The hopping motion of charged light particles in superconducting metals was considered within the framework of a 2-state model. In addition to a coupling to the superconducting electrons, the effect of phonons was investigated. It was shown that, sufficiently far below the critical temperature, the hopping rate was dominated by 1-phonon processes if the static energy shifts between the particle ground states (so-called energy asymmetries) were finite but were smaller than twice the BCS energy gap. The role of special 2-phonon processes (so-called di-phonon processes) which resulted from a non-linear coupling to the lattice was investigated. It was found that, in the limit of energy asymmetries which were larger than twice the BCS energy gap, phonon coupling did not greatly affect the jump rates.

T.Regelmann, L.Schimmele, A.Seeger: Zeitschrift für Physik B, 1994, 95[4], 441-52