Low-energy excitations in nuclear systems: From exotic nuclei to the crust of neutron stars

We study the evolution of low-lying quadrupole modes as a function of the neutron excess, from neutron-rich nuclei to the nuclear systems located in the crust of a neutron star. The microscopic analysis is performed within the Hartree-Fock-Bogoliubov + quasiparticle random-phase approximation framework. The Wigner-Seitz approximation is adopted to describe the lattice of nuclear clusters embedded in neutron star crusts. A systematic analysis of Z=50 nuclear systems, performed by increasing the isospin asymmetry, reveals that a low-energy 2+ mode is found in all the systems. However, the nature of the relevant configurations that construct this mode drastically changes when the drip line is crossed. This result is confirmed by the study of the transition density associated to the mode in the inner crust system with Z=40 and N=1460. It is shown that the transition density profile is different with respect to typical profiles found for 2+ low-lying modes in nuclei: the excitation is mostly constructed with neutrons belonging to the cluster surface and the external free gas