Line mixing sum rules for the analysis of multiplet spectra

In the impact approximation, the spectrum of transitions overlapped by collisional broadening is given by a sum over Lorentzian absorption and dispersion profiles about each transition. The dispersion components arise from the interference among lines coupled by the collisions, and their magnitudes and signs are given by the line mixing parameters. The line mixing parameters, as well as the transition intensities, widths and shifts, are obtained from inversion of the relaxation matrix and may be highly non-linear in pressure when the coupled lines are strongly overlapped. For any overlap, however, the line mixing parameters summed over all coupled lines is zero and the total integrated intensities, widths and shifts are conserved. These sum rules may be used as constraints in least-squares fitting of multiplet spectra to reduce the number of free parameters and their correlation. Also for the fitting of spectra at atmospheric pressures, a prescription is given for incorporating Doppler broadening and Dicke narrowing.