R-matrix calculations for opacities: V. Temperature-density dependence of photoabsorption cross sections and opacity spectra of oxygen ions O VI and O VII

Technical Summary: R-Matrix Calculations for Opacities: V. Temperature-Density Dependence of Photoabsorption Cross Sections and Opacity Spectra of Oxygen Ions O VI and O VII

Problem Statement
This work addresses the need for accurate atomic data to resolve discrepancies in solar interior models, specifically the "solar abundances problem" where modern 3D NLTE spectroscopic analyses suggest lower C, N, and O abundances than previously thought. Incorporating these reduced abundances into Standard Solar Models (SSMs) creates significant conflicts with helioseismic data, including deviations in sound-speed profiles and the depth of the base of the convection zone (BCZ). While previous papers in the R-Matrix Opacity (RMOP) series focused on iron ions, oxygen is 17 times more abundant than iron in the Sun and contributes approximately 25% of the total Rosseland mean opacity at the BCZ. Accurate modeling of oxygen ions, particularly O VI (Li-like) and O VII (He-like), is essential for resolving these discrepancies. Furthermore, existing Opacity Project (OP) data lacks the necessary energy range and resonance detail required for high-energy-density (HED) plasma conditions.

Methodology
The authors employ the Breit–Pauli R-matrix (BPRM) method to calculate photoionization cross sections and monochromatic opacities for O VI and O VII. The computational framework involves:

1. Atomic Structure: Using close-coupling (CC) wavefunction expansions that include fine-structure levels of the next higher ion as core states (up to $n \le 10, \ell \le 9$). This approach captures quantum interference between open and closed channels, generating dense series of autoionizing (AI) resonances, including strong photoexcitation-of-core (PEC) features.
2. Plasma Broadening: The intrinsic, unbroadened BPRM cross sections are modified to account for plasma environment effects (electron collisions, ion microfields/Stark effect, thermal Doppler, and free-free transitions). This is achieved via a Lorentzian convolution of the unbroadened cross sections, where the total width $\Gamma$ is the sum of collisional, Stark, Doppler, and free-free contributions. At BCZ conditions ($T \sim 10^6$ K, $N_e = 10^{22}–10^{23}$ cm$^{-3}$), electron-impact broadening is identified as the dominant mechanism.
3. Grid and Conditions: Calculations are performed along two representative isotherms corresponding to the solar BCZ: $T = 1 \times 10^6$ K and $T = 2 \times 10^6$ K. Electron densities ($N_e$) span $10^{18}$ to $10^{23}$ cm$^{-3}$.
4. Opacity Calculation: Monochromatic opacities ($\kappa_\nu$) are derived by combining the broadened bound-free cross sections with bound-bound line profiles (treated with standard broadening formalisms) and level populations supplied by the Mihalas-Hummer-D¨appen (MHD) equation of state.

Key Contributions

• Extended Energy Range and Resonance Structure: Unlike the OP database, which terminates at lower energies and lacks autoionizing resonances, the RMOP calculations extend continuously to high energies ($\sim 250$ Ry for O VI and $\sim 700$ Ry for O VII). They explicitly resolve rich AI resonance structures converging to various core thresholds.
• Plasma Broadening Systematics: The study maps the temperature-density dependence of resonance dissolution. It identifies specific density thresholds where AI resonances begin to broaden and where they fully dissolve into the continuum, flattening the background cross section.
• Comparison with OP: The work provides a direct comparison between the new BPRM data and the legacy OP results, highlighting quantitative differences in both cross sections and resulting opacities.

Results

• Photoionization Cross Sections:
  • O VI (Li-like): The RMOP cross sections exhibit a rich structure of AI resonances spanning several orders of magnitude above the continuum, absent in OP data. As electron density increases, these resonances progressively wash out. At BCZ densities ($N_e = 10^{23}$ cm$^{-3}$), the resonance structure is largely dissolved, resulting in a nearly flat cross section in the 40–60 Ry region.
  • O VII (He-like): Similar behavior is observed, with dense resonance clusters in the 40–63 Ry window. The study notes a differential response between resonance clusters (e.g., 47–50 Ry vs. 57–60 Ry), where clusters with more closely spaced resonances dissolve at lower densities.
• Monochromatic Opacities:
  • O VI: RMOP yields systematically higher opacities than OP in the low-energy region (0.02–0.2 keV), which is critical for the Rosseland mean opacity at $T \sim 10^6$ K. The mean RMOP/OP ratio is $\sim 7$ (median $\sim 4$), with local enhancements exceeding an order of magnitude at resonance features.
  • O VII: RMOP opacities are also higher than OP, though the discrepancy is smaller (mean ratio $\sim 1.4$, median $\sim 1.2$). The enhancement is attributed to the dissolution of resonance structures raising the background opacity and the inclusion of more correlation effects in the BPRM treatment.
• Broadening Limits: Table 2 summarizes the density limits for resonance broadening. For O VI and the O VII 47–50 Ry cluster, broadening onset occurs around $N_e \sim 10^{20}$ cm$^{-3}$, with dissolution occurring near $10^{22}–10^{23}$ cm$^{-3}$. The O VII 57–60 Ry cluster persists to higher densities ($\sim 10^{23}$ cm$^{-3}$).

Significance
The paper asserts that these ion-resolved results are fundamental building blocks for future total oxygen opacity and solar-mixture calculations. The findings suggest that improved R-Matrix treatments, which include relativistic fine structure, extensive correlation, and plasma broadening, lead to systematically higher opacities than previously predicted. This work is presented as generally applicable to modeling HED plasmas in astrophysics and to the analysis of transmission spectra in laboratory experiments, such as those conducted on inertial confinement fusion (ICF) devices. The authors note that while total oxygen opacity has been measured at facilities like Sandia Z, individual ion contributions could not be inferred from those experiments, underscoring the necessity of the theoretical data presented here. The work is part of a broader effort to address discrepancies in standard stellar models using updated atomic data.