Spectroscopy with random and displaced random ensembles

Because of the time reversal invariance of the angular momentum operator J2 , the average energies and variances at fixed J for random two-body Hamiltonians exhibit odd-even-J staggering that may be especially strong for J=0 . It is shown that upon ensemble averaging over random runs, this behavior is reflected in the yrast states. Displaced (attractive) random ensembles lead to rotational spectra with strongly enhanced B(E2) transitions for a certain class of model spaces. It is explained how to generalize these results to other forms of collectivity