On the statistical properties of a hydrogenic atom broadened by linear Stark effect

摘要

Spectroscopy based on Stark broadening is a very efficient and successful method for diagnosing the physical conditions in laboratory or astrophysical plasmas. The studies are often focused on the lines of hydrogen or hydrogen-like ions due to the simple atomic structure. However, the Stark modeling may be difficult even for one-electron systems, in particular when radiative transitions with highly-degenerate Rydberg states are considered. Besides, the computations may become challenging for the modeling of line shapes in an optically thick plasma and accounting for non-local thermodynamical equilibrium (non-LTE) effects on the state populations. The statistical approach is a powerful technique which can be used to simplify complex coupled problems by replacing the numerous levels or lines by a single continuous distribution characterized by a reduced number of exact moments: area, center-of-gravity, variance, etc. In this paper, we study various statistical properties of a hydrogenic atom broadened by Stark effect. First, we derive the moments of level energies accounting for linear and quadratic Stark effects, electric-quadrupole and fine structure corrections. The resulting formulas allows one to estimate the relative importance of these corrections on the energies. We then derive the moments of the strength-weighted line energies for the Lyman and Balmer series in the framework of Linear-Stark effect. The moments are then used in a Gram?Charlier expansion series to represent the line shape, the resolution of the spectrum being controlled by the order at which the series is truncated. We show that the line shape of the transition n?n?n and n?