Phase transitions for rotational states within an algebraic cluster model

The catastrophe theory, an effective method for the description of phase transitions, is applied to the Semimicroscopic Algebraic Cluster Model (SACM) as an example of a non-trivial theory. The ground state and excited, rotational phase transitions are investigated. A short introduction to the SACM and the catastrophe theory is given. We apply the formalism to the test case of 16O+alpha–>20Ne.