GEOMETRICAL INTERPRETATION OF THE SEMIMICROSCOPIC ALGEBRAIC CLUSTER MODEL

A geometrical mapping of the semimicroscopic algebraic cluster model i s given. The geometrical variables are the relative radius vector and the quadrupole deformation parameters. The last ones correspond to abs olute beta and gamma values, while the orientation of the deformed nuc leus in the laboratory can be changed. We show that the position of th e minimum of the nuclear molecular potential is determined by the mini mal number of pi bosons describing the relative motion. The minimal nu mber of pi bosons is determined by the implementation of the Pauli pri nciple. Applications to simple systems (O-16+alpha and C-12+alpha) are presented.