Cover: Problem of Overlapping Lines in the Theory of Pressure Broadening

Problem of Overlapping Lines in the Theory of Pressure Broadening

Published in: The Physical Review, v. 111, no. 2, July 15, 1958, p. 494-504

Posted on 1958

by Michel Baranger

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 no 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.

This report is part of the RAND external publication series. Many RAND studies are published in peer-reviewed scholarly journals, as chapters in commercial books, or as documents published by other organizations.

RAND is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.