Based on the microscopic mechanism of the particle-hole (p-h) excitations in the proton and neutron single-particle energy levels relative to the Fermi energy, a search for islands of shape coexistence (SC) is performed over a wide range of even-even nuclei from $Z=38$ to 84 using nonrelativistic self-consistent mean field with the Hartree-Fock-Bogoliubov theory using the Skyrme-SKI3 functional. The results of the present study show that neutron-induced islands of SC, corresponding to proton p-h excitations, are found around the magic numbers $Z=82$ and 50, centered at the relevant neutron midshells of $N=104$ and 66 respectively, while proton-induced islands of SC, corresponding to neutron p-h excitations, are found around the neutron numbers $N=90$ and 60, centered at the relevant proton midshells $Z=66$ and 38 respectively. In addition, islands of SC due to both neutron and proton particle-hole excitations are found around $N=40, Z=40$. The results of the present study are compared with the results of covariant density functional theory using the DDME2 functional, using the same p-h mechanism. The islands of SC that appeared in the covariant density functional theory work with the DDME2 functional are corroborated by the present study with the Skyrme-SKI3 functional, thus confirming the robustness of the particle-hole excitations mechanism in searching for islands of SC. In addition, the current study reveals new regions of SC, adjacent to the earlier islands and expanding their shores.

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• Nuclear fusion
• Nuclear shapes and moments
• Nuclear structure & decays
• 150 ≤ A ≤ 189
• 190 ≤ A ≤ 219
• Nuclear density functional theory