Abstract
A geometrical mapping of the semimicroscopic algebraic cluster model is given. The geometrical variables are the relative radius vector and the quadrupole deformation parameters. The last ones correspond to absolute \ensuremath{\beta} and \ensuremath{\gamma} values, while the orientation of the deformed nucleus in the laboratory can be changed. We show that the position of the minimum of the nuclear molecular potential is determined by the minimal number of \ensuremath{\pi} bosons describing the relative motion. The minimal number of \ensuremath{\pi} bosons is determined by the implementation of the Pauli principle. Applications to simple systems ${(}^{16}$O+\ensuremath{\alpha} and $^{12}\mathrm{C}$+\ensuremath{\alpha}) are presented. \textcopyright{} 1996 The American Physical Society.
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