In this paper, we construct metastable states of atoms interacting with the quantized radiation field. These states emerge from the excited bound states of the non-interacting system. We prove that these states obey an exponential time-decay law. In detail, we show that their decay is given by an exponential function in time, predicted by Fermi's Golden Rule, plus a small remainder term. The latter is proportional to the (4+β)th power of the coupling constant and decays algebraically in time. As a result, though it is small, it dominates the decay for large times. A central point of the paper is that our remainder term is significantly smaller than the one previously obtained in [1] and as a result we are able to show that the time interval during which the Fermi's Golden Rule can be observed is significantly longer that the time interval obtained in [1]. This improvement is achieved by incorporating a part of the complex dilatation resonance states into our construction of the metastable states rather than using the unperturbed eigenstates (the excited bound states of the non-interacting system). Thus, the connection to resonance states allows us to introduce metastable states which qualify better in the description of unstable excited states of the interacting system.
Beyond Fermi’s Golden Rule in Free-Electron Quantum Electrodynamics: Acceleration/Radiation Correspondence
