Exactly separable Bohr Hamiltonian with the Killingbeck potential for triaxial nuclei

After pioneering work by Bohr, Mottelson and their numerous colleagues, the essential framework for understanding collective model is introduced. One of the applications of this framework is the study of shape phase transition, vibrational and rotational energy spectrum of nuclei. We consider the Bohr Hamiltonian and solve the beta and gamma part equation of it, by considering that reduced potential and wave function are exactly separable. In the beta part equation we consider the Killingbeck potential and derive the wave function and energy spectrum of it.