Standard line broadening impact theory for hydrogen including penetrating collisions

Abstract

In recent years there has been significant interest in the emission spectra from high-density plasmas, as manifested by a number of experiments. At these high densities short range (small impact parameter) interactions become important and these cannot be adequately handled by the standard theory, whose predictions depend on some cutoffs, necessary to preserve unitarity, the long range approximation, and to ensure the validity of a semiclassical picture. Very recently, as a result of a debate concerning the broadening of isolated ion lines, the importance of penetration of bound electron wave functions by plasma electrons has been realized. By softening the interaction, penetration makes perturbative treatments more valid. The penetration effect has now been included analytically into the standard theory. It turns out that the integrations may be done in closed form in terms of the modified Bessel functions K0 and K1. This work develops the new theory and applies it to experimental measurements.

The Fourth Workshop on Lineshape Code Comparison: Line Merging

“…With respect to the bound-bound transitions, the present comparison confirms the importance of strong collisions, even for H α at the lowest density as well as penetrating collisions, which significantly reduce the strong collision phase space [9]. This is evidenced by the good agreement of DWE and CONVPST which both account for penetrating collisions.…”

“…In addition, for each ST and PST [9,10] calculations, runs were contributed with or without account of strong collisions. In CONVST, strong are collisions with impact parameters that are either smaller than n 2 a 0 or violate unitarity in a perturbative treatment for a given velocity.…”

“…In CONVST, strong are collisions with impact parameters that are either smaller than n 2 a 0 or violate unitarity in a perturbative treatment for a given velocity. In CONVPST, strong collisions are slow enough collisions that violate unitarity in a perturbative treatment accounting for penetration [9]. In either case, if strong collisions are accounted for, a strong collision term corresponding to the assumption that for impact parameters ρ and velocities v in the strong collision phase space, the angular averaged matrix…”

“…This effect softens the interaction and makes perturbative treatments valid for a larger part of the phase space, resulting in a much reduced strong collision term and relatively small difference (practically zero for the present work) in the CONVPST calculations with and without the strong collision term. As a result for hydrogen and H-like lines, this effect can be accounted for analytically and this has been done for the dipole part of the interaction [2,9,10]. It is, therefore, probably not a coincidence that agreement between CONVPST and DWE is very good for all lines in the series.…”

The Fourth Workshop on Lineshape Code Comparison: Line Merging

“…In CONVST, strong are collisions with impact parameters that are either smaller than n 2 a 0 or violate unitarity in a perturbative treatment for a given velocity. In CONVPST, strong collisions are slow enough collisions that violate unitarity in a perturbative treament accounting for penetration [9]. In either case, if strong collisions are accounted for, a strong collision term corresponding to the assumption that for impact parameters ρ and velocities v in the strong collision phase space, the angular averaged matrix…”