The doubly-odd nucleus La136 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)PRVCAN0556-281310.1103/PhysRevC.91.054305]. 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 (νh11/2-1- πh11/2) configuration is investigated, revealing a staggering nature in M1 transition rates.
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