Shaping the archipelago of stability by the competition of proton and neutron shell closures

The evolution of superheavy nuclei in proton and neutron number is explored by investigating the ground-state shell correction energy in the $Z=112\text{--}126$ and $N=170\text{--}190$ region of the $(Z,N)$ plane. Cuts through the $(Z,N)$-dependent distribution of shell corrections are chosen for constant neutron-proton differences as accessible in $\ensuremath{\alpha}$-decay chains and varying the neutron number at fixed charge number. A new approach is used, integrating elements of energy-density functional theory into the microscopic-macroscopic method. The topology of the shell correction implies for binding energies a distribution resembling in shape a ridge on a coral reef, formed by the competition of proton and neutron shell closures at $Z=114$ and $Z=120$, and $N=174$ and $N=184$, respectively. $^{288}\mathrm{Fl}$ is predicted as the next double magic nucleus after $^{208}\mathrm{Pb}$, and $^{304}120$ is identified as the most likely candidate for next-to-next double magic nucleus.