Two-body random ensemble for nuclei

The nuclear shell model exhibits dynamical and geometrical aspects. The former are determined by the two-body matrix elements of the residual interaction while the latter are due to the two-body operators that couple pairs of fermions to good quantum numbers of spin, isospin, and parity. We analyze the geometric aspects of the shell model and understand some of its generic properties regarding the generation of chaos in nuclear spectra and correlations between spectra with different quantum numbers. In particular, we address the preponderance of spin-O ground,states.