Description of the critical point symmetry in 124Te by IBM-2

Based on the neutron and proton degrees of freedom, the low-lying energy levels, the $E2$, $M1$ and $E0$ transition strengths of nucleus $^{124}$Te have been calculated by the neutron-proton interacting boson model. The calculated results are quite consistent with the experimental data. By comparing the key observables of states at the critical point of $\textrm{U}_{\pi \nu}(5)$--$\textrm{O}_{\pi \nu}(6)$ transition with experimental data and calculated results, we show that the $^{124}$Te is a possible nucleus at the critical point of the second order phase transition from vibration to unstable rotation and such a critical point contains somewhat triaxial rotation. The 0$^+_2$ state of $^{124}$Te can be interpreted as the lowest state of the first excited family of intrinsic levels in the critical point symmetry.