Dual origin of pairing in nuclei

The pairing correlations of the nucleus ¹²⁰Sn are calculated by solving the Nambu–Gor'kov equations, including medium polarization effects resulting from the interweaving of quasiparticles, spin and density vibrations, taking into account, within the framework of nuclear field theory (NFT), processes leading to self-energy and vertex corrections and to the induced pairing interaction. From these results one can not only demonstrate the inevitability of the dual origin of pairing in nuclei, but also extract information which can be used at profit to quantitatively disentangle the contributions to the pairing gap Δ arising from the bare and from the induced pairing interaction. The first is the strong ¹S₀ short-range NN potential resulting from meson exchange between nucleons moving in time reversal states within an energy range of hundreds of MeV from the Fermi energy. The second results from the exchange of vibrational modes between nucleons moving within few MeV from the Fermi energy. Short- (v_p^bare) and long-range (v_p^ind) pairing interactions contribute essentially equally to nuclear Cooper pair stability. That is to the breaking of gauge invariance in open-shell superfluid nuclei and thus to the order parameter, namely to the ground state expectation value of the pair creation operator. In other words, to the emergent property of generalized rigidity in gauge space, and associated rotational bands and Cooper pair tunneling between members of these bands.