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 $u(\ensuremath{\beta})+u(\ensuremath{\gamma})/{\ensuremath{\beta}}^{2}$, with the Davidson potential $u(\ensuremath{\beta})={\ensuremath{\beta}}^{2}+{\ensuremath{\beta}}_{0}^{4}/{\ensuremath{\beta}}^{2}$ (where ${\ensuremath{\beta}}_{0}$ is the position of the minimum) and a stiff harmonic oscillator for $u(\ensuremath{\gamma})$ centered at $\ensuremath{\gamma}={0}^{\ifmmode^\circ\else\textdegree\fi{}}$. In the resulting solution, called the exactly separable Davidson (ES-D) solution, the ground-state, $\ensuremath{\gamma},$ 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 (${\ensuremath{\beta}}_{0},\ensuremath{\gamma}$ stiffness). Insights are also obtained regarding the recently found correlation between \ensuremath{\gamma} stiffness and the \ensuremath{\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.