  The possibility for our visible world to be a 3-brane embedded in a
multidimensional bulk is at the heart of many theoretical edifices in
high-energy physics. Probing the braneworld hypothesis is thus a major
experimental challenge. Following recent theoretical works showing that matter
swapping between braneworlds can occur, we propose a
neutron-shining-through-a-wall experiment. We first show that an intense
neutron source such as a nuclear reactor core can induce a hidden neutron flux
in an adjacent hidden braneworld. We then describe how a low-background
detector can detect neutrons arising from the hidden world and quantify the
expected sensitivity to the swapping probability. As a proof of concept, a
constraint is derived from previous experiments.
