  An exactly separable version of the Bohr Hamiltonian is developed using a
potential of the form u(beta)+u(gamma)/beta^2, with the Davidson potential
u(beta)= beta^2 + beta_0^4/beta^2 (where beta_0 is the position of the minimum)
and a stiff harmonic oscillator for u(gamma) centered at gamma=0. In the
resulting solution, called exactly separable Davidson (ES-D), the ground state
band, gamma 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 (beta_0,
gamma stiffness). Insights regarding the recently found correlation between
gamma stiffness and the gamma-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.
