The proxy-SU(3) symmetry has been proposed for spin-orbit like nuclear shells using the asymptotic deformed oscillator basis for the single particle orbitals, in which the restoration of the symmetry of the harmonic oscillator shells is achieved by a change of the number of quanta in the z-direction by one unit for the intruder parity orbitals. The same definition suffices within the cartesian basis of the Elliott SU(3) model. Through a mapping of the cartesian Elliott basis onto the spherical shell model basis, we translate the proxy-SU(3) approximation into spherical coordinates, proving, that in the spherical shell model basis the proxy-SU(3) approximation corresponds to the replacement of the intruder parity orbitals by their de Shalit–Goldhaber partners. Furthermore it is shown, that the proxy-SU(3) approximation in the cartesian Elliott basis is equivalent to a unitary transformation in the z-coordinate, leaving the x–y plane intact, a result which in the asymptotic deformed oscillator coordinates implies, that the z-projections of angular momenta and spin remain unchanged. The present work offers a microscopic justification of the proxy-SU(3) approximation and in addition paves the way, for taking advantage of the proxy-SU(3) symmetry in shell model calculations.

已经针对单粒子轨道使用渐近形变振荡器基础，为自旋轨道状核壳提出了proxy-SU（3）对称性，其中谐波谐振器壳的对称性是通过改变数目来恢复的z中的量子数量入侵者的奇偶校验轨道按一个方向定向。在Elliott SU（3）模型的笛卡尔基础内，相同的定义就足够了。通过将笛卡尔Elliott基础映射到球壳模型基础，我们将proxy-SU（3）近似转换为球坐标，证明在球壳模型基础上proxy-SU（3）近似对应于替换他们的de Shalit–Goldhaber合作伙伴确定了入侵者的平价轨道。此外，还表明，笛卡尔Elliott基中的proxy-SU（3）近似等效于z坐标中的unit正变换，而使x – y平面保持不变，这在渐近变形的振荡器坐标中意味着：那个z-角动量和自旋的投影保持不变。本工作提供了代理SU（3）近似的微观证明，此外，还为在壳模型计算中利用代理SU（3）的对称性铺平了道路。