In panel (b), the ion-acoustic peak height and the ratio of the ion-acoustic peak height to the Rayleigh peak height are presented; the ratio of heights is fitted by a ${10}^{\alpha \left(ka\right)}$ law at $0.5<ka<2.2$.

Figure 6

Ion-acoustic peak positions at $r_s=1.0$ and different values of the degeneracy parameter. The solid line corresponds to the linear dispersion at small wave numbers. Data for $\theta =0.5$ and $\theta =1.0$ are shifted by 0.1 and 0.2, respectively.

Figure 7

Ion-acoustic peak height (a) and width (b) at $r_s=1.0$ and three values of the degeneracy parameter. For better illustration, the values of the ion-acoustic peak height for $\theta =0.1$ ($\theta =1)$ are shifted by $+1$ ($-0.1$). Further, the ion-acoustic peak width values at $\theta =0.5$ and $\theta =1.0$ are shifted by $+0.45$ and $+0.9$, respectively.

Figure 8

(a) Dynamical structure factor of the ions at $r_s=1.5$ and $\theta =0.1$. (b) Ion-acoustic peak positions. (c) Static structure factor of the ions. The STLS- and RPA-potential-based data are compared to the results of the Yukawa model.