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Register a new userQuantitative comparison of opacities calculated using the $R$-matrix and Distorted-Wave methods: Fe XVII
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We present here a detailed calculation of opacities for Fe~XVII at the physical conditions corresponding to the base of the Solar convection zone. Many ingredients are involved in the calculation of opacities. We review the impact of each ingredient on the final monochromatic and mean opacities (Rosseland and Planck). The necessary atomic data were calculated with the $R$-matrix and the distorted-wave (DW) methods. We study the effect of broadening, of resolution, of the extent of configuration sets and of configuration interaction to understand the differences between several theoretical predictions as well as the existing large disagreement with measurements. New Dirac $R$-matrix calculations including all configurations up to the $n=$ 4, 5 and $6$ complexes have been performed as well as corresponding Breit--Pauli DW calculations. The DW calculations have been extended to include autoionizing initial levels. A quantitative contrast is made between comparable DW and $R$-matrix models. We have reached self-convergence with $n=6$ $R$-matrix and DW calculations. Populations in autoionizing initial levels contribute significantly to the opacities and should not be neglected. The $R$-matrix and DW results are consistent under the similar treatment of resonance broadening. The comparison with the experiment shows a persistent difference in the continuum while the filling of the windows shows some improvement. The present study defines our path to the next generation of opacities and opacity tables for stellar modeling.
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The present debate on the reliability of astrophysical opacities has reached a new climax with the recent measurements of Fe opacities on the Z-machine at the Sandia National Laboratory citep{Bailey2015}. To understand the differences between theoretical results, on the one hand, and experiments on the other, as well as the differences among the various theoretical results, detailed comparisons are needed. Many ingredients are involved in the calculation of opacities; deconstructing the whole process and comparing the differences at each step are necessary to quantify their importance and impact on the final results. We present here such a comparison using the two main approaches to calculate the required atomic data, the $R$-Matrix and distorted-wave methods, as well as sets of configurations and coupling schemes to quantify the effects on the opacities for the $Fe XVII$ and $Ni XIV$ ions.
A comprehensive study of high-accuracy photoionization cross sections is carried out using the relativistic Breit-Pauli R-matrix (BPRM) method for (hnu + Fe XVII --> Fe XVIII + e). Owing to its importance in high-temperature plasmas the calculations cover a large energy range, particularly the myriad photoexciation-of-core (PEC) resonances including the n = 3 levels not heretofore considered. The calculations employ a close coupling wave function expansion of 60 levels of the core ion Fe XVIII ranging over a wide energy range of nearly 900 eV between the n = 2 and n = 3 levels. Strong coupling effects due to dipole transition arrays 2p^5 --> 2p^4 (3s,3d) manifest themselves as large PEC resonances throughout this range, and enhance the effective photoionization cross sections orders of magnitude above the background. Comparisons with the erstwhile Opacity Project (OP) and other previous calculations shows that the currently available cross sections considerably underestimate the bound-free cross sections. A level-identification scheme is used for spectroscopic designation of the 454 bound fine structure levels of Fe XVII. Level-specific photoionization cross sections are computed for all levels. In addition, partial cross sections for leaving the core ion Fe XVII in the ground state are also obtained. These results should be relevant to modeling of astrophysical and laboratory plasma sources requiring (i) photoionization rates, (ii) extensive non-local-thermodynamic-equilibrium models, (iii) total unified electron-ion recombination rates including radiative and dielectronic recombination, and (iv) plasma opacities. We particularly examine PEC and non-PEC resonance strengths and emphasize their expanded role to incorporate inner-shell excitations for improved opacities, as shown by the computed monochromatic opacity of Fe XVII.
Extensive resonance structures are manifest in R-Matrix (RM) calculations. However, there exist a large number of highly excited electronic configurations that may contribute to background non-resonant bound-free opacity in high-temperature plasmas. Since RM calculations are very complex, and not essential for background contributions, the Relativistic Distorted Wave (RDW) method is utilized to complement (top-up) photoionization cross sections of Fe XVII obtained using Close-Coupling Breit-Pauli R-Matrix (CC-BPRM) method. There is good agreement between RDW and BPRM for background cross sections where resonances are not present, and individual fine structure levels can be correctly matched spectroscopically, though resonances are neglected in the RDW. To ensure completeness, a high energy range up to 500 Ry above the ionization threshold for each level is considered. Interestingly, the hydrogenic Kramers approximation also shows the same energy behavior as the RDW. Grouping separately, the BPRM configurations consist of 454 bound levels with resonances corresponding to configurations $1s^22s^22p^4nlnl$ (n $leq$ 3, n $leq$ 10); including RDW configurations there are 51,558 levels in total. The topup contribution results in $sim$20% increment, in addition to the 35% enhancement from BPRM calculations over the Opacity Project value for the Rosseland Mean Opacity at the Z-temperature of 2.11 $times 10^6$K (Pradhan and Nahar 2017).
A comprehensive study of relativistic and resonance effects in electron impact excitation of (e+Fe XVII) is carried out using the BPRM method in the relativistic close coupling approximation. Two sets of eigenfunction expansions are employed; first, up to the n = 3 complex corresponding 37 fine-structure levels (37CC) from 21 LS terms; second, up to the n = 4 corresponding to 89 fine-structure levels (89CC) from 49 LS terms. In contrast to previous works, the 37CC and the 89CC collision strengths exhibit considerable differences. Denser and broader resonances due to n = 4 are present in the 89CC results both above and {it below} the 37 thresholds, thus significantly affecting the collision strengths for the primary X-ray and EUV transitions within the first 37 n = 3 levels. Extensive study of other effects on the collision strengths is also reported: (i) electric and magnetic multipole transitions E1, E2, E3 and M1, M2, (ii) J-partial wave convergence of dipole and non-dipole transitions, (iii) high energy behaviour compared to other approximations. Theortical results are benchmarked against experiments to resolve longstanding discrepancies -- collision strengths for the three prominent X-ray lines 3C, 3D and 3E at 15.014, 15.265, and 15.456 AA are in good agreement with two independent measurements on Electron-Beam-Ion-Traps (EBIT). Finally, line ratios from a collisional-radiative model using the new collisional rates are compared with observations from stellar coronae and EBITs to illustrate potential applications in laboratory and astrophysical plasmas.
We present what constraints on opacities can be derived from the analysis of stellar pulsations of BA-type main-sequence stars. This analysis consists of the construction of complex seismic models which reproduce the observed frequencies as well as the bolometric flux amplitude extracted from the multi-colour photometric variations. Stellar seismology, i.e., {it asteroseismology}, is a relatively young branch of astrophysics and, currently, provides the most accurate test of the theory of internal structure and evolution. We show that opacities under stellar conditions need to be modified at the depth of temperatures $T=110~000-290~000$,K. The revision of opacity data is of great importance because they are crucial for all branches of astrophysics.
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