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 Fano theory, described here, does not adopt the impact approximation, and is not confined to the line core. The main concession, implicit in an impact theory like that of Baranger or Anderson, is the neglect of initial correlations between the states of radiator and bath, allowing a separate average to be taken over the bath variables at the initial time. For Fano, the correlation function describes the linear response to the driving field and is governed dynamically by the Liouville operator, which, in Baranger’s line space, has a role similar to that of the Hamiltonian in the original state space. The response, in its Fourier transform, provides the line shape, and this is governed here by a relaxation operator that looks, formally, like a transition operator in quantum scattering. This is a very general theory that will, nevertheless, reduce to that of Baranger as soon as the impact approximation is imposed. Although the neglect of initial correlations will invalidate the fluctuation–dissipation theorem, this will only affect the line far-wing, where, unless remedied, it will cause an imbalance between the radiative processes induced by the field.