  Complex quantum systems consisting of large numbers of strongly coupled
states exhibit characteristic level repulsion, leading to a non-Poisson spacing
distribution which can be described by Random Matrix Theory. Scattering
resonances observed in ultracold atomic and molecular systems exhibit similar
features as a consequence of their energy level structure. We study how the
overlap between Feshbach resonances affects the distribution of resonance
spacings. The spectrum of strongly overlapping resonances turns out to be
non-Poisson even when the assumptions of Random Matrix Theory are not
fulfilled, but the spectrum is also not completely chaotic and tends towards
being semi-Poisson.
