The theory of line shapes relevant to the spectra of cool stars

Accurate pressure broadened profiles of alkali resonance doublets are needed for modelling of the atmospheres of cool stars and for generating their synthetic spectra in the region 400-900 nm. When the usual impact theory of line broadening is used, the profile is simply Lorentzian and the widths and shifts of the lines can be calculated, provided that interaction potentials for the emitter-perturber system are available. However when the lines utterly dominate their region of the spectrum, it becomes important to also accurately represent the profile in the line wings, where the impact theory is no longer valid. The original development of line broadening theory by Baranger in 1958 is reexamined and calculations have been carried out in which it is shown that it is not necessary to invoke the impact approximation. To test the validity of different approximations, results for line widths and shifts are presented for the lithium and sodium resonance lines broadened by helium for 0.1 K ⩽ T ⩽ 3000 K.