2019/12/04 by K. Dzikowski, Dzikowski, K., O. D. Skoromnik +7 · 1 citation
Materials Science · Physics and Astronomy · #Advanced Chemical Physics Studies #Atomic Physics (physics.atom-ph) #Atomic and Molecular Physics #Electron and X-Ray Spectroscopy Techniques #FOS: Physical sciences #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1912.02619
openalex publication_date 2019/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.