A novel dual–shell mechanism for the phenomenon of shape coexistence in nuclei within the Elliott SU(3) and the proxy-SU(3) symmetry is proposed for all mass regions. It is supposed, that shape coexistence is activated by large quadrupole-quadrupole interaction and involves the interchange among the spin–orbit (SO) like shells within nucleon numbers 6–14, 14–28, 28–50, 50–82, 82–126, 126–184, which are being described by the proxy-SU(3) symmetry, and the harmonic oscillator (HO) shells within nucleon numbers 2–8, 8–20, 20–40, 40–70, 70–112, 112–168 of the Elliott SU(3) symmetry. The outcome is, that shape coexistence may occur in certain islands on the nuclear map. The dual–shell mechanism predicts without any free parameters, that nuclei with proton number (Z) or neutron number (N) between 7–8, 17–20, 34–40, 59–70, 96–112, 146–168 are possible candidates for shape coexistence. In the light nuclei the nucleons flip from the HO shell to the neighboring SO–like shell, which means, that particle excitations occur. For this mass region, the predicted islands of shape coexistence, coincide with the islands of inversion. But in medium mass and heavy nuclei, in which the nucleons inhabit the SO–like shells, shape coexistence is accompanied by a merging of the SO–like shell with the open HO shell. The shell merging can be accomplished by the outer product of the SU(3) irreps of the two shells and represents the unification of the HO shell with the SO–like shell.

针对所有质量区域，提出了一种新的双壳机制，用于解决Elliott SU（3）和proxy-SU（3）对称性内原子核形状共存的现象。据推测，形状共存是通过大四极-四极相互作用而激活的，并且涉及自旋轨道（SO）之间的互换，如核子数6-14、14-28、28-50、50-82、82-中的壳126，126–184，这是通过proxy-SU（3）对称性描述的，并且子振子号2–8、8–20、20–40、40–70、70–112内的谐波振荡器（HO）壳，Elliott SU（3）对称性的112–168。结果是，形状共存可能发生在核图上的某些岛上。双壳机制可以在没有任何自由参数的情况下预测具有质子数（Z）或中子数（N）在7-8、17-20、34-40、59-70、96-112、146-168之间可能是形状共存的候选对象。在轻核中，核子从HO壳翻转到相邻的SO样壳，这意味着发生了粒子激发。对于这个质量区域，形状共存的预测岛与反演岛重合。但是在中等质量和较重的核中，核子居住在类SO壳中，形状共存伴随有类SO壳与开放式HO壳合并。可以通过两个壳的SU（3）irrep的外积来完成壳的合并，并表示HO壳与类SO壳的统一。