GCM analysis of the collective properties of lead isotopes with exact projection on particle numbers

We present a microscopic analysis of the collective behaviour of the lead i sotopes in the vicinity of Pb-208. In this study, we rely on a coherent app roach based on the Generator Coordinate Method (GCM) including exact projec tion on IV and Z numbers within a collective space generated by means of th e constrained Hartree-Fock BCS method. With the same Hamiltonian used in HF + BCS calculations, we have performed a comprehensive study including mono pole, quadrupole and octupole excitations as well as pairing vibrations. We find that, for the considered nuclei, the collective modes which modify th e most the conclusions drawn from the mean-field theory are the octupole an d pairing vibrations.