Two-body random ensemble in nuclei

Combining analytical and numerical methods, we investigate properties of the two-body random ensemble (TBRE). We compare the TBRE with the Gaussian orthogonal ensemble of random matrices. Using the geometric properties of the nuclear shell model, we discuss the information content of nuclear spectra and gain insight in the difficulties encountered when fitting the effective interaction. We exhibit the existence of correlations between spectral widths pertaining to different quantum numbers. Using these results, we deduce the preponderance of zero-spin ground states in the TBRE. We demonstrate the existence of correlations between spectra with different quantum numbers and/or in different nuclei.