Orbital collapse and dual states of the $5g$ electrons in superheavy elements

The problem of orbital collapse of the $5g$ and $6f$ electrons in atoms of superheavy elements (SHEs) is considered. Previously, the presence of the orbital collapse was established for the $4f$ and $5f$ elements of the periodic table. Because of the large centrifugal term for the $f$ and $g$ electrons, the effective radial potential has two wells, one narrow and deep and the other wide but shallow. Depending on the external parameters, the electron can be localized in either the outer well with low binding energy and large average radius or the inner well with higher energy and smaller radius. In this paper, we demonstrate the existence of the orbital collapse for the $5g$ electrons when changing the total angular momentum $J$ of the atom. We also find that for some SHEs two different solutions of the same Dirac-Fock equations may coexist, with the $5g$ electron localized in either the inner or outer well. In both cases, the radial wave functions are nodeless. The problem of the dual-state coexistence is studied by the configuration-interaction method in the Dirac-Fock-Sturm orbital basis as well.

Figure 1

Effective radial potential $V_a^{\mathrm{rad}}\left(r\right)$ for the shell $a=5g_{7/2}$ of the superheavy atom with $Z=125$. The solid line is the potential with the exchange, while the dashed line is the potential without the exchange.

Figure 2

$Z=125$ ($\left[\mathrm{Og}\right]8s^{2}8p_{1/2}^{1}6f_{5/2}^{3}5g_{7/2}^1$). Large components of the radial wave functions: the solid line $\left[P_{\mathrm{in}}\left(r\right)\right]$ and dashed line $\left[P_{\mathrm{out}}\left(r\right)\right]$ correspond to the $5g_{7/2}$ orbitals localized in the inner and outer wells, respectively. All the values are given in atomic units.