Shell corrections of superheavy nuclei in self-consistent calculations

Shell corrections to the nuclear binding energy as a measure of shell effects in superheavy nuclei are studied within the self-consistent Skyrme-Hartree-Fock and relativistic mean-field theories. As a result of the presence of a low-lying proton continuum resulting in a free particle gas, special attention is paid to the treatment of the single-particle level density. To cure the pathological behavior of the shell correction around the particle threshold, a method based on the Green’s function approach has been adopted. It is demonstrated that for the vast majority of Skyrme interactions commonly employed in nuclear structure calculations, the strongest shell stabilization appears for $Z=124\mathrm{}$ and 126, and for $N=184.\mathrm{}$ On the other hand, in the relativistic approaches the strongest spherical shell effect appears systematically for $Z=120\mathrm{}$ and $N=172.\mathrm{}$ This difference probably has its roots in the spin-orbit potential. We have also shown that, in contrast to shell corrections which are fairly independent of the force, macroscopic energies extracted from self-consistent calculations strongly depend on the actual force parametrization used. That is, the A and Z dependence of the mass surface when extrapolating to unknown superheavy nuclei is prone to significant theoretical uncertainties.