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

Abstract

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 $\hat{I}½1i_{13/2}$, $\hat{I}½1h_{9/2}$, $\ddot{I}€1h_{9/2}$, and $\ddot{I}€3s_{1/2}$ 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 $\ddot{I}€1h_{9/2}$ state, but mainly by the increase of the OPs of $\hat{I}½1i_{11/2}$ and $\hat{I}½2g_{9/2}$ states.