  In dimension $d=1,2,3$ we define a family of two-channel Hamiltonians
obtained as point perturbations of the generator of the free decoupled
dynamics. Within the family we choose two Hamiltonians, $\hat H_0$ and $\hat
H_\ve$, giving rise respectively to the unperturbed and to the perturbed
evolution. The Hamiltonian $\hat H_0$ does not couple the channels and has an
eigenvalue embedded in the continuous spectrum. The Hamiltonian $\hat H_\ve$ is
a small perturbation, in resolvent sense, of $\hat H_0$ and exhibits a small
coupling between the channels.
  We take advantage of the complete solvability of our model to prove with
simple arguments that the embedded eigenvalue of $\hat H_0$ shifts into a
resonance for $\hat H_\ve$. In dimension three we analyze details of the time
behavior of the projection onto the region of the spectrum close to the
resonance.
