The odd-even parity splittings in low-lying parity-doublet states of atomic nuclei with octupole correlations have usually been interpreted as rotational excitations on top of octupole vibration in the language of collective models. In this paper, we report a deep analysis of the odd-even parity splittings in the parity-doublet states of neutron-rich Ba isotopes around neutron number N = 88 within a full microscopic framework of beyond mean-field multi-reference covariant energy density functional theory. The dynamical correlations related to symmetry restoration and quadrupoleoctupole shape fluctuation are taken into account with a generator coordinate method combined with parity, particle-number, and angular-momentum projections. We show that the behavior of odd-even parity splittings is governed by the interplay of rotation, quantum tunneling and shape evolution. Similar to 224 Ra, a picture of rotation-induced octupole shape stabilization in the positiveparity states is exhibited in the neutron-rich Ba isotopes.
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