Shell model foundations of the proxy-SU(3) symmetry: Nucleon pairs creating nuclear deformation

Abstract

Abstract    Proxy-SU(3) symmetry is an approximation scheme extending the Elliott SU(3) algebra of the sd shell to heavier shells, in order to make possible the application of the symmetry properties in cutting down the size of the required calculations. When introduced in 2017, the approximation had been justified by calculations carried out within the Nilsson model, an elementary shell model based on a 3-dimensional harmonic oscillator with cylindrical symmetry, applicable to deformed nuclei. 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 and  Federman-Pittel pairs has been clarified. 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.