Hyperheavy spherical and toroidal nuclei: The role of shell structure

The properties of toroidal hyperheavy even-even nuclei and the role shell structure are extensively studied within covariant density functional theory. general trends in evolution shapes $Z\approx 130-180$ region nuclear chart established for first time. These stable with respect breathing deformations. most compact fat located 136, N\approx 206$ chart, but thin become dominant increasing proton number on moving towards neutron drip lines. structure, its regularity, supershell gaps as well different groups pairs orbitals formation investigated detail. lowest energy solutions at axial symmetry characterized either by large or low single-particle states vicinity Fermi level least one subsystems (proton neutron). Related quantum effects expected to act against instabilities sausage deformations these subsystems. investigation set functionals reveals that substantial $Z=154$ 186 $N=228$, 308 406 spherical exist all functionals. combination particle numbers form islands stability nuclei. study suggests $N=210$ gap plays a stabilization