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A microscopic particle-vibration coupling approach for atomic nuclei. Giant resonance properties and the renormalization of the effective interaction

The self-consistent mean-field (SCMF) theory describes many properties of the ground state and excited states of the atomic nucleus, such as masses, radii, deformations and giant resonance energies. SCMF models are based on the independent particle picture where nucleons are assumed to move in a self-generated average potential. In the first part of this work, we apply a state-of-the-art SCMF approach, based on the Skyrme effective interaction, to two different excitations (viz. the pygmy dipole resonance and the isovector giant quadrupole resonance), investigating their relation with the nuclear matter symmetry energy, which corresponds to the energy cost for changing protons into neutrons and is a key parameter for the nuclear equation of state. However, SCMF models present well known limitations which require the inclusion of further dynamical correlations, e.g. the ones coming from the interweaving between single-particle and collective degrees of freedom (particle-vibration coupling - PVC). In the second part of this work, we report on the application to inclusive (namely, the strength function of giant resonances) and exclusive (the gamma decay of giant resonances) observables of a new self-consistent model based on the PVC idea in the Skyrme framework. In our model we use an effective interaction fitted at mean-field level to some selected experimental data. In principle, when these interactions are used in beyond mean-field theories, one would need to re-determine the parameters of the interaction at the same level of approximation. Moreover, due to the zero-range nature of the employed interaction, divergences arise. In the last and most innovative part of this thesis, we develop, for the first time in finite nuclei, a possible way to cure the divergences, paving the way to the possibility of producing an effective interaction fitted at PVC level.