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

摘要

The γ -rigid solution of the Bohr Hamiltonian with the β-soft potential and 0? ≤ γ ≤ 30? 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 γ -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 ~(158)Er 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 γ deformation.