Using covariant density functional theory with the DDME2 functional and labeling single-particle energy orbitals by Nilsson quantum numbers, a search for particle-hole (p-h) excitations connected to the appearance of shape coexistence is performed for $Z=38$ to 84. Islands of shape coexistence are found near the magic numbers $Z=82$ and $Z=50$, restricted in regions around the relevant neutron midshells $N=104$ and $N=66$, respectively, in accordance with the well-accepted p-h interpretation of shape coexistence in these regions, which we call neutron-induced shape coexistence, since the neutrons act as elevators creating holes in the proton orbitals. Similar but smaller islands of shape coexistence are found near $N=90$ and $N=60$, restricted in regions around the relevant proton midshells $Z=66$ and $Z=39$, respectively, related to p-h excitations across the three-dimensional isotropic harmonic-oscillator magic numbers $N=112$ and $N=70$, which correspond to the beginning of the participation of the opposite parity orbitals $1i_{13/2}$ and $1h_{11/2}$, respectively, to the onset of deformation. We call this case proton-induced shape coexistence, since the protons act as elevators creating holes in the neutron orbitals, thus offering a possible microscopic mechanism for the appearance of shape coexistence in these regions. In the region around $N=40$, $Z=40$, an island is located on which both neutron p-h excitations and proton p-h excitations are present.

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• Nuclear structure & decays
• Nucleon distribution
• Nuclear density functional theory