Soft triaxial rotor in the vicinity of $\gamma=\pi/6$ and its extensions

The collective Bohr hamiltonian is solved for the soft triaxial rotor around $\gamma_0=\pi/6$ with a displaced harmonic oscillator potential in $\gamma$ and a Kratzer-like potential in $\beta$. The properties of the spectrum are outlined and a generalization for the more general triaxial case with $0<\gamma<\pi/6$ is proposed.