Exactly separable version of the Bohr Hamiltonian with the Davidson potential

Abstract

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(4)(0)/beta(2) (where beta(0) is the position of the minimum) and a stiff harmonic oscillator for u(gamma) centered at gamma = 0(degrees). In the resulting solution, called the exactly separable Davidson (ES-D) solution, the ground-state, gamma, and 0(2)(+) 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 (beta(0), gamma stiffness). Insights are also obtained 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.