Bohr Hamiltonian for $\gamma = 30^{\circ}$ γ = 30 ∘ with Davidson potential

Abstract

A $\gamma$ -rigid solution of the Bohr Hamiltonian for $\gamma = 30^{\circ}$ 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.