Configuration mixing of angular momentum projected self-consistent mean-field states for neutron-deficient Pb isotopes

We study the low-lying collective excitation spectra of the neutron-deficient lead isotopes $^{182\char21{}194}\mathrm{Pb}$ by performing a configuration mixing of angular momentum and particle-number projected self-consistent mean-field states. The same effective interaction is used to generate the mean-field states and for the configuration mixing. We choose the Skyrme interaction SLy6 supplemented by a density-dependent zero-range pairing force. Our study supports the interpretation of the excitation spectra made on the grounds of more schematic models in terms of coexisting spherical, oblate, prolate, and superdeformed prolate structures. The model qualitatively reproduces the variation of the spectra with neutron number. Our results for $E0$ and $E2$ transition probabilities are compared with the few existing experimental data. Finally, we predict the presence of superdeformed bands at low excitation energy in the most neutron-deficient isotopes.