Unified picture of nucleon pairs playing leading roles in nuclear collectivity

Proxy-SU(3) symmetry is an approximation scheme extending the Elliott SU(3) algebra of the sd shell to heavier shells. When introduced in 2017, the approximation had been justified by calculations carried out within the Nilsson model, with nucleon pairs differing by $\Delta K [\Delta N \Delta n_z \Delta \Lambda]=0[110]$ in the Nilsson quantum numbers playing a major role in the approximation. Recently our group managed to map the cartesian basis of the Elliott SU(3) model onto the spherical shell model basis, fully clarifying the approximations used within the proxy-SU(3) scheme and paving the way for using the proxy-SU(3) approximation in shell model calculations for heavy nuclei. As a by-product, the relation of the 0[110] Nilsson pairs used in proxy-SU(3) to the earlier used de Shalit-Goldhaber pairs $|\Delta n \Delta l \Delta j \Delta m_j\rangle = | 0110\rangle$ in spherical shell model notation is clarified, while the Federman-Pittel (FP) pairs known to play a major role at the onset of deformation are identified as $| 0010\rangle$ pairs, and the FP pairs further increasing the deformation after its onset are found to be $| 0110\rangle$ pairs, i.e. identical to the de-Shalit-Goldhaber pairs. The connection between the proxy-SU(3) scheme and the spherical shell model has also been worked out in the original framework of the Nilsson model, with identical results.