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Register a new userA Quantitative Comparison of Opacities Calculated Using the Distorted- Wave and $boldsymbol{R}$-Matrix Methods
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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.
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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.
We present R-matrix calculations of photoabsorption and photoionization cross sections across the K edge of the Li-like to Ca-like ions stages of Ni. Level-resolved, Breit-Pauli calculations were performed for the Li-like to Na-like stages. Term-resolved calculations, which include the mass-velocity and Darwin relativistic corrections, were performed for the Mg-like to Ca-like ion stages. This data set is extended up to Fe-like Ni using the distorted wave approximation as implemented by AUTOSTRUCTURE. The R-matrix calculations include the effects of radiative and Auger dampings by means of an optical potential. The damping processes affect the absorption resonances converging to the K thresholds causing them to display symmetric profiles of constant width that smear the otherwise sharp edge at the K-shell photoionization threshold. These data are important for the modeling of features found in photoionized plasmas.
A review of a renewed effort to recalculate astrophysical opacities using the R-Matrix method is presented. The computational methods and new extensions are described. Resulting enhancements found in test calculations under stellar interior conditions compared to the Opacity Project could potentially lead to the resolution of the solar abundances problem, as well as discrepancies between recent experimental measurements at the Sandia Z-pinch inertial confinement fusion device and theoretical opacity models. Outstanding issues also discussed are: (i) accuracy, convergence, and completeness of atomic calculations, (ii) improvements in the Equation-of-State of high-temperature-density plasmas, and (iii) redistribution of resonant oscillator strength in the bound-free continuum, and (iv) plasma broadening of auotionizing resonances.
Siegert pseudostates are purely outgoing states at some fixed point expanded over a finite basis. With discretized variables, they provide an accurate description of scattering in the s wave for short-range potentials with few basis states. The R-matrix method combined with a Lagrange basis, i.e. functions which vanish at all points of a mesh but one, leads to simple mesh-like equations which also allow an accurate description of scattering. These methods are shown to be exactly equivalent for any basis size, with or without discretization. The comparison of their assumptions shows how to accurately derive poles of the scattering matrix in the R-matrix formalism and suggests how to extend the Siegert-pseudostate method to higher partial waves. The different concepts are illustrated with the Bargmann potential and with the centrifugal potential. A simplification of the R-matrix treatment can usefully be extended to the Siegert-pseudostate method.
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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