A brief overview is given of many topics that are covered later, followed by a detailed plan of the book. The concern is with interactions that take place between molecular dipoles in an equilibrium gas when probed by an externally sourced electromagnetic wave train. This will lead to the appearance of otherwise sharp spectral lines that may be broadened in various ways. After a brief mention of the early ideas of Lorentz and Weisskopf, the discussion moves to the real starting point for this book, which is the idea that the line shape will be determined by the fluctuating response of the active dipole to molecular collisions. Three broadening effects are distinguished. Firstly, an elastic collision at the radiating molecule may cause a sudden change in the phase of the wave train. Secondly, where an elastic collision exerts a torque on the radiator, there may be an elastic reorientation and a sudden change in the wave train amplitude. Thirdly, an inelastic collision may lead to a sudden change in the frequency of the wave train, and, if these collisions are frequent enough, there may also be interference, or coupling, between the lines as they are broadened.

Starting from the very general Fano theory of pressure broadening, ways are sought to express the shape of a band of lines in a form that is more amenable to calculation. Initially, the far-wing is considered, and care is taken to ensure, by an adjustment, that the fluctuation–dissipation theorem is satisfied, despite Fano’s neglect of the initial correlations between the states of the radiator and the bath of its perturbers. The far-wing also requires, in a Fourier sense, the use of a very fine time scale, which allows the approach taken by Rosenkranz and Ma & Tipping, described first, to adopt the quasi-static approximation. In obtaining the overall line shape, the average over collisions may then be run across an ensemble of essentially static binary configurations. In the line core, the initial correlations may be ignored anyway, and, because a much coarser time scale is appropriate, the impact approximation may be invoked. Here, Fano’s theory is shown to reduce to that of Baranger, yielding expressions for fixed line shifts and widths, and allowing, through a perturbative approximation due to Rosenkranz, a simple expression to be derived to take account of line coupling.