The protons in H2O confined in carbon nanotubes have been shown to delocalize coherently at low temperatures, exhibiting a rich phenomenology that is sensitive to the diameter of the nanotubes. It is not known whether the dramatic narrowing of the momentum distribution in single wall nanotubes at low temperature is a result of the development of quantum coherence between nearby protons or a modification of the Born-Oppenheimer surface for individual protons. We propose to measure the momentum distribution of the deuterons in D2O in the SWNT sample to distinguish between these possibilities.