Exactly separable version of the Bohr Hamiltonian with the Davidson potential

An exactly separable version of the Bohr Hamiltonian is developed using a potential of the form u(β)+u(γ)/β², with the Davidson potential u(β)=β²+β₀⁴/β² (where β₀ is the position of the minimum) and a stiff harmonic oscillator for u(γ) centered at γ=0^°. In the resulting solution, called the exactly separable Davidson (ES-D) solution, the ground-state, γ, and 0₂⁺ bands are all treated on an equal footing. The bandheads, energy spacings within bands, and a number of interband and intraband B(E2) transition rates are well reproduced for almost all well-deformed rare-earth and actinide nuclei using two parameters (β₀,γ stiffness). Insights are also obtained regarding the recently found correlation between γ stiffness and the γ-bandhead energy, as well as the long-standing problem of producing a level scheme with interacting boson approximation SU(3) degeneracies from the Bohr Hamiltonian.