Theory of Line Broadening in Multiplet Spectra

Abstract

A theory of line broadening in the impact approximation is developed which includes the case of overlapping lines. It is assumed that the collisions which give rise to the broadening do not cause transitions between states with different principal quantum numbers. The theory has been worked out in detail in two cases: (1) the broadening arises only from perturbations of the upper state with arbitrary splitting of the substates. This approximation may be used if the perturbations of the lower state are relatively unimportant (e.g., the higher series members of the Balmer lines), and is exact if the perturbations do not affect the lower state as in the case of the ground state of hydrogen perturbed by electron collisions; (2) complete degeneracy of the initial and final states. This approximation is also valid on the far wing of the line if there is splitting, i.e., for frequencies large compared to the splitting, and is a generalization of Anderson's theory. The formal theory is worked out by two different methods. The method of calculation for nearly degenerate initial and final states with splitting is indicated. Method I is particularly suited for calculating the wing distribution while Method II is more suitable for finding the intensity distribution at the line center for overlapping lines. The line profile is made up of a sum of dispersion profiles and asymmetric terms which arise from interferences when the transition operator is not diagonal. The shift and half-width parameters are found from the roots of a secular equation and depend on the splitting as well as the density, temperature, and the character of the perturbation.