  A simple model of an atom interacting with the quantized electromagnetic
field is studied. The atom has a finite mass $m$, finitely many excited states
and an electric dipole moment, $\vec{d}_0 = -\lambda_{0} \vec{d}$, where $\|
d^{i}\| = 1,$ $ i=1,2,3,$ and $\lambda_0$ is proportional to the elementary
electric charge. The interaction of the atom with the radiation field is
described with the help of the Ritz Hamiltonian, $-\vec{d}_0\cdot \vec{E}$,
where $\vec{E}$ is the electric field, cut off at large frequencies. A
mathematical study of the Lamb shift, the decay channels and the life times of
the excited states of the atom is presented. It is rigorously proven that these
quantities are analytic functions of the momentum $\vec{p}$ of the atom and of
the coupling constant $\lambda_0$, provided $|\vec{p}| < mc$ and $| \Im\vec{p}
|$ and $| \lambda_{0} |$ are sufficiently small. The proof relies on a somewhat
novel inductive construction involving a sequence of `smooth Feshbach-Schur
maps' applied to a complex dilatation of the original Hamiltonian, which yields
an algorithm for the calculation of resonance energies that converges
super-exponentially fast.
