Shape phase transition, shape coexistence and mixing phenomena within the Bohr Model

Two methods of solving the Bohr Hamiltonian with sextic oscillator potential in the β variable are presented, namely a quasi-exact method involving polynomials and a numerical diagonalization in a basis of Bessel functions of the first kind. The formalisms are used to describe shape phase transitions and critical points, respectively shape coexistence and mixing phenomena in nuclei.