  There has been renewed interest in the possibility that dark matter exists in
the form of atoms, analogous to those of the visible world. An important input
for understanding the cosmological consequences of dark atoms is their
self-scattering. Making use of results from atomic physics for the potentials
between hydrogen atoms, we compute the low-energy elastic scattering cross
sections for dark atoms. We find an intricate dependence upon the ratio of the
dark proton to electron mass, allowing for the possibility to "design"
low-energy features in the cross section. Dependences upon other parameters,
namely the gauge coupling and reduced mass, scale out of the problem by using
atomic units. We derive constraints on the parameter space of dark atoms by
demanding that their scattering cross section does not exceed bounds from dark
matter halo shapes. We discuss the formation of molecular dark hydrogen in the
universe, and determine the analogous constraints on the model when the dark
matter is predominantly in molecular form.
