Unified Model for Stark Broadening

Stark broadening of spectral lines is considered as a semi-classical many-body problem. Starting from a Liouville equation for a distribution function depending on the atomic Hilbert space vector and the coordinates and velocities of the classical plasma particles, BBGKY hierarchy techniques are used to derive a complete line profile for the electron contribution. The line shape formula is expressed in terms of the atomic time evolution operator for a collision with a single plasma electron. This operator is approximated by a strictly unitary exponential expression, yielding more accuracy than second order perturbation theory and being valid also in the quasi-static limit. The resulting line shape expression covers the whole frequency domain from the impact regime to the quasi-static regime. The results of the impact and quasi-static approximations are recovered as special cases for small and large distances from the line center. A numerical application to Lyman - α shows very good agreement with an experiment of Boldt and Cooper.