A new method for line-shape modeling of hydrogen-like and Rydberg transitions in plasma

Calculations of line shapes of hydrogen and hydrogen-like transitions (including Rydberg ones) are important for many topics of plasma physics and astrophysics. However, the Stark effect of the radiative transitions originating from high-$n$ levels is rather complex, making the detailed calculations of their spectral structure very cumbersome. Surprisingly, the complex structure of such transitions can be approximated, under certain assumptions, with a quasi-contiguous (QC) rectangular shape. This formed the basis of an analytical method for the calculation of line broadening\,[1], resulting in a simple expression for the full width at half-maximum of the Stark line broadening in plasma. Although the method is especially suitable for transitions with $\Delta n \gg 1$, it describes rather well even first members of the spectroscopic series with $\Delta n$ as low as 2. Recently, the QC method was extended\,[2] to analytical calculations of line {\em shapes} (not mere line {\em widths}) in plasmas. To this end, we employed a formulation\,[3] of the frequency fluctuation model. Accurate computer simulations\,[4] as well as comparison with experimental data, where available, were used to verify the validity of the method. Applications of the method to a range of physical problems are shown.\\[4pt] [1] E. Stambulchik and Y. Maron, J. Phys. B: At. Mol. Opt. Phys. {\bf 41}, 095703 (2008).\\[0pt] [2] E. Stambulchik and Y. Maron, in {\it Atomic Processes in Plasmas}, AIP Conf. Proc. (AIP, 2012) accepted for publication.\\[0pt] [3] A. Calisti, C. Moss\'{e}, S. Ferri, B. Talin, F. Rosmej, L. A. Bureyeva, and V. S. Lisitsa, Phys. Rev. E {\bf 81}, 016406 (2010); L. A. Bureeva, M. B. Kadomtsev, M. G. Levashova, V. S. Lisitsa, A. Calisti, B. Talin, and F. Rosmej, JETP Letters {\bf 90}, 647 (2010).\\[0pt] [4] E. Stambulchik and Y. Maron, J. Quant. Spectr. Rad. Transfer {\bf 99}, 730--749 (2006).