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.

A sample of gas, originally treated as a single quantum system, is now described in terms of its molecular constituents, starting with the case of a single radiating molecule in an equilibrium bath of perturbers. First, the isolated radiator is considered, as if the bath had been deactivated, allowing a discussion of how its internal energy and angular momentum may change when, in the presence of an electromagnetic field , a radiant transition takes place, and of how the transition amplitude may be reduced under the Wigner–Eckart theorem. Then, the interaction between radiator and bath is reinstated, but the initial correlations between the two are neglected, so that a separate average over the bath may be taken. There is then an examination of various approximations that may be of use elsewhere. These are the restrictions to collisions that are binary in nature, the possibility that a collision may be said to follow a classical trajectory, and the validity of treating it under the impact approximation, which carries a restriction to the core region of a spectral line, but offers a great simplification when collisions may be regarded as very brief, well-separated events.

The focus here is on the approach taken by Anderson, which extends previous work by including the possibility that collisions will cause transitions in the radiator. Anderson confines himself to spectral lines that may be considered isolated from one another, and will, therefore, be broadened independently, and the start point is the correlation function of the radiatively active dipole, a quantum mechanical average formed from the states and operators of the gas system. This is treated as an ensemble average, in line with later chapters, and Anderson’s use of a time average is relegated to an appendix. However, the two approaches eventually converge, and both lead to a concern for the average effect on the lines as the radiator encounters an ensemble of single binary collisions on classical trajectories. Under the impact approximation, the correlation function may be greatly simplified, and expressions arise for the shift and width of a spectral line in terms of an optical cross-section that may be approached through a low order perturbative approximation. Within this, contributions due to phase shifts, elastic reorientations and inelastic transfers may all be distinguished.