Pair potentials for warm dense matter and their application to x-ray Thomson scattering in aluminum and beryllium

Ultrafast laser experiments yield increasingly reliable data on warm dense matter, but their interpretation requires theoretical models. We employ an efficient density functional neutral-pseudoatom hypernetted-chain (NPA-HNC) model with accuracy comparable to ab initio simulations and which provides first-principles pseudopotentials and pair potentials for warm-dense matter. It avoids the use of (i) ad hoc core-repulsion models and (ii) “Yukawa screening” and (iii) need not assume ion-electron thermal equilibrium. Computations of the x-ray Thomson scattering (XRTS) spectra of aluminum and beryllium are compared with recent experiments and with density-functional-theory molecular-dynamics (DFT-MD) simulations. The NPA-HNC structure factors, compressibilities, phonons, and conductivities agree closely with DFT-MD results, while Yukawa screening gives misleading results. The analysis of the XRTS data for two of the experiments, using two-temperature quasi-equilibrium models, is supported by calculations of their temperature relaxation times.

Figure 1

The XRTS ion feature $W\left(k\right)$ of Ref. [10] for Al-I, and from the DFT-MD, NPA-MHNC, and YSRR models, as indicated. The inset magnifies the peak region.

Figure 2

(a) NPA and YSRR potentials for Al-I (cf. experiment of Ref. [10]); (b) $S\left(k\right)$ from the $V_{ii}\left(r\right)$ using HNC and MHNC; (c) $k\to 0$ region of $S\left(k\right)$.

Figure 3

The XRTS ion feature $W\left(k\right)$ of Ma et al. [12] for Al-II, compared with the $W\left(k\right)$ from YSRR, NPA, the DFT-MD calculation of Rütter et al. with $T_i=T_e$, and our $2T$-NPA calculation with $T_i=1.8$ eV and $T_e=10$ eV; the inset magnifies the peak region.

Figure 4

(a) The NPA-HNC and YSRR pair potentials for Al-II; (b) corresponding $S\left(k\right)$; (c) the $k\to 0$ limit of $S\left(k\right)$.

Figure 5

The longitudinal phonon spectrum for the FCC crystal of (a) Al-I, i.e., compression of 2.32 and $T_e=T_i=1.75$ eV [10]; (b) Al-II, i.e., compression of 3.0, $T_i$=1.8 eV, and $T_e=10$ eV [12]. The $\mathrm{\Gamma }$, X, K, and L point are symmetry points of the first Brillouin zone of the FCC crystal.

Figure 6

The electrical resistivity of Al at $T=1.75$ eV for different compressions calculated using NPA and YSRR.

Figure 7

The XRTS ion feature $W\left(k\right)$ of Lee et al. [13] compared with the NPA-HNC $W\left(k\right)$ (full lines) and with DFT-MD results (dashed lines) of Plagemann et al. [62] for equilibrium and for $T_e\ne T_i$, as indicated.

Figure 8

Static ion-ion structure factor $S\left(k\right)$ for Be-I from the NPA-HNC and DFT-MD simulation of Plagemann et al. [62], including their $k=0$ value marked as dots, for different equilibrium temperatures.

Figure 9

Total $N\left(k\right)$, bound-electron $f\left(q\right)$ and free-electron $q\left(f\right)$ form factor for the Be-I conditions.

Figure 10

The XRTS ion feature $W\left(k\right)$ of Glenzer et al. [14] compared with the $W\left(k\right)$ of the NPA-HNC model (full lines) and with the DFT-MD simulation (dashed lines) of Plagemann et al. [62] for the equilibrium and $2T$ situations.

Figure 11

Static ion-ion structure factor $S\left(k\right)$ for Be-II from the NPA-HNC model and from the DFT-MD simulations of Plagemann et al. [62], including the $k=0$ values marked as dots, for different equilibrium temperatures.