  For two discrete-level quantum systems in interaction, we follow the
displacement in the complex plane of the eigen-energies of the compound system
when the spectrum of one of the two systems becomes continuous. These new
points are usually called resonances. This allows us to define and to calculate
a critical value of the coupling constant which separates two well-known
coupling regimes. We also give an example of these resonances for the hydrogen
atom coupled to the continuum of the states of the transverse electromagnetic
field in the vacuum. We justify that some resonances be neglected.
