Multiple scattering theory for dense plasmas

Dense plasmas occur in stars, giant planets, and in inertial fusion experiments. Accurate modeling of the electronic structure of these plasmas allows for prediction of material properties that can in turn be used to simulate these astrophysical objects and terrestrial experiments. But modeling them remains a challenge. Here we explore the Korringa-Kohn-Rostoker Green's function (KKR-GF) method for this purpose. We find that it is able to predict equation of state in good agreement with other state-of-the-art methods, where they are accurate and viable. In addition, it is shown that the computational cost does not significantly change with temperature, in contrast with other approaches. Moreover, the method does not use pseudopotentials—core states are calculated self consistently. We conclude that KKR-GF is a very promising method for dense plasma simulation.

Figure 1

Flow chart describing the computational workflow. Inside the shaded (blue) region is the self-consistent field (SCF) procedure, outside the shaded area, in orange boxes, are one-off steps that are decided or calculated before the SCF procedure starts.

Figure 2

Schematic example of power tessellation. Top panel shows the 2D tessellation for eight centers, which would correspond to the nuclear positions in 3D. The circles correspond to the muffin tin spheres, and the black line demarcate the cells. In the bottom panel 35 extra centers have been added in such a way as to minimize the area (volume) not in the muffin tins. Notice that the power tessellation preserves the original eight spheres as more centers are added.

Figure 3

Example of geometry in which one of the inequalities is violated. The circles represent the muffin tin spheres and the vertical line is the boundary plane. For the points $\mathit{r}$ and ${\mathit{r}}^{\prime }$, the inequality $|{\mathit{r}}^{\prime }|<|\mathit{x}-{\mathit{R}}^{n^{\prime }}|$ is violated, while the others are satisfied.

Figure 4

Schematic of the different types of states that occur on the real energy axis. For large negative energy only discrete core states exist, and one only needs the numerically inexpensive single-site solution. Between $E_{\text{min}}$ and $E_{\text{max}}^{\text{ms}}$ valence states exit, which are strongly affected by multisite effects. In this region the full Green's function expression is evaluated for $l\le l_{\text{max}}^{\text{ms}}$. For $l>l_{\text{max}}^{\text{ms}}$ only the single-site contribution is needed. For energies greater than $E_{\text{max}}^{\text{ms}}$, again only the single site solution is needed.

Figure 5

Convergence of pressure with the number of extra centers for 8 aluminum atoms, at solid density and temperatures of 10 eV (top panel) and 100 eV (bottom panel). The dotted lines serve as a guide to the eye. The two lines correspond to two sets of ion configurations (i.e., positions). The results are for $l_{\text{max}}^{\text{ms}}=2$.

Figure 6

Total pressure for solid density aluminum at 10 eV (top panel) and 100 eV (bottom panel), versus simulated time. Shown are results for $l_{\text{max}}^{\text{ms}}=2,3,\text{and}4$. These results use 35 extra centers.

Figure 7

Density of states of solid density aluminum with $l_{\text{max}}^{\text{ms}}=2$ for temperatures of 10 eV (top panel) and 100 eV (bottom panel). We also show the result from the average atom model Tartarus [28]. We have made the zero of energy at the chemical potential. For both cases the density of states shown is focused on the valence region, where states transition from bound to free. The dashed vertical line shows the average energy of the muffin tin constant.