Elastic response of the atomic nucleus in gauge space: Giant Pairing Vibrations

Abstract

Due to quantal fluctuations, the ground state of a closed shell system $ A_{0}$ can become virtually excited in a state made out of the ground state of the neighbour nucleus $ \vert gs(A_0+2) \rangle $ ( $ \vert gs(A_0-2) \rangle $ ) and of two uncorrelated holes (particles) below (above) the Fermi surface. These $ J^{\pi} = 0^{+}$ pairing vibrational states have been extensively studied with two-nucleon transfer reactions. Away from closed shells, these modes eventually condense, leading to nuclear superfluidity and thus to pairing rotational bands with excitation energies much smaller than $ \hbar\omega_{0}$ , the energy separation between major shells. Pairing vibrations are the plastic response of the nucleus in gauge space, in a similar way in which low-lying quadrupole vibrations, i.e. surface vibrations with energies much smaller than $ \hbar\omega_{0}$ whose eventual condensation leads to quadrupole deformed nuclei, provide an example of the plastic nuclear response in 3D space. While much is known, in particular concerning its damping, regarding the counterpart of quadrupole plastic modes, i.e. regarding the giant quadrupole resonances (GQR), $ J^{\pi} = 2^{+}$ elastic response of the nucleus with energies of the order of $ \hbar\omega_{0}$ , little is known regarding this subject concerning pairing modes (giant pairing vibrations, GPV). Consequently, the recently reported observation of L = 0 resonances, populated in the reactions 12C(18O,16O)14C and 13C(18O,16O)15C and lying at an excitation energy of the order of $ \hbar\omega_{0}$ , likely constitutes the starting point of a new field of research, that of the study of the elastic response of nuclei in gauge space. Not only that, but also the fact that the GPV have likely been serendipitously observed in these light nuclei when it has failed to show up in more propitious nuclei like Pb, provides unexpected and fundamental insight into the relation existing between basic mechanisms --Landau, doorway, compound damping-- through which giant resonances acquire a finite lifetime, let alone the radical difference regarding these phenomena displayed by correlated (ph) and (pp) modes.