The purpose of the present work is to make an exhaustive study of the line shape of the triplet 3p-4s Mg line (Mgb triplet), which is perturbed by He in the extreme physical conditions found in the cool atmosphere of DZ white dwarfs. This study is undertaken by inferring both a unified theory of spectral line broadening and ab initio potential energies. Cool white dwarfs require a specific treatment for line broadening owing to the high helium densities that are involved. Beyond the conventional symmetrical Lorentzian core at low density, we show that the line profiles are asymmetrical and have significant additional contributions on the short wavelength side. This blue asymmetry is a consequence of low maxima in the corresponding Mg-He potential energy difference curves at short and intermediate internuclear distances. The new profiles are shown to provide a good fit to an SDSS (Sloan Digital Sky Survey) observation.