Extended study on a quasi-exact solution of the Bohr Hamiltonian

A unified presentation of the quasi-exact solutions of the Bohr Hamiltonian with a sextic oscillator potential is offered by evidencing the similarities and the differences between them. An extended study of the Bohr Hamiltonian with sextic potential for γ -rigid triaxial nuclei is conducted, focusing on the evolution of the energy spectra and B(E2) transition probabilities when the order of the quasi-exactly solvable system is increased. The effect is analyzed throughout the shape phase transition from a γ -rigid triaxial vibrator to an anharmonic one and especially in its critical point. The new results are tested by several applications for experimental data, improving the previous calculations and providing new possible triaxial nuclei.