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An exactly separable version of the Bohr Hamiltonian is developed using a potential of the form u(β) + u(γ)/β 2 , with the Davidson potential u(β) = β 2 + β 4 0 /β 2 (where β 0 is the position of the minimum) and a stiff harmonic oscillator for u(γ) centered at γ = 0 • . In the resulting solution, called exactly separable Davidson (ES-D), the ground state band, γ band and 0 + 2 band 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 (β 0 , γ stiffness). Insights 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, are also obtained.

One-parameter exactly separable versions of the X(5) and X(5)-beta^2 models, labelled as ES-X(5) and ES-X(5)-beta^2 respectively, are derived by using in the Bohr Hamiltonian potentials of the form u(beta)+u(gamma)/beta^2. Unlike X(5), in these models the beta_1 and gamma_1 bands are treated on equal footing. Spacings within the gamma_1 band are well reproduced by both models, while spacings within the beta_1 band are well reproduced only by ES-X(5)-beta^2, for which several nuclei with R_{4/2}=E(4_1^+)/E(2_1^+) ratios and [normalized to E(2_1^+)] beta_1 and gamma_1 bandheads corresponding to the model predictions have been found.Comment: 12 pages, LaTeX, including three .eps figure