Double shape quantum phase transitions in the SU3-IBM: new γ-soft phase and the shape phase transition from the new γ-soft phase to the prolate shape

Shape quantum phase transition is an important topic in nuclear structure. In this paper, we begin to study the shape quantum phase transition in the SU3-IBM. In this new proposed model, spherical-like spectra was found to resolve the spherical nucleus puzzle, which is a new $\gamma$-soft rotational mode. In this paper, the shape phase transition along the new $\gamma$-soft line is first discussed, and then the neighbouring case at the prolate side is also studied. We find that double shape phase transitions occur along a single parameter path. The new $\gamma$-softness is really a shape phase and the shape phase transition from the new $\gamma$-soft phase to the prolate shape is found. The experimental support is also found and $^{108}$Pd may be the critical nucleus.