Effect of nuclear deformation on Gamow-Teller strength distributions of Hg isotopes

Recent studies \cite{1,2} predicted the sensitivity of the Gamow-Teller (GT) strength distributions to nuclear deformation in neutron-deficient Hg isotopes. Motivated by this work, we investigate nuclear ground-state properties and GT strength distributions for neutron-deficient Hg isotopes (${}^{177\text{-}193}$Hg). The nuclear deformation ($\beta (E2)$) values were calculated using the Relativistic Mean Field (RMF) model. The RMF approach, with different density-dependent interactions (DD-ME2 and DD-PC1), was employed to compute nuclear shape parameters. These computed deformation values were then used within the framework of the deformed proton-neutron quasi-particle random phase approximation (pn-QRPA) model, with a separable interaction, to calculate the allowed GT strength distributions for these Hg isotopes. Our calculations validate the findings of \cite{1} and confirm the effect of deformation on GT strength distributions. This study may further provide a complementary signature for nuclear shape isomers. Noticeable differences are highlighted between our results and previous calculations. The study of \cite{1} suggests that ${}^{177\text{-}182}$Hg possess prolate shapes, while ${}^{184\text{-}196}$Hg exhibit oblate shapes. In contrast, our calculations predict prolate shapes for ${}^{177\text{-}188}$Hg and oblate shapes for ${}^{189\text{-}193}$Hg isotopes.