Odd-even parity splittings and octupole correlations in neutron-rich Ba isotopes

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 multireference covariant energy density functional theory. The dynamical correlations related to symmetry restoration and quadrupole-octupole 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 ${}^{224}\mathrm{Ra}$, a picture of rotation-induced octupole shape stabilization in the positive-parity states is exhibited in the neutron-rich Ba isotopes.

Figure 1

The ratio $R_{J/2}$ [defined as $E_x\left(J^{\pi }\right)/E_x(2_1^{+}\left)\right]$ of the excitation energy of each $J^{\pi }$ state to that of $2_1^{+}$ state as a function of the angular momentum $J\left(\hslash \right)$. The filled symbols are for data, while the open symbols are for the results from the present configuration-mixing calculations.

Figure 2

(Upper panels) The excitation energy of states projected onto particle number, angular momentum, and parity based on an individual configuration for ${}^{144}\mathrm{Ba}$. (Lower panels) The ratio $R_{J/2}$ as a function of angular momentum $J\left(\hslash \right)$.

Figure 3

Mean-field energy surfaces (normalized to the energy minimum) for the neutron-rich Ba isotopes in ${\beta }_2-{\beta }_3$ deformation plane, where two neighboring lines are separated by 0.5 MeV.

Figure 4

Systematics of the excitation energy of $2_1^{+}$ state and the $E2,E3$ transition strengths in neutron-rich Ba isotopes around neutron number $N=88$.

Figure 5

Evolution of collective wave functions for the parity-doublet states in the deformation ${\beta }_2-{\beta }_3$ plane for ${}^{144,146}\mathrm{Ba}$. See text for details.

Figure 6

Same as Fig. 5, but for ${}^{148,150}\mathrm{Ba}$.

Figure 7

The distribution of the overlap $\langle \mathbf{q}\left|\widehat{P}\right|\mathbf{q}\rangle$ of parity operator for each intrinsic state of ${}^{144}\mathrm{Ba}$ in the ${\beta }_2-{\beta }_3$ plane. The average deformation $\langle {\beta }_{\lambda }\rangle \equiv {\sum }_q{\beta }_{\lambda }{\left|g_{\alpha }^{J\pi }\right|}^2$ with $\lambda =2,3$ and $J=0,1,...,10$ for the parity-doublet states in ${}^{144}\mathrm{Ba}$ is indicated with filled circles $\left(\pi =+\right)$ and open squares $\left(\pi =-\right)$.