Nuclear collective states at the mean-field level and beyond

Nuclear physics is experiencing a new blooming due to several circumstances, like the improvement in the theoretical techniques and the availability of new data on unstable nuclei and new astrophysical observations. In this talk, the focus is on the nuclear collective vibrations, that are a clear signature of the properties of the Hamiltonian and of the many-body correlations. We will discuss first how state-of-the-art mean-field calculations can link the measurements of vibrational properties to the nuclear equation of state. In the second part of the seminar, we will show how calculations that go beyond the mean-field approximation are currently feasible on a fully microscopic basis.