Continuum Lowering and Fermi-Surface Rising in Strongly Coupled and Degenerate Plasmas

Continuum lowering is a well known and important physics concept that describes the ionization potential depression (IPD) in plasmas caused by thermal- or pressure-induced ionization of outer-shell electrons. The existing IPD models are often used to characterize plasma conditions and to gauge opacity calculations. Recent precision measurements have revealed deficits in our understanding of continuum lowering in dense hot plasmas. However, these investigations have so far been limited to IPD in strongly coupled but nondegenerate plasmas. Here, we report a first-principles study of the $K$-edge shifting in both strongly coupled and fully degenerate carbon plasmas, with quantum molecular dynamics calculations based on the all-electron density-functional theory. The resulting $K$-edge shifting versus plasma density, as a probe to the continuum lowering and the Fermi-surface rising, is found to be significantly different from predictions of existing IPD models. In contrast, a simple model of “single-atom-in-box,” developed in this work, accurately predicts $K$-edge locations as ab initio calculations provide.

Figure 1

The mass absorption coefficient ${\alpha }_m$ as a function of photon energy ($h\nu$) for extremely compressed carbon at a temperature of $T=15625\mathrm{K}$ but different densities of (a) $\rho =10$, (b) $\rho =50$, (c) $\rho =100$, and (d) $\rho =150\mathrm{g}/{\mathrm{cm}}^3$. The black arrow in each panel marks the location of the carbon $K$ edge in such extremely dense plasmas.

Figure 2

The electronic density of state (DOS) as a function of the band energy, for the four cases corresponding to Fig. 1. The dashed black line in each panel marks the location of the Fermi energy.

Figure 3

The QMD-predicted $K$ edges of carbon plasmas as a function of the corresponding ion charge state $Z$ (or the mass density), in comparison with predictions from the various continuum-lowering models of Ecker-Kröll [1], Stewart-Pyatt [2], modified ion sphere [3], and Crowley. [4] The proposed simple model SAIB accurately predicts the correct $K$-edge positions.

Figure 4

(a) The electronic density of state (DOS) as a function of the band energy, for the dense carbon plasma of $\rho =100\mathrm{g}/{\mathrm{cm}}^3$ at two different temperatures of $T=15625$ (blue solid) and $T=125000\mathrm{K}$ (red dashed). (b) The corresponding photoabsorption spectra. The temperature induced broadening of the $1s$ band in (a) is indicated by the less-sharp $K$ edge in the absorption spectrum.