Hierarchical trapping of resonance states at high level density

On the basis of a simple S-matrix model we show that, at high average level density, local fluctuations in the density of states of an open quantum mechanical system create locally a few broad resonance states together with a larger number of narrow (trapped) ones. The widths of the broad states are of the order of the length which characterizes the local fluctuations in the spectrum. They serve as a background for the narrow ``fine-structure resonances.'' If the spectrum shows a hierarchical fluctuation pattern in energy, this behavior repeats on all energy scales. From these results, we conjecture that the well-known intermediate structures in nuclei at high level density, described by the doorway mechanism, are formed due to such a trapping effect.