Quantum Diffusion of Muons Interacting with Superconducting Electrons

The quantum diffusion of muons in superconductors is studied for two cases: superconductors with impurities and without impurities. The result shows that in the case of pure superconductors the tunneling probability from one site to a nearest neighbor site increases exponentially with the decrease of temperature. In the case of impure superconductors there is a competition among three energies: temperature, superconducting energy gap, and the energy difference between two neighbouring sites. As a consequence the tunneling probability has an interesting structure which reflects sensitively the energy gap.