Ion structure in warm dense matter: Benchmarking solutions of hypernetted-chain equations by first-principle simulations

We investigate the microscopic structure of strongly coupled ions in warm dense matter using ab initio simulations and hypernetted chain (HNC) equations. We demonstrate that an approximate treatment of quantum effects by weak pseudopotentials fails to describe the highly degenerate electrons in warm dense matter correctly. However, one-component HNC calculations for the ions agree well with first-principles simulations if a linearly screened Coulomb potential is used. These HNC results can be further improved by adding a short-range repulsion that accounts for bound electrons. Examples are given for recently studied light elements, lithium and beryllium, and for aluminum where the extra short-range repulsion is essential.

Figure 1

(Color online) Ion-ion pair distribution functions $g_{ii}\left(r\right)$ in warm dense beryllium at multiples of the normal density ${\rho }_0=1.848\mathrm{g}∕{\mathrm{cm}}^3$: (a) normal density, (b) $\rho =2{\rho }_0$ (2 times compressed), and (c) $\rho =3{\rho }_0$. The temperature and the ion charge state (for HNC) are $T=13\mathrm{eV}$ and $Z=2$, respectively.

Figure 2

(Color online) Static ion-ion structure factor $S_{ii}\left(k\right)$ for compressed beryllium under conditions as in Fig. 1c.

Figure 3

(Color online) Ion-ion pair distribution of lithium with $T=5\mathrm{eV}$, $\rho =0.85\mathrm{g}∕{\mathrm{cm}}^3$, and $Z=1.6$.

Figure 4

(Color online) Ion-ion pair distribution for aluminum with $T=1.1\mathrm{eV}$, $\rho =3.4\mathrm{g}∕{\mathrm{cm}}^3$, and $Z=3$.