Pain, J.-C. | Engineering Papers

DOE OSTI2019

Free-free matrix-elements for two-photon opacity

Recent opacity measurements have inspired a close study of the two-photon contributions to the opacity of hot plasmas. The absorption and emission of radiation is controlled by dipole matrix-elements of electrons in an atom or ion. This paper describes two independent methods to calculate matrix-elements needed for the two-photon opacity and tests the results by the f-sum rule. The usual f-sum rule is extended to a matrix f-sum that offers a rigorous test for bound-bound, bound-free and free-free transitions. An additional higher-order sum-rule for the two-photon transition amplitudes is described. In this work, we obtain a simple parametric representation of a key plasma density effect on the matrix-elements. The perturbation theory calculation of two-photon cross-sections is compared to an independent method based on the solution of the time-dependent Schroedinger equation for an atom or ion in a high-frequency electromagnetic field. This is described as a high frequency Stark effect or AC Stark effect. Two-photon cross sections calculated with the AC Stark code agree with perturbation theory to within about 5%. In addition to this cross check, the AC Stark code is well suited to evaluating important questions such as the variation of two-photon opacity for different elements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

First systematic study of L-shell opacity at stellar interior temperatures

The first systematic study of opacity dependence on atomic number at stellar interior temperatures is used to evaluate discrepancies between measured and modeled iron opacity [J. E. Bailey et al., Nature (London) 517, 56 (2015)]. High-temperature ( > 180 eV) chromium and nickel opacities are measured with ± 6-10% uncertainty, using the same methods employed in the previous iron experiments. The 10%-20% experiment reproducibility demonstrates experiment reliability. The overall model-data disagreements are smaller than for iron. However, the systematic study reveals shortcomings in models for density effects, excited states, and open L-shell configurations. The 30%-45% underestimate in the modeled quasicontinuum opacity at short wavelengths was observed only from iron and only at temperature above 180 eV. Thus, either opacity theories are missing physics that has nonmonotonic dependence on the number of bound electrons or there is an experimental flaw unique to the iron measurement at temperatures above 180 eV.

74 ATOMIC AND MOLECULAR PHYSICS↗