The consequences of the short-range nature of the nucleon–nucleon interaction, which forces the spatial part of the nuclear wave function to be as symmetric as possible, on the pseudo-SU(3) scheme are examined through a study of the collective deformation parameters β and γ in the rare earth region. It turns out that beyond the middle of each harmonic oscillator shell possessing an SU(3) subalgebra, the highest weight irreducible representation (the hw irrep) of SU(3) has to be used, instead of the irrep with the highest eigenvalue of the second order Casimir operator of SU(3) (the hC irrep), while in the first half of each shell the two choices are identical. The choice of the hw irrep predicts a transition from prolate to oblate shapes just below the upper end of the rare earth region, between the neutron numbers N = 114 and 116 in the W, Os, and Pt series of isotopes, in agreement with available experimental information, while the choice of the hC irrep leads to a prolate to oblate transition in the middle of the shell, which is not seen experimentally. The prolate over oblate dominance in the ground states of even–even nuclei is obtained as a by-product.

通过对集体变形的研究，研究了核子-核子相互作用的短程性质对伪SU（3）方案的影响，这种相互作用迫使核波函数的空间部分尽可能对称。参数β和γ在稀土区域。事实证明，除了每个拥有SU（3）子代数的谐波振荡器壳的中部之外，还必须使用SU（3）的最大权重不可约表示（hw irrep），而不是具有最大特征值的irrep。 SU（3）的二阶Casimir运算符（hC irrep），而在每个外壳的前半部分，两个选择是相同的。硬质合金的选择可预测在中子数N之间，正好在稀土区域上端下方的扁长形到扁圆形的过渡W，Os和Pt系列同位素中的114和116，与可用的实验信息相符，而hC irrep的选择导致壳中部扁圆形到扁圆形的转变，这在实验上是看不到的。副产物获得了在偶数-偶数原子核的基态中扁长的支配于扁长的优势。