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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.