  We study the bound-state spectrum in a simple model of pseudo-Dirac dark
matter, and examine how the rate of bound-state formation through radiative
capture compares to Sommerfeld-enhanced annihilation. We use this model as an
example to delineate the new features induced by the presence of a mass
splitting between the dark matter and a nearly-degenerate partner, compared to
the case where only a single dark-matter-like state is present. We provide a
simple analytic prescription for estimating the spectrum of bound states in
systems containing a mass splitting, which in turn allows characterization of
the resonances due to near-zero-energy bound states, and validate this estimate
both for pseudo-Dirac dark matter and for the more complex case of wino dark
matter. We demonstrate that for pseudo-Dirac dark matter the capture rate into
deeply bound states is, to a good approximation, simply related to the
Sommerfeld enhancement factor.
