Statistical Broadening of Spectral Lines Emitted by Ions in a Plasma

Abstract

The Holtsmark theory of line broadening omits the factor $e^{-\frac{V_{\mathrm{ij}}}{\mathrm{kT}}}$ in the evaluation of probabilities, $V_{\mathrm{ij}}$ being the Coulomb interaction between the $i\mathrm{th}$ and the $j\mathrm{th}$ ions. This leads to serious errors in the wings of a line where frequency shifts arise from close encounters which are inhibited by the Boltzmann factor. In part I of the present article a consistent binary approximation to the line shape is given, the assumption being made that only a single perturber is involved in a collision. Part II treats the case of many particles, retains $V_{\mathrm{ij}}$ for all perturbers $j$ interacting with a single radiating ion $i$, but ignores forces between the perturbers themselves. Comparison is made with other treatments.