Quantum Diffusion in Metals

Protons or positive muons trapped in interstitial sites in metals tunnel into neighbouring sites at low temperatures. The metalel eletrons form a screening cloud around the particle. When the particle tunnels into a neighbouring site, the electrons cannot follow the particle adiabatically. This is because low energy excitations of the metal electrons are too slow to respond the particle's motion quickly. This non-adiabatic effect results in a renormalization of the tunneling integral, which turns out to vary as a power of the temperature. Such a power law has been observed for the positive muon in Cu and other metals. For the proton in a Nb-O system a detailed comparison has been made between inelastic neutron scattering experiment and a theory which takes full account of the mentioned effect.