The no-binding regime of the Pauli-Fierz model

The Pauli-Fierz model H(α) in nonrelativistic quantum electrodynamics is considered. The external potential V is sufficiently shallow and the dipole approximation is assumed. It is proven that there exist constants 0 < α- < α+ such that H(α) has no ground state for |α| < α-, which complements an earlier result stating that there is a ground state for |α| > α+.We develop a suitable extension of the Birman-Schwinger argument.Moreover, for any givend δ > 0 examples of potentials V are provided such that α+ - α- < δ.