Second-order, full-Coulomb electron broadening calculations for multi-electron radiators in hot, dense plasmas: A focus on dense plasma line shifts

This work presents a full-Coulomb, multi-electron formalism of line broadening due to perturbation by plasma electrons. This work is based on the relaxation theory of Smith and Hooper, which was extended to treat highly ionized radiators by Tighe and Hooper. A further extension by Woltz and Hooper introduced a full-Coulomb expression of the perturber-radiator interaction in the electron broadening operator, rather than applying the dipole approximation. The term of the electron broadening operator, first order in the radiator-perturbing electron interaction is reintroduced, causing a red line shift and asymmetries. This formalism is also generalized to treat multi-electron radiating ions, using the formalism to calculate general transition arrays presented by Cowan. The effects of the plasma ions are treated dynamically using an ion microfield probability distribution with the model introduced by Boercker, Iglesias, and Dufty.; The line shapes calculated using this model are dramatically shifted and distorted with respect to lineshapes calculated in the dipole approximation of the radiator-perturbing electron interaction. They also are narrower and the differences between the two models increase as the principal quantum number of the upper state of the transition increases. This can be attributed to the fact that the orbital size is greater relative to the average plasma electron spacing. The asymmetries are attributed to the dependence of the level shifts on angular momentum state. There is good agreement between the shift calculations compared with those of Griem et al. and Nguyen et al. The line profiles are also compared to those calculated using a semi-classical model that is carried to all orders in the radiator-perturbing electron interaction. Analysis of K-shell Ar spectra using the shifted line spectra is shown. Finally, the impact of the line shift on merging of adjacent lines in a Rydberg series at ultra-high densities, <3 x 10 24cm-3, is considered.