  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.
