Abstract
We consider two competing sets of nuclear magic numbers, namely the harmonic oscillator (HO) set (2, 8, 20, 40, 70, 112, 168, 240,...) and the set corresponding to the proxy-SU(3) scheme, possess- ing shells 0-2, 2-4, 6-12, 14-26, 28-48, 50-80, 82-124, 126-182, 184-256... The two sets provide 0+bands with different deformation and bandhead energies. We show that for proton (neutron) numbers starting from the regions where the quadrupole-quadrupole (Q · Q) interaction, as derived by the HO, becomes weaker than the one obtained in the proxy-SU(3) scheme, to the regions of HO shell clo- sure, the shape coexistence phenomenon may emerge. Our analysis suggests that the possibility for appearance of shape coexistence has to be investigated in the following regions of proton (neutron) numbers: 8, 18-20, 34-40, 60-70, 96-112, 146-168, 210-240,...
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