Effects of Screening and Pressure Ionization on the Electron Broadening of Spectral Lines in Dense Plasmas

Abstract

Collisions between electrons and radiating atoms broaden spectral absorption and emission lines in dense plasmas. High densities also introduce screening and pressure ionization effects that distort the wavefunctions of both bound and free electrons. In order to study how dense plasma effects influence the electron broadening of spectral lines, this paper incorporates electron wavefunctions from an average-atom (AA) model to calculate the line width of the B III $2p-2s$ transition at $T = 10$ eV for mass densities ranging from $ρ=10^{-4}-0.4$ g/cc. The calculation method uses the impact approximation, allowing the line width to be written in terms of electron-collision cross sections and an interference term. Compared to an otherwise identical calculation that uses Coulomb free wavefunctions, the AA method is found to modify both the cross sections and the resulting line width at sufficiently high density by introducing screening and pressure ionized bound states. Screening lowers the cross sections at low energies and near electron excitation thresholds, while pressure ionized bound states introduce resonances into the continuum. Thus, as the density increases, the relative line width between the AA and Coulomb calculations follows a general decrease because of screening, with sharp increases at various intervals due to pressure ionization. The AA results are also compared with a common approach to introduce screening through the interaction potential and reduced models that use the Bethe formula for the inelastic electron-collision cross sections.

Figures (7)

• Figure 1: (a) Radial bound wavefunctions computed in the AA model for the $1s$, $2s$, and $2p$ states. (b) Inset showing the increase in bound energies of the $2s$ and $2p$ states for increasing B iii mass density.
• Figure 2: Continuum DOS of B iii at $T = 10$ eV as a function of free electron energy. The solid-black line corresponds to the solution from Eq. (\ref{['eq:continuumDOS']}) with free electron wavefunctions calculated in the AA potential. The dashed-red line is the ideal continuum DOS $\chi_{i}(E_{\mathbf{k}})=\sqrt{2E_{\mathbf{k}}}/\left(n_{i}\pi^{2}\right)$.
• Figure 3: Cross sections for the electron-collision cross sections appearing in Eqs. (\ref{['eq:uppercross']}) and (\ref{['eq:lowercross']}) as a function of the incoming free electron energy for a mass density of $\rho = 10^{-3}$g/cc and temperature $T = 10$eV. The two curves compare calculations based on free-electron wavefunctions calculated in the AA (solid black) and Coulomb (dashed red) potentials. The vertical blue line in (b) represents the threshold energy needed for the inelastic ($\sigma_{2s\rightarrow2p}$) cross section to be nonzero. The cross sections calculated using the AA potential show a reduced value at low energies and resonances that are due to self-consistent screening and the presence of pressure-ionized bound states.
• Figure 4: Inelastic cross section for the $2s\rightarrow2p$ transition at two different densities using AA and Coulomb free wavefunctions. Modifications due to screening and pressure ionization from the AA free wavefunctions move to higher energy as the density increases.
• Figure 5: (a) Line widths calculated using AA (open squares) and Coulomb (solid red line) free wavefunctions differ at higher density. These two calculations use the Coulomb interaction potential given by Eq. (\ref{['eq:V']}) inside the matrix elements. The dashed lines show the line width calculated using the Coulomb free wavefunctions and the screened interaction potential in Eq. (\ref{['eq:Vscr']}). (b) Relative line width between AA and Coulomb free wavefunctions shows a general decrease due to screening and sharp increases due to pressure ionization of bound states. The principal quantum number of the states corresponding to the pressure ionization peaks are labeled accordingly.