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A measurement of the b 87 Rb spin-lattice relaxation rate in a Rb 0.58 (ND 4 ) 0.42 D 2 PO 4 single crystal in a wide temperature range allowed for a discrimination between classical thermally activated deuteron jumping across the potential barrier between the two equilibrium sites in the H-bond and phonon assisted incoherent deuteron tunnelling. The results show that thermally activated deuteron intra-bond jumping dominates above 55 K whereas at lower temperatures phonon assisted deuteron tunnelling becomes rate determining.