Relativistic effective charge model of a multi-electron atom

TL;DR

This paper introduces a relativistic effective charge model for multi-electron atoms that simplifies calculations while maintaining accuracy, especially for highly charged ions, and can replace more complex models like Thomas-Fermi-Dirac.

Contribution

A new relativistic effective charge model employing a Dirac hydrogen basis set with a single parameter for all electrons, improving accuracy and computational efficiency.

Findings

The leading-order approximation's accuracy is independent of electron number.

The model is highly accurate for highly charged ions.

Atomic characteristics like scattering factors are effectively computed.

Abstract

A relativistic version of the effective charge model for computation of observable characteristics of multi-electron atoms and ions is developed. A complete and orthogonal Dirac hydrogen basis set, depending on one parameter -- effective nuclear charge $Z^{*}$ -- identical for all single-electron wave functions of a given atom or ion, is employed for the construction of the secondary-quantized representation. The effective charge is uniquely determined by the charge of the nucleus and a set of electron occupation numbers for a given state. We thoroughly study the accuracy of the leading-order approximation for the total binding energy and demonstrate that it is independent of the number of electrons of a multi-electron atom. In addition, it is shown that the fully analytical leading-order approximation is especially suited for the description of highly charged ions since our wave functions are almost coincident with the Dirac-Hartree-Fock ones for the complete spectrum. Finally, we evaluate various atomic characteristics, such as scattering factors and photoionization cross-sections, and thus envisage that the effective charge model can replace other models of comparable complexity, such as the Thomas-Fermi-Dirac model for all applications where it is still utilized.