A MICROSCOPIC PARTICLE-VIBRATION COUPLING APPROACH FOR ATOMIC NUCLEI. GIANT RESONANCE PROPERTIES ANDTHE RENORMALIZATION OF THE E FFECTIVE INTERACTION

The atomic nucleus can be described, to a first approximation, as composed by independent particles, moving in an average potential created by all of them. Self-consistent mean-field (SCMF) methods are based on this basic idea, and they are known to produce overall successful results for ground state and excited state properties, such as masses, radii, deformations and giant resonance energies. In the first part of this work, we present our theoretical predictions on two different excitations: the pygmy dipole resonance and the isovector quadrupole resonance. The calculations are performed within a fully self-consistent framework, in which the Skyrme zero-range effective interaction is used. However, SCMF approaches present well-known limitations which require the inclusion of further correlations coming e.g. 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 of a self-consistent model based on the PVC idea in the Skyrme framework to inclusive (namely, the strength function of giant resonances) and exclusive (the gamma-decay width of giant resonances) observables. The main limitation of our beyond mean-field model is the use of an effective interaction fitted at mean-field level to some selected experimental data. Therefore, when these interactions are used in beyond mean-field theories the parameters of the interactions need to be determined at the desired level of approximation. Moreover, due to the zero range character of the employed interaction, divergences arise. In the last and most innovative part of this thesis, we develop a possible way to cure the divergences, paving the way to the possibility of designing an effective interaction fitted at PVC level.