Beyond nearest-neighbor spacing distributions: A new indicator for core-induced chaos

We present a method for the statistical analysis of quantum spectra which goes beyond the standard nearest-neighbor spacing distribution. The method exploits a peculiar correlation of oscillator strength and level spacing distributions. For diamagnetic Rydberg spectra we demonstrate that core-induced chaos and generic chaos can be distinguished in an experimentally accessible regime far below the semiclassical limit and with already a few hundred lines per spectrum. We present two hypotheses for a generalization of our findings.