Theory of Wing Broadening of the Hydrogen Lyman-αLine by Electrons and Ions in a Plasma

Abstract

The frequency distribution of the absorption and emission coefficients on the wings of the hydrogen Lyman-$\alpha$ line broadened by local fields of both electrons and (quasistatic) ions in a plasma is calculated in the classical path approximation for regions well outside the half-intensity points. Depending on velocities and frequency separations from the line center, electron collisions are treated by an impact theory, which accounts both for Debye shielding and for the finite duration of the collisions, or by the quasistatic theory. Quadrupole interactions are considered in addition to the usual dipole interactions, and the (dominant) contribution of dipole interactions to the impact broadening is calculated to higher orders in the iterated solution of the time-dependent Schrödinger equation. Asymmetries introduced by quadratic Stark effect, by quadrupole interactions, by field-strength dependence of the oscillator strengths, and by the ion broadening of the central component through quadratic-Stark-effect and quadrupole interactions are evaluated. Also considered are asymmetries from the variation of factors usually assumed to be constant (frequencies and Boltzmann factors), and from the transformation from frequency to wavelength increments. Remaining theoretical uncertainties in the absolute values of absorption or emission coefficients for typical plasma conditions are estimated to be less than 10% over ranges in which these coefficients vary by three orders of magnitude.