Octupole correlations in ${}^{220,222,224,226}$Rn

The octupole correlations in ${}^{220,222,224,226}$Rn are investigated by using multi-dimensionally constrained covariant density functional theory. The ground-state properties and potential energy surfaces are analyzed, revealing that octupole deformation appears in ${}^{222,224}$Rn, but not in ${}^{220,226}$Rn. The relationship between pairing correlations and octupole deformation is examined, showing that the neutron pairing energy decreases as octupole deformation develops, whereas the proton pairing energy shows the opposite behavior. The microscopic origin of octupole correlations in these radon isotopes are explored based on an examination of the single-particle levels near the Fermi surface and a schematic two-level model. Experiments have indicated that these isotopes undergo octupole vibrations and the present prediction of octupole deformation in ${}^{222,224}$Rn awaits further confirmation.