Background: Radon isotopes are important candidates of observing octupole deformation. Octupole vibrational bands have been observed in but no octupole deformation has been confirmed experimentally.
Purpose: To investigate whether octupole deformation exists in and explore the possible octupole minima in the potential energy surfaces (PESs).
Methods: The PESs and ground-state properties are calculated by using the mutidimensionally constrained relativistic mean-field model with different covariant energy density functionals PC-PK1, DD-PC1, and DD-ME2. Pairing correlations are treated in the BCS approach with the separable pairing force of finite range.
Results: The calculations show that the PESs of all these isotopes exhibit softness with respect to octupole distortion and octupole minima appear in the PESs of with the above-mentioned functionals and several sets of pairing parameters used. The energy gain due to octupole deformation is found to be suppressed as the pairing strength increases. As the octupole deformation increases, the neutron pairing energy decreases and the proton pairing energy increases while there is no obvious change in the total pairing energy. Analysis of the single-particle levels indicates that the observed octupole minima in primarily originate from the coupling between neutron orbitals (from ) and (from ) near the Fermi surface.
Conclusion: The ground-state properties and PESs of are studied and predictions are made that octupole minima exist in . The energy gain due to octupole deformation ranges from 0.08 to 0.79 MeV. Whether there is octupole deformation is still awaiting experimental confirmation, e.g., through measurement of the transition strength from the ground state to the first octupole state and observation of parity doublet bands with enhanced transitions between them.