Screening of ionic cores in partially ionized plasmas within linear response

We employ a pseudopotential approach to investigate the screening of ionic cores in partially ionized plasmas. Here, the effect of the tightly bound electrons is condensed into an effective potential between the (free) valence electrons and the ionic cores. Even for weak electron-ion coupling, the corresponding screening clouds show strong modifications from the Debye result for elements heavier than helium. Modifications of the theoretically predicted x-ray scattering signal and implications on measurements are discussed.

Figure 1

(Color online) Effective electron-ion potentials that are considered in this paper. The soft core potential, defined by Eq. (10), is shown for exponents $\alpha =2$ and $\alpha =6$. The curve labeled DFT gives the norm-conserving potential for beryllium used in density functional calculation when the 1s electrons are frozen out.

Figure 2

(Color online) Screening function $q\left(k\right)$ obtained in linear response [Eq. (3)] applying different effective potentials. The plasma parameters were taken for beryllium at solid density $\left(\varrho =1.848\text{g}/{\text{cm}}^{-3}\right)$ and $T=12\text{eV}$. The ion charge state is $Z=2$. The free cutoff parameter in the pseudopotentials is set to be $r_{cut}=1\text{Å}$.

Figure 3

(Color online) Influence of the cutoff radius $r_{cut}$ on the screening function $q\left(k\right)$ using the soft cutoff potential [Eq. (10)] with $\alpha =6$. Plasma conditions as in Fig. 2.

Figure 4

(Color online) Weight of the Rayleigh peak in the scattering signal, that is $W_R\left(k\right)={\left|f_I\left(k\right)+q\left(k\right)\right|}^2{S}_{ii}\left(k\right)$ which is calculated for pseudopotentials and plasma conditions as in Fig. 2. For comparison, we also report $W_R\left(k\right)$ for the case where the screening function is set zero.