Bohr Hamiltonian and the energy spectra of the triaxial nuclei

A Bohr Hamiltonian, with a potential including a displaced harmonic oscillator plus a Coulomb-like term and a centrifuge term for the \( \beta\)-part and a harmonic oscillator centered around \( \gamma= \frac{\pi}{6}\) for the \( \gamma\)-part, which can be approximately separated, has been solved for the \( \beta\)-part and \( \gamma\)-part. The part related to the collective \( \gamma\)-variable has been chosen in such a way that the model describes the triaxial nuclei. The eigenfunctions and eigenvalues of the energy have been obtained. An analytical expression for the total energy spectra is given.