1 Department of Physics, Peking University, Beijing 100871, China; 2 The Key Laboratory of Heavy Ion Physics at Peking University, Ministry of Education, Beijing 100871, China; 3 Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator of Lanzhou, Lanzhou 730000, China
We review the status of the research of nuclear shape phase transitions in this paper. Meanwhile, by taking the coherent state theory and angular momentum projection method, we study the shape phase transitions of axially symmetric even-even nuclei with U(5) symmetry, SU(3) symmetry and those in the transitional region of the two symmetries in the framework of Interacting Boson Model-1 (IBM-1), which does not distinguish the proton bosons from neutron bosons.