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arXiv · 1912.02619

Relativistic effective charge model of a multi-electron atom

K. Dzikowski·O. D. Skoromnik·I. D. Feranchuk·N. S. Oreshkina·C. H. Keitel
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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.

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K. Dzikowski, O. D. Skoromnik, I. D. Feranchuk, N. S. Oreshkina, C. H. Keitel. 2019-12-04. Relativistic effective charge model of a multi-electron atom. https://arxiv.org/abs/1912.02619

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