The angular momentum projected generator coordinate method, with the axially symmetric quadrupole moment as generating coordinate, has been applied to study the shape coexistence and quadrupole collectivity in the neutron-deficient isotopes ${}^{182–192}\mathrm{Pb}$. The finite range and density dependent Gogny interaction, with the parametrization $\mathrm{D}1\mathrm{S}$, has been used in the calculations. A good qualitative agreement with the available experimental results is found. Our results indicate that $Z=82$ remains, on the average, as a magic proton number for the considered nuclei and also support the experimental evidences for rotational bands built on coexisting low-lying states of oblate and prolate shapes.

• Received 10 March 2004

DOI:https://doi.org/10.1103/PhysRevC.69.054319