Fe b 20 03 Spectroscopy of heavy nuclei by configuration mixing of symmetry restored mean - field states : Shape coexistence in neutron - deficient Pb isotopes

We study shape coexistence and low-energy excitation spectra in neutron-deficient Pb isotopes using configuration mixing of angular-momentum and particle-number projected self-consistent mean-field states. The same Skyrme interaction SLy6 is used everywhere in connection with a density-dependent zero-range pairing force. Methods well suited to describe microscopically medium and heavy nuclei are based on effective energy functionals and self-consistent mean-field models [1]. They are successful for the description of many nuclear properties, but do not give direct access to low-energy spectroscopy, which in many cases requires to include correlations beyond the mean field approach. Broken symmetries can be restored by projection. Particle-number projection removes spurious contributions coming from states with different particle numbers, which are an artifact of the usual BCS approach. Angular momentum projection restores ro-tational symmetry and generates wave functions in the laboratory frame which provide transition probabilities and spectroscopic moments without further approximations. Finally, the variational configuration mixing with respect to a collective coordinate by means of the Generator-Coordinate Method (GCM) allows for an improved calculation of nuclear ground-state properties, as it removes the contributions from spurious collective vibrations that are inevitably mixed to the mean-field states. Besides that, a GCM calculation provides the excitation spectrum corresponding to given collective coordinates. A model that combines these extensions of the mean-field approach offers a powerful tool: from a numerical point-of-view it is still simple enough to be applied to all up to superheavy nuclei, using the full model space of single-particle states with realistic asymptotics and the proper coupling to the continuum. Correlations corresponding to collective modes can be incorporated step by step into the modeling which helps to identify the relevant degrees of freedom.