Influence of local-field corrections on Thomson scattering in collision-dominated two-component plasmas

The dynamic structure factor, which determines the Thomson scattering spectrum, is calculated via an extended Mermin approach. It incorporates the dynamical collision frequency as well as the local-field correction factor. This allows to study systematically the impact of electron-ion collisions as well as electron-electron correlations due to degeneracy and short-range interaction on the characteristics of the Thomson scattering signal. As such, the plasmon dispersion and damping width is calculated for a two-component plasma, where the electron subsystem is completely degenerate. Strong deviations of the plasmon resonance position due to the electron-electron correlations are observed at increasing Brueckner parameters $r_s$. These results are of paramount importance for the interpretation of collective Thomson scattering spectra, as the determination of the free electron density from the plasmon resonance position requires a precise theory of the plasmon dispersion. Implications due to different approximations for the electron-electron correlation, i.e., different forms of the one-component local-field correction, are discussed.

Figure 1

(Color online) Real (black curves) and imaginary part (gray curves) of the collision frequency $\nu \left(\omega \right)$ as a function of the frequency $\omega$. Various values of the Brueckner parameter $r_s$ are considered. The thin lines indicate the position of the plasma frequency ${\omega }_{\text{pl}}$ for $r_s=1$ (solid), $r_s=2$ (dashed), and $r_s=5$ (dash-dotted). Crosses at $\omega =0.1E_F/\hslash$ indicate the static limit for the collision frequency (Ziman formula). The vertical lines give the plasma frequency ${\omega }_{\text{pl}}$.

Figure 2

Static local-field correction $G_{ee}\left(k\right)$ for $r_s=2$. Approximations: Hubbard (dotted), Born (dashed), Singwi-Tosi-Land-Sjoelander (STLS) (dash-dotted), Utsumi and Ichimaru (dash-dash-dotted), Farid et al. (solid), and Moroni et al. (points with error bars).

Figure 3

(Color online) Plasmon shift $\omega \left(k\right)$ and plasmon width $\Gamma \left(k\right)$ as a function of the wave vector $k$ for $r_s=1$. We compare the static local-field correction (dashed) to the dynamic local-field correction (solid). Dotted curve: RPA, thin dotted curve: Gross-Bohm approximation. No collisions are included. The (yellow) hatched area indicates the range of finite Landau damping.

Figure 4

(Color online) Plasmon shift $\omega \left(k\right)$ and plasmon width $\Gamma \left(k\right)$ as a function of the wave vector $k$ for $r_s=5$. Dashed: static local-field correction, solid: dynamic local-field correction. Dotted: RPA, thin dotted: Gross-Bohm approximation. No collisions are included.

Figure 5

(Color online) Plasmon shift $\omega \left(k=0\right)$ (solid black) and width $\Gamma \left(k=0\right)$ (solid gray) as a function of the Brueckner parameter $r_s$. Here, we account for electron-ion collisions using only the traditional Born-Mermin approximation. No local-field corrections are considered. Dashed black: plasma frequency ${\omega }_{\text{pl}}/E_F\propto \sqrt{r_s}$, dashed gray: Ziman collision frequency.

Figure 6

(Color online) Plasmon shift $\omega \left(k\right)$ as a function of the wave vector $k$ for $r_s=1$ BM: traditional Born-Mermin approximation. $\text{BM}+\text{sLFC}$: Born-Mermin including static local-field corrections. $\text{BM}+\text{dLFC}$: Born-Mermin including dynamic local-field corrections.

Figure 7

(Color online) Plasmon shift $\omega \left(k\right)$ as a function of the wave vector $k$ for $r_s=2$. BM: traditional Born-Mermin approximation. $\text{BM}+\text{sLFC}$: Born-Mermin including static local-field corrections. $\text{BM}+\text{dLFC}$: Born-Mermin including dynamic local-field corrections.

Figure 8

(Color online) Plasmon shift $\omega \left(k\right)$ as a function of the wave vector $k$ for $r_s=5$. BM: traditional Born-Mermin approximation. $\text{BM}+\text{sLFC}$: Born-Mermin including static local-field corrections. $\text{BM}+\text{dLFC}$: Born-Mermin including dynamic local-field corrections.

Figure 9

(Color online) Real and imaginary part for dynamic local-field correction at $r_s=2$ for two different wave vectors as a function of the frequency.

Figure 10

(Color online) Plasmon width $\Gamma \left(k\right)$ as a function of the wave vector $k$ for $r_s=1$. The traditional Born-Mermin (BM) without local-field corrections is compared to the extended approach with static $\left(\text{BM}+\text{sLFC}\right)$ and dynamic local-field corrections $\left(\text{BM}+\text{dLFC}\right)$. The onset $k_0$ of Landau damping in RPA is also shown.

Figure 11

(Color online) Plasmon width $\Gamma \left(k\right)$ as a function of the wave vector $k$ for $r_s=2$. BM: traditional Born-Mermin approximation. $\text{BM}+\text{sLFC}$: Born-Mermin including static local-field corrections. $\text{BM}+\text{dLFC}$: Born-Mermin including dynamic local-field corrections.

Figure 12

(Color online) Plasmon width $\Gamma \left(k\right)$ as a function of the wave vector $k$ for $r_s=5$. BM: traditional Born-Mermin approximation. $\text{BM}+\text{sLFC}$: Born-Mermin including static local-field corrections. $\text{BM}+\text{dLFC}$: Born-Mermin including dynamic local-field corrections.