gamma-rigid solution of the Bohr Hamiltonian for the critical point description of the spherical to gamma-rigidly deformed shape phase transition

The gamma- rigid solution of the Bohr Hamiltonian with the beta-soft potential and 0 degrees <= gamma <= 30 degrees is worked out. The resulting model, called T(4), provides a natural dynamical connection between the X(4) and the Z(4) critical-point symmetries, which thus serves as the critical-point symmetry of the spherical to gamma-rigidly deformed shape phase transition. This point is further justified through comparing the model dynamics with those of the interacting boson model. As a preliminary test, the low-lying structures of Er-158 are taken to compare the theoretical calculations, and the results indicate that this nucleus could be considered as the candidate of the T(4) model with an intermediate. deformation.Natural Science Foundation of China [11375005, 11675071, 11375080, 11435001, 11475091]; U.S. National Science Foundation [OCI-0904874]; Southeastern Universities Research Association; LSU-LNNU joint research program [9961]; NationalKey Basic Research Program of China [G2013CB834400]SCI(E)ARTICLE39