Tunneling of H within nearly undistorted substitutional-H pairs in Nb: a centrosymmetric four-level system

The geometry and dynamics of the tunnel systems of H trapped by substitutional atoms in Nb has been studied by anelastic spectroscopy on very diluted NbZrx(H/D)y alloys (x<0.0015). At such low impurity levels the features of the anelastic spectrum of the nearly non-interacting complexes are observable, and finally provide clear evidence of the delocalization of H in centrosymmetric four-level systems (FLS). An additional process is found at liquid He temperatures, besides that present also at higher concentrations, and similar to the anelastic response of a two-level system. The new process has an intensity that does not vanish for small asymmetries and a slow rate dominated by two-phonon transitions. Such features can be easily explained in terms of a simple perturbative approach, in which the transitions with the intermediate energy levels of a FLS turn out to be prohibited in the first order.