A unified description of the shape phase transition, shape coexistence and mixing phenomena in nuclei

The shape phase transition, shape coexistence and mixing phenomena can be described in a unified way within the framework of the phenomenological Bohr-Mottelson model involving a sixth order anharmonic oscillator potential in the intrinsic deformation variable. This potential can have alternatively, depending on its parameters, a single spherical minimum, a single deformed minimum, a flat shape and simultaneously spherical and deformed minima, respectively. Thus, an entire phase transition from a spherical shape to a deformed one can be covered, crossing the critical point where the potential is flat (second order phase transition) or it has a small barrier (first order phase transition), while the shape coexistence and mixing phenomena emerge by simply increasing the barrier in the critical point. The type of axial deformations (prolate, triaxial, γ -unstable) are given here by the additional degree of freedom γ in relation to the γ potential shape.