Electron and Nucleon Localization Functions of Oganesson: Approaching the Thomas-Fermi Limit

Fermion localization functions are used to discuss electronic and nucleonic shell structure effects in the superheavy element oganesson, the heaviest element discovered to date. Spin-orbit splitting in the $7p$ electronic shell becomes so large ($\sim 10\mathrm{eV}$) that Og is expected to show uniform-gas-like behavior in the valence region with a rather large dipole polarizability compared to the lighter rare gas elements. The nucleon localization in Og is also predicted to undergo a transition to the Thomas-Fermi gas behavior in the valence region. This effect, particularly strong for neutrons, is due to the high density of single-particle orbitals.

Figure 1

ELFs from nonrelativistic (NR, left) and Dirac-Hartree-Fock calculations (R, right) for the heavy rare gas atoms Xe (top), Rn (middle), and Og (bottom).

Figure 2

ELFs for Xe (a) and Og (b) from nonrelativistic (NR), scalar-relativistic (SR), and Dirac-Hartree-Fock (R) calculations as a function of the distance from the nucleus as in Ref. [41]. The relativistic contraction of inner shells and smearing out of the shell structure in the valence and subvalence shells of Og are clearly seen.

Figure 3

Orbital energy levels of Xe (left), Rn (middle), and Og (right) for the ${}^1{S}_0$ ground state as obtained from nonrelativistic (NR) and scalar-relativistic (SR) Hartree-Fock and Dirac-Hartree-Fock (R) calculations. $6s$ (Xe), $7s$ (Rn), and $8s$ (Og) orbital energies are taken from the first excited ${}^3{P}_2$ state.

Figure 4

NLFs of ${}^{132}\mathrm{Sn}$, ${}^{302}\mathrm{Og}$, and ${}^{472}164$ calculated with the energy density functional UNEDF1.