Bound photons in the lowest order Weisskopf-Wigner theory

The lowest order Weisskopf-Wigner theory of the interaction of a two-level atom with one photon is investigated on a rigorous mathematical base. Within this theory we show that the processes of spontaneous emission and resonance fluorescence take place in the conventional way if and only if the energy differenceE _b-E_a between the upper and the lower level is not too small. IfE _b-E_a is below a certain, always positive, threshold? _ba the hamiltonian of the interacting system assumes an eigenstate. This leads to effects which can be described only by saying that with a certain probability the photon is “bound” to the atom. This is related with a certain binding energy. For the case that the “levels” of the atom are certain interesting states of the Dirac hydrogen atom we compute numerical values for the thresholds, for the binding energies below, and for the line shifts above threshold. Thresholds, binding energies, and line shifts are typically of the order of the experimental Lambshift separation of the 2S _1/2-2P _1/2 level complex.