The consequences of the attractive, short-range nucleon–nucleon (NN) interaction on the wave functions of the Elliott SU(3) and the proxy-SU(3) symmetry are discussed. The NN interaction favors the most symmetric spatial SU(3) irreducible representation, which corresponds to the maximal spatial overlap among the fermions. The percentage of the symmetric components out of the total in an SU(3) wave function is introduced, through which it is found, that no SU(3) irrep is more symmetric than the highest weight irrep for a certain number of valence particles in a three dimensional, isotropic, harmonic oscillator shell. The consideration of the highest weight irreps in nuclei and in alkali metal clusters, leads to the prediction of a prolate to oblate shape transition beyond the mid-shell region

讨论了Elliott SU（3）和proxy-SU（3）对称波函数吸引人的，短程核子-核子（NN）相互作用的后果。NN相互作用有利于最对称的空间SU（3）不可约表示，它对应于费米子之间的最大空间重叠。引入SU（3）波函数中对称分量占总数的百分比，由此发现，对于一定数量的价态粒子，没有SU（3）irrep比权重最高的irrep更对称。三维各向同性的三维谐振器壳。考虑到原子核和碱金属团簇中最高重量的irreps，可以预测扁壳到扁壳形状的转变超过中壳区域