Odd-even shape staggering and kink structure of charge radii of Hg isotopes by the deformed relativistic Hartree-Bogoliubov theory in continuum

We examined the shape staggering of relative charge radii in $^{180 - 186}$Hg isotopes, which was first measured in 1977 and recently confirmed using advanced spectroscopy techniques. To understand the nuclear structure underlying this phenomenon, we employed the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc). Our analysis revealed that the shape staggering can be attributed to nuclear shape transition in the Hg isotopes. Specifically, we demonstrated that prolate shapes of $^{181,183,185}$Hg lead to an increase in the charge radii compared to oblate shapes of $^{180,182,184,186}$Hg isotopes. We explained the nuclear shape staggering in terms of the evolution of occupation probability (OP) of $\nu 1 i_{13/2}$, $\nu 1 h_{9/2}$, $\pi 1 h_{9/2}$, and $\pi 3 s_{1/2}$ states. Additionally, we clarified the kink structure of the charge radii in the Hg isotopes near $N = 126$ magic shell does not come from the change of the OP of $\pi 1 h_{9/2}$ state, but mainly by the increase of the OPs of $\nu 1 i_{11/2}$ and $\nu 2 g_{9/2}$ states.