Triple point in the phase transition diagram of a cold nucleus

The current status of research on the problem of phase transitions in cold nuclei of different geometrical shape is reviewed. The phase transitions between different nuclear shapes are treated in the framework of the interacting boson model in the space of three reference parameters, which are the parameters of the Hamiltonian of the model. Depending on the values of these parameters the equilibrium shape of a nucleus can be spherical, deformed axially symmetric, or triaxial. It is shown that, in the phase diagram of a nucleus, the Casten triangle, the spherical phase is separated from deformed axially symmetric phases by the lines of the first order phase transitions. Similarly, two deformed phases with axial deformation of different sign are separated by the line of the first order phase transition. These lines cross at the triple point, the point of the second order phase transition. The problem of dynamical symmetries in the critical points is discussed. Experimental data on nuclei with properties close to those predicted for the critical points of phase transitions are discussed. The phase transition from axially symmetric to triaxial deformation is shown to be the second order phase transition. An approximate solution describing a nucleus close to the critical point of the phase transition from spherical to triaxial deformation is obtained in terms of the Bohr-Mottelson model.