Refinement of the semiclassical theory of the Stark broadening of hydrogen spectral lines in plasmas

- Perturbing electrons actually move not as free particles, but in a dipole potential.
- Choices of the Weisskopf radius and the strong collision constant are interrelated.
- Result: an increase of the Stark broadening by electrons in warm dense plasmas.

Stark broadening (SB) of hydrogen, deuterium, and tritium lines (H-lines) is an important diagnostic tool for many applications. The most “user-friendly” are semiclassical theories of the SB of H-lines: their results can be expressed analytically in a relatively simple form for any H-line. The simplest semiclassical theory is the so-called Conventional Theory (CT), which is frequently referred to as Griem׳s theory. While by now there are several significantly more advanced semiclassical “non-CT” theories of the SB, Griem׳s CT is still used by a number of groups performing laboratory experiments or astrophysical observations for the comparison with their experimental or observational results. In the present study we engage unexplored capabilities of the CT for creating analytically a more accurate CT. First, we take into account that the perturbing electrons actually do not move as free particles: rather they move in a dipole potential V=〈R〉·r/r3, where r is the radius-vector of the perturbing electrons and 〈R〉 is the mean value of the radius vector of the atomic electron. Second, Griem׳s definition of the so-called Weisskopf radius was not quite accurate. Third, in his book of year 1974, Griem suggested changing so-called strong collision constant without changing the Weisskopf radius, while in reality the choices of the Weisskopf radius and of the strong collision constant are interrelated. We show that the above refinements of the CT increase the electron broadening - especially for warm dense plasmas emitting H-lines. By comparison with benchmark experiments concerning the Hα line we demonstrate that the effect of the ion dynamics (neglected in any CT) might be slightly smaller than previously thought, while the effect of the acceleration of perturbing electrons by the ion field in the vicinity of the radiating atom (neglected in any CT) might be greater than previously thought.