Phonon-assisted asymmetric tunneling in a double-well potential: consequences for neutron scattering and diffusion

Abstract

We investigate the dynamics of a light interstitial atom in a double-well potential and extend the small polaron theory to include tunneling transitions from the ground state to excited states as well as asymmetry between sites. Starting from a generalized spin-boson Hamiltonian we use the resolvent of the time-development operator to derive formulas for transition rates and neutron-scattering structure factors. We show how with only two parameters the model allows for a quantitative description of hydrogen diffusion in bcc metals up to high temperatures. Asymmetry between the wells strongly reduces the mobility, particularly at low temperatures.