Deuteron Momentum Distribution in KD2HPO4

The momentum distribution in KD2PO4(DKDP) has been measured using neutron Compton scattering above and below the weakly first order paraelectric-ferroelectric phase transition(T=229K). There is very litte difference between the two distributions, and no sign of the coherence over two locations for the proton observed in the paraelectric phase, as in KH2PO4(KDP). We conclude that the tunnel splitting must be much less than 20mev. The width of the distribution indicates that the effective potential for DKDP is significantly softer than that for KDP. As electronic structure calculations indicate that the stiffness of the potential increases with the size of the coherent region locally undergoing soft mode fluctuations, we conclude that there is a mass dependent quantum coherence length in both systems.