Probing strongly coupled chameleons with slow neutrons

We consider different methods to probe the chameleon scalar field with slow neutrons. Chameleons modify the potential of bouncing neutrons over a flat mirror in the terrestrial gravitational field. This induces a shift in the energy levels of the neutrons which could be detected in current experiments like GRANIT. Chameleons between parallel plates have a field profile which is bubblelike and which would modify the phase of neutrons in interferometric experiments. We show that this new method of detection is competitive with the bouncing neutron one, hopefully providing an efficient probe of chameleons when strongly coupled to matter.