Static or dynamic pear shapes in radioactive nucleus ²²⁴Rn?

We report a comprehensive study on low-lying parity doublet states of ²²⁴Rn by mixing both quadrupole- and octupole-shaped configurations in multireference covariant density functional theory, in which broken symmetries in configurations are restored using projection techniques. The low-lying energy spectrum is reasonably reproduced when the shape fluctuations in both the quadrupole and octupole shapes are considered. Electric octupole transition strength in ²²⁴Rn is found to be \(B(E3; 3^-_1 \rightarrow 0^+_1)=43\) $B(E3;3_1^{-}\to 0_1^{+})=43$ W.u., comparable to that in ²²⁴Ra, whose data are 42(3) W.u.. Our results indicate that ²²⁴Rn shares similar low-energy structure with ²²⁴Ra despite the excitation energy of first \(3^-\) $3^{-}$ state of the former nucleus is higher than that of the latter. This study suggests ²²⁴Rn is a candidate for the search for permanent electric dipole moment.