  Ultracool stellar atmospheres show absorption by alkali resonance lines
severely broadened by collisions with neutral perturbers. In the coolest and
densest atmospheres, such as those of T dwarfs, Na I and K I broadened by
molecular hydrogen and helium can come to dominate the entire optical spectrum.
Their profiles have been successfully modelled with accurate interaction
potentials in the adiabatic theory, computing line profiles from the first few
orders of a density expansion of the autocorrelation function. The line shapes
in the emergent spectrum also depend on the distribution of absorbers as a
function of depth, which can be modelled with improved accuracy by new models
of dust condensation and settling.
  The far red K I wings of the latest T dwarfs still show missing opacity in
these models, a phenomenon similar to what has been found for the Na I line
profiles observed in extremely cool, metal-rich white dwarfs. We show that the
line profile in both cases is strongly determined by multiple-perturber
interactions at short distances and can no longer be reproduced by a density
expansion, but requires calculation of the full profile in a unified theory.
Including such line profiles in stellar atmosphere codes will further improve
models for the coolest and densest dwarfs as well as for the deeper atmosphere
layers of substellar objects in general.
