Large-scale shell model study of the newly found isomer in ${}^{136}\mathrm{La}$

The doubly-odd nucleus ${}^{136}\mathrm{La}$ is theoretically studied in terms of a large-scale shell model. The energy spectrum and transition rates are calculated and compared with the most updated experimental data. The isomerism is investigated for the first ${14}^{+}$ state, which was found to be an isomer in the previous study [Phys. Rev. C 91, 054305 (2015)]. It is found that the ${14}^{+}$ state becomes an isomer due to a band crossing of two bands with completely different configurations. The yrast band with the ($\nu h_{11/2}^{-1}\otimes \pi h_{11/2}$) configuration is investigated, revealing a staggering nature in $M1$ transition rates.

Figure 1

Calculated energy spectra up to 3.0 MeV for ${}^{136}\mathrm{La}$ (calc.) in comparison with the experimental data (expt.) [4, 15]. For theoretical results, the calculation with the strength set used in Ref. [10] [calc. (set A)] and the calculation with the modified strength set [calc. (Set B)] are shown. States with positive (negative) parity are shown with solid (dashed) lines. Experimentally parity-unassigned states are shown with dotted lines.

Figure 2

Calculated energy levels for positive-parity states using the modified interaction (Set B) in comparison with the experimental data [4, 15]. The legend “calc.$(+,+)$” represents theoretical results for the $(+,+)$ configuration and “calc.$(-,-)$” represents theoretical results for the $(-,-)$ configuration. Calculated states are shown up to four levels with the same configuration for each spin. Spin and parity of the state at 0.03 MeV is assigned as the $\left(7^{+}\right)$ state in experiment (shown with the diamond). However, there are other possibilities for this assignment (see text).

Figure 3

Calculated positive-parity yrast states with the $(+,+)$ and $(-,-)$ configurations with $I\ge 9$ in comparison with the experimental data.

Figure 4

Comparison of the kinematic moment of inertia $\mathcal{J}\left(I\right)$ between the experimental results and the theoretical ones.

Figure 5

(a) Calculated $B\left(E2\right)$, (b) $B\left(M1\right)$, and (c) $B\left(M1\right)/B\left(E2\right)$ values among the yrast states and the ($\nu h_{11/2}^{-1}\otimes \pi h_{11/2}$) configurations in comparison with the experimental data [4]. Yrast states are connected by dotted lines and the states with the ($\nu h_{11/2}^{-1}\otimes \pi h_{11/2}$) configuration are connected by solid lines.