All-Order Full-Coulomb Quantum Spectral Line-Shape Calculations

Understanding how atoms interact with hot dense matter is essential for astrophysical and laboratory plasmas. Interactions in high-density plasmas broaden spectral lines, providing a rare window into interactions that govern, for example, radiation transport in stars. However, up to now, spectral line-shape theories employed at least one of three common approximations: second-order Taylor treatment of broadening operator, dipole-only interactions between atom and plasma, and classical treatment of perturbing electrons. In this Letter, we remove all three approximations simultaneously for the first time and test the importance for two applications: neutral hydrogen and highly ionized magnesium and oxygen. We found 15%–50% change in the spectral line widths, which are sufficient to impact applications including white-dwarf mass determination, stellar-opacity research, and laboratory plasma diagnostics.

Figure 1

(a) Comparison of different approximations for H $\mathrm{Ly}\beta$ at $T_e=1\mathrm{eV}$ and $n_e={10}^{18}e/{\mathrm{cm}}^3$: $\mathrm{SO}+\mathrm{D}$ is second order with dipole; $\mathrm{AO}+\mathrm{D}$ is all order with dipole; $\mathrm{SO}+\mathrm{FC}$ is second $\text{order}+\text{full}$ Coulomb; and $\mathrm{AO}+\mathrm{FC}$ is all $\text{order}+\text{full}$ Coulomb. (b) Comparison of $\mathrm{Ly}\alpha$ calculations between this Letter and VCS [49] and Ref. [37] at $n_e={10}^{18}e/{\mathrm{cm}}^3$ with different temperatures; correspondence is achieved at high temperatures, but not at low temperatures.

Figure 2

(a) Comparison of wing behavior between our new calculation and VCS. (b) Emergent white-dwarf spectrum with new $\mathrm{Ly}\alpha$ line shapes. (c) Same as (b) but focusing on the visible. The visible flux is raised beyond previously estimated uncertainties because of the broader $\mathrm{Ly}\alpha$ profile.

Figure 3

Comparison of Mg $\mathrm{He}\gamma$ ($n=1\to 4$) line-shape models at $T_e=180\mathrm{eV}$ and $n_e=3.1\times {10}^{22}e/{\mathrm{cm}}^3$. (a) Comparison of our work against Lee [67] and OH [68], plus our attempts to reproduce each calculation, indicated by the * for each model; line shapes here are Doppler and instrument [18] convolved. (b) Same as Fig. 1 but for Mg $\mathrm{He}\gamma$ (same legend). Contrary to hydrogen, second order is valid, but the full Coulomb is necessary, causing the redshift that is not present in either Lee or OH.

Figure 4

Comparison of O viii calculations at $T_e=180\mathrm{eV}$ and $n_e={10}^{23}e/{\mathrm{cm}}^3$ that include and neglect the frequency dependence in the calculated $T$ matrices for (a) $\mathrm{Ly}\alpha$ and (b) $\mathrm{Ly}\beta$, $\mathrm{Ly}\gamma$, $\mathrm{Ly}\delta$, and $\mathrm{Ly}\epsilon$. The frequency-dependent $T$ matrices result in decreased opacity in the red wing of $\mathrm{Ly}\alpha$, but raised opacity between $\mathrm{Ly}\alpha$ and $\mathrm{Ly}\beta$ and more intense $\mathrm{Ly}\delta$ and $\mathrm{Ly}\epsilon$ transitions.