Signature splitting of the $g_{7/2}\left[404\right]{7/2}^{+}$ bands in ${}^{131}\mathrm{Ba}$ and ${}^{133}\mathrm{Ce}$

Excited states in ${}^{131}\mathrm{Ba}$ and ${}^{133}\mathrm{Ce}$ were studied using in-beam $\gamma$-ray spectroscopy through the ${}^{122}\mathrm{Sn}({}^{13}\mathrm{C},4n){}^{131}\mathrm{Ba}$ and ${}^{125}\mathrm{Te}({}^{12}\mathrm{C},4n){}^{133}\mathrm{Ce}$ reactions, respectively. A strongly coupled band, associated with the $\nu g_{7/2}\left[404\right]{7/2}^{+}$ configuration, was identified in ${}^{131}\mathrm{Ba}$ and ${}^{133}\mathrm{Ce}$. It is the first time to observe the $\nu g_{7/2}\left[404\right]{7/2}^{+}$ bands in the $N=75$ isotones. The signature partners exhibit considerable energy splitting in comparison with those in the $\pi g_{7/2}\left[404\right]{7/2}^{+}$ bands in the odd-$A$ Ta and Re isotopes. Extensive cranked shell model and quasiparticle-plus-triaxial-rotor model calculations reveal the origin of the signature splitting, which depends not only on the triaxiality, but also on the configuration mixing with nearby low-$j$ orbitals.

Figure 1

Partial level schemes of ${}^{131}\mathrm{Ba}$ and ${}^{133}\mathrm{Ce}$ deduced from the present work. Newly observed transitions are marked in red.

Figure 2

Typical double-gated coincidence spectra for the new structures in ${}^{131}\mathrm{Ba}$. Newly observed levels are marked in red.

Figure 3

Similar to Fig. 2, but for ${}^{133}\mathrm{Ce}$. The spectrum is obtained by summing the double-gated spectra on all combinations of the 303-, 693-, and 819-keV transitions.

Figure 4

(a) Experimental quasiparticle alignments ($i_x$), (b) dynamical moments of inertia $J^{\left(2\right)}$, and (c) quasineutron Routhian energies ($e$) of the $\nu g_{7/2}$ bands in $N=75$ isotones ${}^{131}\mathrm{Ba}$ and ${}^{133}\mathrm{Ce}$, as well as in $N=73$ isotones ${}^{129}\mathrm{Ba}, {}^{131}\mathrm{Ce}$, and ${}^{133}\mathrm{Nd}$. The data for ${}^{131}\mathrm{Ba}$ and ${}^{133}\mathrm{Ce}$ are from this work, and the others are taken from Ref. [57] for ${}^{129}\mathrm{Ba}$, Ref. [58] for ${}^{131}\mathrm{Ce}$, and Ref. [59] for ${}^{133}\mathrm{Nd}$.

Figure 5

The experimental excitation energies of the $\pi g_{7/2}$ bands in Re and Ta isotopes, and the $\nu g_{7/2}$ bands in Ba and Ce isotopes. An average liquid-drop energy $E_{\mathrm{rig}}=({\hslash }^2/2{\mathcal{J}}_{\mathrm{rig}})I(1+1)$, where ${\mathcal{J}}_{\mathrm{rig}}=$2/5${\mathrm{AMR}}^2$, was subtracted. The data on ${}^{131}\mathrm{Ba}$ and ${}^{133}\mathrm{Ce}$ are from this work, while those on the other isotopes are from the following references: ${}^{129}\mathrm{Ba}$ [57], ${}^{131}\mathrm{Ce}$ [58], ${}^{133}\mathrm{Nd}$ [59], ${}^{175}\mathrm{Re}$ [70], ${}^{177}\mathrm{Re}$ [71], ${}^{183}\mathrm{Re}$ [72], ${}^{173}\mathrm{Ta}$ [60], ${}^{175}\mathrm{Ta}$ [61], and ${}^{181}\mathrm{Ta}$ [62].

Figure 6

Signature splittings of the $\pi g_{7/2}$ and $\nu g_{7/2}$ bands in the $Z=73,75$ isotopes and $N=73,75$ isotones. The data are the same as in Fig. 5.

Figure 7

Calculated quasineutron Routhians as a function of quadrupole deformation (${\beta }_2$), rotational frequency ($\hslash \omega$), and triaxiality ($\gamma$). The parity and signature ($\pi , \alpha$) of the Routhians are represented as follows: ($+,+1/2$), solid lines; ($+,-1/2$), dotted lines; ($-,+1/2$), dash-dotted lines; and ($-,-1/2$), dashed lines. Two signature branches of the $\nu g_{7/2}\left[404\right]{7/2}^{+}$ orbital are shown on a shaded background.

Figure 8

Experimental and theoretical signature splittings for the $\nu g_{7/2}\left[404\right]{7/2}^{+}$ band in ${}^{133}\mathrm{Ce}$. The calculations are carried out for standard Coriolis interaction ($\chi$ = 1) and (a) $\gamma ={10}^{\circ }$ and (b) $\gamma ={20}^{\circ }$, and for attenuated Coriolis interaction ($\chi$ = 0.7) and (c) $\gamma$ = ${10}^{\circ }$ and (d) $\gamma ={20}^{\circ }$.

Figure 9

Experimental and theoretical signature splittings for the $\nu g_{7/2}\left[404\right]{7/2}^{+}$ band in ${}^{131}\mathrm{Ba}$ and the $\pi g_{7/2}\left[404\right]{7/2}^{+}$ band in ${}^{183}\mathrm{Re}$. The calculations are carried out for standard Coriolis interaction ($\chi$ = 1) and (a) $\gamma$ = ${15}^{\circ }$ and (b) $\gamma =0^{\circ }$, and for attenuated Coriolis interaction ($\chi$ = 0.7) and (c) $\gamma$ = ${15}^{\circ }$ and (d) $\gamma ={20}^{\circ }$.

Figure 10

Similar to Fig. 6, but for the $\nu d_{5/2}$[402]${5/2}^{+}$ bands in the $N=65$ and 67 isotones. Data are taken from Ref. [76] for ${}^{125}\mathrm{Ba}$, Ref. [77] for ${}^{127}\mathrm{Ce}$, Ref. [78] for ${}^{129}\mathrm{Nd}$, Ref. [79] for ${}^{127}\mathrm{Ba}$, Ref. [77] for ${}^{129}\mathrm{Ce}$, and Ref. [80] for ${}^{131}\mathrm{Nd}$.