Properties of Some Exact Solutions of the Pairing Force Problem

A discussion is given of the collective modes of excitation of the nuclear pairing field, on which experimental evidence from the two-nucleon transfer reactions is accumulating. In regions of closed shells, the excitations have a vibrational character. The neutron 0+ pair vibrations around 208Pb are considered in the harmonic approximation and with the inclusion of interaction effects between the quanta of excitation. The relation between the vibrational treatment of pair correlations and the treatment in terms of superfluidity (dynamic and static pairing) is compared with the relation between vibrational and rotational descriptions of shape oscillations. The role of the isospin of the pairs is discussed with special attention to the spectrum of O+ pairing modes based on 56Ni. When the isospin degree of freedom is included, a static pairing (superfluidity) produces a deformation in isospace, with a resulting rotational spectrum in isospace. Finally, the coupling between particles and pair vibrational quanta is briefly discussed. (author)