The scope of the paper is to apply a state-of-the-art beyond mean-field model to the description of the Gamow-Teller response in atomic nuclei. This topic recently attracted considerable renewed interest, due, in particular, to the possibility of per
forming experiments in unstable nuclei. We study the cases of $^{48}$Ca, $^{78}$Ni, $^{132}$Sn and $^{208}$Pb. Our model is based on a fully self-consistent Skyrme Hartree-Fock plus random phase approximation. The same Skyrme interaction is used to calculate the coupling between particles and vibrations, which leads to the mixing of the Gamow-Teller resonance with a set of doorway states and to its fragmentation. We compare our results with available experimental data. The microscopic coupling mechanism is also discussed in some detail.
Nuclear $beta$-decay in magic nuclei is investigated, taking into account the coupling between particle and collective vibrations,on top of self-consistent random phase approximation calculations based on Skyrme density functionals. The low-lying Gam
ow-Teller strength is shifted downwards and at times becomes fragmented; as a consequence, the $beta$-decay half-lives are reduced due to the increase of the phase space available for the decay. In some cases, this leads to a very good agreement between theoretical and experimental lifetimes: this happens, in particular, in the case of the Skyrme force SkM*, that can also reproduce the line shape of the high energy Gamow-Teller resonance as it was previously shown.
Although many random-phase approximation (RPA) calculations of the Gamow-Teller (GT) response exist, this is not the case for calculations going beyond the mean-field approximation. We apply a consistent model that includes the coupling of the GT res
onance to low-lying vibrations, to nuclei of the $fp$ shell. Among other motivations, our goal is to see if the particle-vibration coupling can redistribute the low-lying GT$^+$ strength that is relevant for electron-capture processes in core-collapse supernova. We conclude that the lowering and fragmentation of that strength are consistent with the experimental findings and validate our model. However, the particle-vibration coupling cannot account for the quenching of the total value of the low-lying strength.
Correlations between the behavior of the nuclear symmetry energy, the neutron skins, and the percentage of energy-weighted sum rule (EWSR) exhausted by the Pygmy Dipole Resonance (PDR) in 68Ni and 132Sn have been investigated by using different Rando
m Phase Approximation (RPA) models for the dipole response, based on a representative set of Skyrme effective forces plus meson-exchange effective Lagrangians. A comparison with the experimental data has allowed us to constrain the value of the derivative of the symmetry energy at saturation. The neutron skin radius is deduced under this constraint.
