Tunneling in fermion systems

We calculate the tunneling rate of a heavy particle in a metal, which can hop between two sites at ±a with a frequency rate Δ/(2ℎ) and can interact with the conduction electrons with the screened potential G. The tunneling rate presents an asymmetric peak, centered at the reduced energy Δ*, that decreases with increasing G. The integrated tunneling rate has a finite value for the phase shift at the Fermi level δ0=π/2. Our results point to no localization of the heavy particle in this model