The island of deformation and shape co-existence in neutron-deficient nuclei of the Pb region using relativistic mean field model

We have investigated the ground-state structures of even-even neutron-deficient isotopes of Hg and Pb nuclei within the framework of a deformed relativistic mean field formalism for a number of commonly used parameter sets, namely NL1, NL3, NL-SH, NL-RA1 and TM1. The ground states of a bunch of Hg and Pb-isotopes towards the proton-dripline are found to be deformed for all the forces, with a constant pairing gap. The small differences in the ground- and the first-excited state binding energies predict a sea of low-lying excited states, and hence of shape co-existence, for both the Hg and Pb nuclei. In general, a discrepancy between the experimentally observed and theoretically predicted (sign of) quadrupole deformations is noticed in this mass region. The constrained potential energy surfaces and the single-particle energy spectra analyzed for some selected nuclei show that the known large shell gap for Pb nuclei at Z=82 is almost extinguished for its proton-rich isotopes.