Quantum stabilization of superheavy elements is quantified in terms of the
shell-correction energy. We compute the shell correction at spherical shape
using self-consistent nuclear models: the non-relativistic Skyrme-Hartree-
Fock approach and the relativistic mean-field model, for a number of parame
trizations. All the forces applied predict a broad valley of shell stabiliz
ation around Z = 120 and N = 172-184. We also predict two broad regions of
shell stabilization in hyperheavy elements with N approximate to 258 and N
approximate to 308. Due to the large single-particle level density, shell c
orrections in the superheavy elements differ markedly from those in lighter
nuclei. With increasing proton and neutron numbers, the regions of nuclei
stabilized by shell effects become poorly localized in particle number, and
the familiar pattern of shells separated by magic gaps is basically gone.
(C) 2001 Published by Elsevier Science B.V.