  The geometrical mapping of algebraic nuclear cluster models is investigated
within the coherent state formalism. Two models are considered: the
Semimicroscopic Algebraic Cluster Model (SACM) and the Phenomenological
Algebraic Cluster Model (PACM), which is a special limit of the SACM. The SACM
strictly observes the Pauli exclusion principle while the PACM does not. The
discussion of the SACM is adapted to the coherent state formalism by
introducing the new SO(3) dynamical symmetry limit and third-order interaction
terms in the Hamiltonian. The potential energy surface is constructed in both
models and it is found that the effects of the Pauli principle can be simulated
by higher-order interaction terms in the PACM. The present study is also meant
to serve as a starting point for investigating phase transitions in the two
algebraic cluster models.
