Shape dependence of pairing gap energies and the structure of Hg and Pb isotopes

Abstract

The ground states of Hg and Pb isotopes are studied in the framework of deformed relativistic mean field theory with pairing interactions in the BCS theory. We show that the neutron and proton gap parameters strongly depend on deformation, and demonstrate that it is crucially important to solve the gap equations for each deformation in order to discuss the shape and the charge radius of these isotopes. The oblate shape and the charge radius of neutron deficient Hg isotopes are well reproduced. Our calculations suggest that the atomic number 82 stays a magic number for all the Pb isotopes we studied, and well reproduce the isotope shifts of Pb isotopes.