Phase Transitions In Algebraic Cluster Models

Two algebraic cluster models are studied from the point of view of phase transitions: one in which the Pauli exclusion principle is taken into account and one in which it isn't. A third-order interaction is introduced to avoid instabilities in the model spectra, which is generally not taken into account. It is shown that both first- and second-order phase transitions occur. The Ne-20 -> O-16+alpha system is considered as an example. Without taking into account the Pauli exclusion principle the transition from the SU(3) to the SO(4) dynamical symmetry is of first or second order, depending on the strength of the quadrupole-quadrupole interaction. It is shown that the inclusion of the Pauli-principle can be simulated by higher-order interactions when the model space is not truncated.