D ec 2 00 3 Regularities in Many - body Systems Interacting by a Two - body Random Ensemble

The ground states of all even-even nuclei have angular momentum, I, equal to zero, I = 0, and positive parity, π = +. This feature was believed to be a consequence of the attractive short-range interactions between nucleons. However, in the presence of two-body random interactions, the predominance of I = 0 ground states (0 g.s.) was found to be robust both for bosons and for an even number of fermions. For simple systems, such as d bosons, sp bosons, sd bosons, and a few fermions in single-j shells for small j, there are a few approaches to predict and/or explain the distribution of angular momentum I ground state probabilities. An empirical recipe to predict the I g.s. probabilities is available for general cases, but a more fundamental understanding of the robustness of 0 g.s. dominance is still out of reach. Other interesting results are also reviewed concerning other robust phenomena of many-body systems in the presence of random interactions, such as odd-even staggering of binding energies, generic collectivity, behavior of average energies, correlations, and regularities of many-body systems interacting by a displaced two-body random ensemble. PACS: 05.30.Fk, 05.45.-a, 21.60Cs, 24.60.Lz key words: I g.s. probabilities, 0 g.s. dominance, random interactions, correlation, generic collectivity, average energies.