Background: Various mean-field calculations suggest that most superheavy nuclei (SHN) with are deformed. The existence of the SHN is due to the shell stabilization. While the shell stabilization effect of spherical SHN has been well studied, there are fewer studies on the deformed SHN based on the self-consistent mean-field models.
Purpose: The purpose of this work is to study the stability of deformed even-even SHN with by extracting the shell correction energies from the single-particle (s.p.) energies obtained from nuclear density functional theory (DFT).
Methods: We calculate s.p. energies using a symmetry-unrestricted nonrelativistic mean-field model based on a mixed basis. The Strutinsky shell correction energies are obtained using these s.p. energies. For the pairing channel, we use the Lipkin-Nogami (LN) pairing model.
Results: Systematic calculations have been performed for even-even nuclei with and using four different energy density functionals (EDFs). The extracted shell correction energies are plotted as functions of proton and neutron numbers. All four EDFs predict the lowest minima at the nucleus . The next minima locate at for SLy4, , and UNEDF1 EDFs. For the EDF, the minimum locates at . The calculated ground-state total energies allow us to extract the two-particle separation energies (), -decay energies (), and -decay half-lives. The experimental data are reasonably reproduced by the calculations with SLy4, UNEDF1, and EDFs. Analyses of the two-particle separation energies and the -decay energies indicate that the variations of the and values along the isotopic and isotonic chains can be attributed to the occurrence of deformed shell gaps at relevant nucleon numbers.
Conclusions: Our calculations suggest that the next deformed shell closure above occurs at . The heavier deformed shell closure for the SHN region is predicted to locate at or .