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.