**Abstract: **
We analyze the spectral structure of a multi-partite quantum system, in
dimension d= 1,2,3, made up of a particle interacting via zero range
interactions with one or many localized quantum spins. In particular we
examine the transition, triggered by the interaction, from bound states
embedded in the continuous spectrum to metastable states. We show that in
any dimension quite explicit formulas and series expansions for the
position of the resonance pole and for the time evolution of the resonant
states can be given. Possible applications to models of a quantum
measurement process are discussed.