Some interesting speculation on dark matter atoms and the types of interaction that might be possible here:
Dark matter interacts only very weakly via the forces we know of. The idea, though, is that there might be some other force or forces that “ordinary” matter doesn’t participate in, but which dark matter does. Now, we have no real reason to suspect that such a force exists, but we also have no real reason to suspect that it doesn’t. Occam’s Razor may not even apply, here: Is it really simplest to assume that we’ve found all of the forces that can affect all forms of matter, when we’ve only actually tested a single-digit percentage of matter?
I don’t think that’s true. We know from galactic rotation curves and gravitational lensing observations that dark matter largely lives in diffuse halos around galaxies.
If dark matter had any significant self-interaction, it should clump together at small scales, but that’s not what we see. It clumps only at galactic sizes.
Furthermore, if there were interaction, it seems like it should be apparent somehow. When a chemical is formed by interacting elements, or an atom by interacting nucleons, there’s an associated change in binding energy (usually a release). This usually shows up as a photon. If two dark matter particles collide to form something new, we should see the same thing, but we don’t observe a glow at the edge of galaxies.
Could the energy be carried away by a “dark photon” or some other unobservable particle? I guess so, but that’s starting to violate Occam’s Razor. And it still doesn’t solve the clumpiness problem.
corement’s link is interesting; it indicates that a small portion of dark matter could be in an interacting form (it also mentions that gamma rays would be released upon interaction). But I don’t see how it could be true for the bulk of it.