Octupole bands and simplex inversion in the neutron-rich nucleus ${}^{145}\mathrm{Ba}$

The issue of the existence of reflection asymmetry in ${}^{145}\mathrm{Ba}$ has stood for the past 30 years without a common conclusion. The recent experimental data show a number of low-lying rotational bands with alternative parities, providing more strict constraints on the relevant modeling. With a proper octupole deformation, all the observed six rotational bands in ${}^{145}\mathrm{Ba}$ have been well reproduced by the reflection asymmetric shell model (RASM). The three octupole deformed neutron single-particle orbitals just above the octupole shell gap 88, with $K=1/2,K=3/2$, and $K=5/2$, respectively, dominate the intrinsic configurations of the observed bands. Based on the analysis of the calculated RASM wave functions, the assignments for the observed bands have been given. The experimental yrast band ($\Delta I=1$) presents a simplex inversion at around the $11/2^{-}$ state where the simplex staggering phase changes. This phenomenon may be explained in the framework of the RASM as from the change of the dominate intrinsic configuration, induced by the band mixing. The present results strongly support the appearance of the reflection asymmetry in the ground and low-lying states of ${}^{145}\mathrm{Ba}$.

Figure 1

The single proton (upper panel) and neutron (lower panel) levels as a function of quadrupole deformation (${\epsilon }_2$) and octupole deformation (${\epsilon }_3$). The hexadecapole deformation was involved through ${\epsilon }_4=(-0.05/0.168){\epsilon }_2$. The adopted orbitals in the present calculations are in red. The vertical dashed line in the box shows the position (${\epsilon }_3\sim 0.07$) of the adopted Nilsson states. The Nilsson parameters $(\kappa ,\mu )$ are taken to be (0.090,0.30), (0.065,0.57), and (0.061,0.066) for $N$ = 3, 4, and 5 proton shells, (0.070,0.39), (0.066,0.33), and (0.063,0.035) for $N$ = 4, 5, and 6 neutron shells, respectively.

Figure 2

Evolution of the energies for the three selected one-neutron quasiparticle states whose orbitals are shown in Fig. 1. From left to right are the quasiparticle energies $E_{\kappa }$, the expectation values ${\overline{H}}_{\kappa }^{\prime }$ of the Hamiltonian, the parity projected energies ${\overline{H}}_{\kappa }^{\prime p}$, and parity plus angular momentum projected energies ${\overline{H}}_{\kappa }^{\prime I=K,p}$. For the right two columns, the solid (open) symbols stand for the positive (negative) parity states.

Figure 3

The rotational bands without configuration mixing (open) calculated by using Eq. (10) for the selected one-neutron quasiparticle configurations. The theoretical levels are shifted up by a constant to keep the ground-state energy as zero. The experimental data (solid) are also shown for a comparison. The experimental data are taken from Refs. [8, 10].

Figure 4

Calculated rotational bands with the configuration mixing (open), and are compared with the experimental data (solid) taken from Refs. [8, 10].

Figure 5

The major components of the $K=1/2,K=3/2$, and $K=5/2$ in the wave function corresponding to bands 1–6. $\pi =$ + or $-$ stands for the parity of the rotational band.

Figure 6

The difference energies $E\left(I\right)-E(I-1)$ for the experimental yrast band ($\Delta I=1$) (solid) and for the calculated bands ($\Delta I=1$) with the pure configurations of $K=3/2$ and $K=5/2$. The simplex inversion presents at around spin 11/2.

Figure 7

Theoretical rotational bands (open), calculated with ${\epsilon }_3=0$, and keeping other parameters being unchanged, are compared with the experimental data (solid).