Making use of the fact that the collective modes associated with the spontaneous (static and dynamic) violation of gauge invariance in atomic nuclei (pairing rotations and pairing vibrations), are amenable to a simple, quite accurate nuclear structure description (BCS and QRPA respectively), it is possible to quantitatively test the reaction mechanism which is at the basis of two-nucleon transfer reactions, specific probe of pairing in nuclei. With the help of the static and dynamic mean field spectroscopic amplitudes, taking into account successive and simultaneous transfer channels properly corrected because of nonorthogonality effects, as well as describing the associated elastic channels in terms of experimentally determined optical potentials, one obtains absolute, two-particle transfer differential cross sections which provide an overall account of the data within experimental errors. One of the first results connected with such quantitative studies of pairing correlations in nuclei is the observation of phonon mediated pairing in the exotic halo nucleus 11 Li, and the associated discovery of a new mechanism to break nuclear gauge symmetry: bootstrap, pigmy-resonance-mediated Cooper pair binding.
Gauge invariant BCS nuclear theory:Pairing vibrations and pairing rotationsA closed shell system like, e.g., 132 Sn (virtually) spends part of the time in the ground state of 134 Sn and part in that of 130 Sn. This is another way to say that addition and removal pairing vibrations, are J π = 0 + , τ = 1, β = ±2 elementary modes of nuclear excitation, τ and β being the isospin and the particle (fermion) quantum numbers. This last quantum number 1 arXiv:1206.1640v1 [nucl-th]