Spontaneous decay of resonant energy levels for molecules with moving nuclei

We consider the Pauli-Fierz Hamiltonian with dynamical nuclei and investigate the transitions between the resonant electronic energy levels under the assumption that there are no free photons in the beginning. Coupling the limits of small fine structure constant and of heavy nuclei allows us to prove the validity of the Born-Oppenheimer approximation at leading order and to provide a simple formula for the rate of spontaneous decay.