Bohr Hamiltonian with Davidson potential for triaxial nuclei

A solution of the Bohr Hamiltonian appropriate for triaxial shapes, involving a Davidson potential in $\ensuremath{\beta}$ and a steep harmonic oscillator in $\ensuremath{\gamma}$, centered around $\ensuremath{\gamma}=\ensuremath{\pi}/6$, is developed. Analytical expressions for spectra and$B(E2)$ transition rates ranging from a triaxial vibrator to the rigid triaxial rotator are obtained and compared to experimental results. Using a variational procedure, we point out that the $Z(5)$ solution, in which an infinite square well potential in $\ensuremath{\beta}$ is used, corresponds to the critical point of the shape phase transition from a triaxial vibrator to the rigid triaxial rotator.

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