  Metal-polluted white dwarfs (DZ stars) are characterized by a helium-rich
atmosphere contaminated by heavy elements traces originating from accreted
rocky planetesimals. As a detailed spectroscopic analysis of those objects can
reveal the composition of the accreted debris, there is a great interest in
developing accurate DZ atmosphere models. However, the coolest DZ white dwarfs
are challenging to model due to the fluidlike density of their atmospheres.
Under such extreme conditions, spectral absorption lines are heavily broadened
by interactions with neutral helium and it is no longer justified to use the
conventional Lorentzian profiles. In this work, we determine the theoretical
profiles of the Ca I resonance line (the most prominent spectral line for the
coolest DZ white dwarfs) in the dense atmospheres of cool DZ white dwarfs. To
do so, we use a unified theory of collisional line profiles and accurate ab
initio potential energies and transition dipole moments for the CaHe molecule.
We present the resulting profiles for the full range of temperatures and helium
densities relevant for the modeling of cool, metal-polluted white dwarfs (from
3000 to 6000 K and from $10^{21}$ to $10^{23}\,{\rm cm}^{-3}$). We also
implement these new profiles in our atmosphere models and show that they lead
to improved fits to the Ca I resonance line of the coolest DZ white dwarfs.
