Bohr Hamiltonian for gamma=30 degrees with Davidson potential

A gamma-rigid solution of the Bohr Hamiltonian for gamma = 30 degrees is constructed with the Davidson potential in the beta part. This solution is going to be called Z(4)-D. The energy eigenvalues and wave functions are obtained by using the analytic method developed by Nikiforov and Uvarov. The calculated intraband and interband B(E2) transitions rates are presented and compared with the Z(4) model predictions. The staggering behavior in gamma-bands is considered to search Z(4)-D candidate nuclei. A variational procedure is applied to demonstrate that the Z(4) model is a solution of the critical point at the shape phase transition from spherical to rigid triaxial rotor.