The thermal decoupling description of dark matter (DM) and co-annihilating partners is reconsidered. If DM is realized at around the TeV-mass region or above, even the heaviest electroweak force carriers could act as long-range forces, leading to the existence of meta-stable DM bound states. The formation and subsequent decay of the latter further deplete the relic density during the freeze-out process on top of the Sommerfeld enhancement, allowing for larger DM masses. While so far the bound-state formation was described via the emission of an on-shell mediator ($W^{pm}$, $Z$, $H$, $g$, photon or exotic), we point out that this particular process does not have to be the dominant scattering-bound state conversion channel in general. If the mediator is coupled in a direct way to any relativistic species present in the Early Universe, the bound-state formation can efficiently occur through particle scattering, where a mediator is exchanged virtually. To demonstrate that such a virtually stimulated conversion process can dominate the on-shell emission even for all temperatures, we analyze a simplified model where DM is coupled to only one relativistic species in the primordial plasma through an electroweak-scale mediator. We find that the bound-state formation cross section via particle scattering can exceed the on-shell emission by up to several orders of magnitude.
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