A universal approach to Rydberg spectral line shapes in plasmas

Abstract

A universal approach for the calculation of Rydberg atom line shapes in plasmas is developed. This approach goes far beyond the calculation capabilities of the standard models. It is based on analytical formulae for the intensity distribution in radiation transitions n − n′ between highly excited atomic states with large values of principal quantum numbers n, n′ ≫ 1, with Δn = n − n′ ≪ n, and on the frequency fluctuation model to account for ion thermal motion effects. The theory allows us to describe a transition from the static to the impact broadening domains for every hydrogen spectral line. The specific cases of broadening of Hn−α(Δn = 1) and Hn−β(Δn = 2) lines are considered in detail for various values of plasma parameters. The line shapes are presented in a universal manner as functions of the relative frequency splitting and of the fluctuation rate ν of the ion plasma microfield, using dimensionless variables. For small values of ν, the static line shapes which generalize the well-known Underhill–Waddell data for the Rydberg state case are presented. For large values of ν, the transition to impact ion broadening is observed, resulting in a narrowing effect. A comparison with the hydrogen Hα line shape calculations shows a good agreement between the universal approach for Rydberg lines and traditional spectral line shapes.