  The consequences of the attractive, short-range nucleon-nucleon (NN)
interaction on the wave functions of nuclear models bearing the SU(3) symmetry
are reviewed. The NN interaction favors the most symmetric spatial SU(3)
irreducible representation (irrep), which corresponds to the maximal spatial
overlap among the fermions. The consideration of the highest weight (hw) irreps
in nuclei and in alkali metal clusters, leads to the prediction of a prolate to
oblate shape transition beyond the mid-shell region. Subsequently, the
consequences of the use of the hw irreps on the binding energies and
two-neutron separation energies in the rare earth region are discussed within
the proxy-SU(3) scheme, by considering a very simple Hamiltonian, containing
only the three dimensional (3D) isotropic harmonic oscillator (HO) term and the
quadrupole-quadrupole interaction. This Hamiltonian conserves the SU(3)
symmetry and treats the nucleus as a rigid rotator.
