Scattering properties of dark atoms and molecules

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.