Investigation the energy surfaces of 180-188Hg isotopic chain in the shape phase transitional region of interacting boson model

In this paper, the 180-188Hg isotopic chain is studied in the transitional region between the prolate and oblate shapes. To this aim, we have used a two parametric transitional Hamiltonian in the interacting boson model. With using Catastrophe theory in combination with coherent state formalism, we have determined the energy surfaces in this transitional region. The results of this study for energy levels and quadrupole transition probabilities are in the satisfactory agreement with experimental counterparts. Also the results for the control parameter of transitional Hamiltonian and the variation of energy surfaces propose a first order phase transition in this isotopic chain and suggest 188Hg nucleus as the best candidate for the O(6) dynamical symmetry limit or Z(5) critical point symmetry.