RESONANT DECAY NEAR AN ACCUMULATION POINT

We consider the quantum mechanics of a model system in which meta-stab le states arise through perturbation of a sequence of embedded simple eigenvalues with an embedded accumulation point. It is shown that the embedded eigenvalues become resonances in the perturbed system. These resonances also accumulate, and the position of the accumulation point is unchanged. The positions of the resonances are estimated uniformly up to the accumulation point. The meta-stable states associated with these resonances have the usual approximately exponential decay with t ime. Some applications to physical models are discussed.