Magic numbers for shape coexistence

The increasing deformation in atomic nuclei leads to the change of the classical magic numbers (2,8,20,28,50,82…) which dictate the arrangement of nucleons in complete shells. The magic numbers of the three-dimensional harmonic oscillator (2,8,20,40,70…) emerge at deformations around epsilon=0.6. At lower deformations the two sets of magic numbers antagonize, leading to shape coexistence. A quantitative investigation is performed using the usual Nilsson model wave functions and the recently introduced proxy-SU(3) scheme.