Problem of Overlapping Lines in the Theory of Pressure Broadening

The theory of pressure broadening is re-examined, in order to include the possibility of overlapping lines, which are a regular feature of pressure broadening in an ionized gas. It is found that a simple treatment can be given using the impact approximation. This approximation is examined in detail, and its validity conditions are discussed. When it is valid, it is permissible to replace the exact time-dependent interaction between the atom and the perturbers by a time-independent effective interaction. The latter is not Hermitian, however, and therefore every level acquires a width. The shape of a group of overlapping lines is then worked out, and is found to consist of a sum of Lorentz line shapes, plus some interference terms. In the particular case of an isolated line, the results given previously by Anderson are obtained. Finally, a study is made of the simplifications brought about by rotational invariance.