Dark sectors in neutron-shining-through-a-wall and nuclear absorption signals

We propose new searches for $n^\prime$, a dark baryon that can mix with the Standard Model neutron. We show that IsoDAR, a proposal to place an intense cyclotron near a large-volume neutrino detector deep underground, can look for $n\to n^\prime \to n$ transitions with much lower backgrounds than surface experiments. This opportune neutron-shining-through-a-wall search would be possible without any modifications to the primary goals of the experiment and would provide the strongest laboratory constraints on the $n$-$n^\prime$ mixing for a wide range of mass splitting. We also consider dark neutrons as dark matter and show that their nuclear absorption at deep-underground detectors such as SNO and Borexino places some of the strongest limits in parameter space. Finally, we describe other $n^\prime$ signatures, such as neutrons shining through walls at spallation sources, reactors, and the disappearance of ultracold neutrons.