The theory of Baranger is discussed, relating it to the approach taken by Anderson in the last chapter and that taken by Fano in the one to follow. Baranger is concerned to describe pressure broadening in a band of close, overlapping lines. His original concern was with line broadening by fast-moving electrons in a plasma, which allowed him to use the impact approximation, but not to assume that collisions may be associated with classical paths. For this reason, although matter here is in the form of neutral molecules, the use of Baranger’s theory in its most general form requires that collisions be treated in terms of quantum scattering theory. In forming the correlation function, Baranger sets the algebra in a product space where line vectors take the place of the energy states used by Anderson, and the optical cross-section that governs line broadening is replaced by the matrix of an operator in line space, with line widths and shifts on the diagonal and line coupling parameters for the other elements. In the case of isolated lines, Anderson’s theory may be regained, but the introduction of line space paved the way, later on, for a much more general viewpoint.

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.