Temperature dependence of the librational tunneling and proton relaxation

A coupling between the librations of the methyl groups or proton tetrahedra (e.g., C${\mathrm{H}}_4$ and N${\mathrm{H}}_4^{+}$) in a solid is shown to explain the experimentally observed decrease of the librational tunneling splitting without significant lifetime broadening when the temperature is raised at low temperatures. Due to the same coupling, the libration amplitude of a given group is influenced by neighboring groups. The amplitude can momentarily increase so much that the group undergoes random jumps to other equilibrium orientations even at liquid-helium temperatures. This model agrees with the nearly temperature-independent spin-lattice relaxation time $T_1$ of protons in some samples for $T\lesssim 4$ K and with the temperature-dependent $T_1$ described by the activation energy equal to the separation between the ground and first-excited-librational levels at somewhat higher temperatures.