Collective and static properties of model two-component plasmas

Classical MD data on the charge-charge dynamic structure factor of two-component plasmas (TCP) modeled in Phys. Rev. A 23, 2041 (1981) are analyzed using the sum rules and other exact relations. The convergent power moments of the imaginary part of the model system dielectric function are expressed in terms of its partial static structure factors, which are computed by the method of hypernetted chains using the Deutsch effective potential. High-frequency asymptotic behavior of the dielectric function is specified to include the effects of inverse bremsstrahlung. The agreement with the MD data is improved, and important statistical characteristics of the model TCP, such as the probability to find both electron and ion at one point, are determined.

Figure 1

The radial distribution functions $g_{ab}\left(r\right)$, $a,b=e,i$ for $\Gamma =0.5$, $r_s=0.4$, calculated with the potential (1). Solid lines are included to join the discrete points for a better visualization.

Figure 2

Normalized dynamic structure factor versus frequency as given by expression (19) at $\Gamma =0.5$, $r_s=0.4$. The model parameter function (18) is used. The values of $ka$ are (1) 0.767, (2) 1.074, (3) 1.381, and (4) 1.534. (a) Classical calculations (solid lines) compared to the results of Ref. 1 with $ka=0.780$ (diamonds), $ka=1.102$ (triangles), $ka=1.350$ (boxes), and $ka=1.559$ (stars). (b) Comparison between classical (dashed) and quantal calculations (solid). In the classical case, the kinetic contribution is approximated by the Vlasov term (25), whereas in the quantal case expression (26) is used.

Figure 3

Same as in Fig. 2, but for $\Gamma =0.5$, $r_s=1$.

Figure 4

Same as in Fig. 2, but for $\Gamma =2$, $r_s=1$.

Figure 5

Dispersion $z\left(k\right)=\mathrm{Re}z\left(k\right)+i\mathrm{Im}z\left(k\right)$, for the collective excitation mode obtained from Eq. (36) in the classical approximation. The damped solution stemming from the model function (18) is compared to the undamped solution corresponding to the Feynman-like approximation (15). For expression (18): $\Gamma =0.5$, $r_s=0.4$ (triangles); $\Gamma =0.5$, $r_s=1$ (stars); $\Gamma =2$, $r_s=1$ (pentagons). For expression (15): $\Gamma =0.5$, $r_s=0.4$ (boxes); $\Gamma =0.5$, $r_s=1$ (diamonds); $\Gamma =2$, $r_s=1$ (circles). Solid lines are included to join the discrete points for a better visualization.

Figure 6

Same as in Fig. 5, but for the quantal case. The degenerate kinetic term (26) is used, instead of the classical one (25).