Abstract. 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 20 Ne→ 16 O+α 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. IntroductionThe study of phase transitions enjoys a substantial interest in algebraic models of nuclear structure. The first examples [1,2] were related to the Interaction Boson Approximation (IBA) [3] and the vibron model [4,5]. In these approaches a coherent state is constructed in terms of collective variables and a semi-classical potential is defined as the expectation value of the Hamiltonian with respect to the coherent state. Phase changes are identified with discontinuities in the derivatives of the potential with respect to specific parameters taken at the potential minima. An important conjucture was that phases are determined by quasi-dynamical symmetries. This approximate symmetry is also denoted as an effective symmetry and its mathematically sound definition, called embedded symmetry [6] has been applied to the shell model of the nucleus in [7]. The role of the quasi-dynamical symmetry in relation with the phase-transition was discussed in [8,9,10].Here we discuss phase transitions within algebraic cluster models, in which the relative motion is described by the vibron model. It was found that the corresponding phase transition is of second order [11]. In [12] phase transitions in U (n) algebraic models were discussed using interaction terms up to second order and the existence of a second-order phase transition was confirmed. In [13] a numerical study was performed within a realistic cluster system and it was argued (without proof) that the transition might be of first order.Here we revisit phase transitions within a particular set of cluster models. One is the Phenomenological Algebraic Cluster Model (PACM), while the other is the Semimicroscopic Algebraic Cluster Model (SACM) [14,15]. The first set does not obey the Pauli exclusion
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