Coherent and chaotic properties of nuclear pairing

The properties of the pairing interaction in the shell model framework are considered with the aid of an exact numerical solution utilizing the quasispin symmetry. We emphasize the features which are out of reach for the usual approximate techniques based on the BCS approach supplemented by the random phase approximation treatment of pair vibrations, especially in the region of weak pairing where the BCS plus random-phase-approximation theory fails. Chaotic aspects of the mixing generated by the pairing interaction are studied. The level repulsion and large information entropy of the eigenstates coexist with the absence of thermalization of single-particle motion. The full spectrum of pair vibration on average displays a spin dependence similar to that for a rigid rotor.