  We examine perturbations of eigenvalues and resonances for a class of
multi-channel quantum mechanical model-Hamiltonians describing a particle
interacting with a localized spin in dimension $d=1,2,3$. We consider
unperturbed Hamiltonians showing eigenvalues and resonances at the threshold of
the continuous spectrum and we analyze the effect of various type of
perturbations on the spectral singularities. We provide algorithms to obtain
convergent series expansions for the coordinates of the singularities.
