Ionization potentials of neutral atoms and positive ions in the limit of large atomic number

Abstract

The many-electron Schr\"odinger equation allows one to make predictions for the nonrelativistic ionization potentials of both highly charged positive atomic ions and neutral atoms in the limit of large atomic number $Z$. Beginning with theoretical configuration interaction data on both Li- and Be-like positive atomic ions by K.T. Chung et al. [Phys. Rev. A 45, 7766 (1992); Phys. Rev. A 47, 1740 (1993)], their nonrelativistic first ionization potentials $I$ are plotted in the form of $I∕{Z}^{2}$ versus $1∕Z$. In these two sequences, it is then clear that ${\mathrm{lim}}_{Z\ensuremath{\rightarrow}\ensuremath{\infty}}(I∕{Z}^{2})$ remains finite and that this limit is approached essentially linearly. Interpretation is afforded by means of the so-called $1∕Z$ expansion of atomic theory. The question of the behavior of the nonrelativistic ionization potentials for large $Z$ is then addressed for neutral atoms. We perform density functional theory (DFT) calculations using the local density approximation with Dirac exchange and neglecting Coulomb correlation for the heavy actinides as well as for the rare gas and alkali atoms from $Z=10$ up to $Z=291$. Our results suggest that there is a nonzero value for ${\mathrm{lim}}_{Z\ensuremath{\rightarrow}\ensuremath{\infty}}I$ for both the noble gases and the alkalis, the second one implying that there is a lower bound of about $2.56\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ to the ionization potential of any nonrelativistic neutral atom. We also explore an alternative approach via the one-body potential $V(r)$ of DFT by calculating the eigenenergies of the highest occupied atomic orbital in neutral atoms. Finally, relativistic corrections needed to compare measured ionization potentials to the predictions from the Schr\"odinger equation are briefly considered.