Recognition of SU (3) → O (6) quantum phase transition in ground-states of 156Gd nucleus within microscopic theory

The γ-ray energy over spin curves identifies that there are the SU (3) and O (6) symmetries in the ground-states of the 156Gd nucleus; by means of the microscopic sdIBM-F-barmax approach and signal-particle experimental energies the spectra of those two symmetries and their transient process are successfully reproduced through two parameters of nucleon-nucleon effective interaction with pairing plus quadrupole pairing plus quadrupole-quadrupole forces. The calculated results reveal a new way to recognize ground-states quantum phase transition, in which the basic-state of the SU (3) symmetry is a low-lying and low-ordered state, while one of the O (6) are a high-lying and high-ordered state, their critical region is between 6+1 - 8+1 states, the high-ordered basic-state releases spare ordered-structure energy, reducing rotation-speed, thus causing the restructure of low-ordered basic-state and accomplishing the quantum phase transition from the high-ordered phase into the low-ordered phase, the shape phase transition takes place along the yrast line of nucleus when it de-excited to the critical region. Because the structural phase transition takes place by no-obvious charge of boson structure constants in the critical region it is a benignancy and calm transition with respect to its macroscopic behave. The potential energy surface of 156Gd nucleus has been illustrated to visualize. (authors)