A relativistic version of the effective charge model (ECM) 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 occupied single-electron orbitals 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 ECM can replace other models of comparable complexity, such as the Thomas–Fermi–Dirac model for all applications where it is still utilized.

开发了用于计算多电子原子和离子的可观察特征的有效电荷模型 (ECM) 的相对论版本。一个完整的正交狄拉克氢基组，取决于一个参数——有效核电荷Z*——对于给定原子或离子的所有单电子波函数相同，用于构建二次量化表示。有效电荷由原子核的电荷和给定状态的一组占据的单电子轨道唯一确定。我们彻底研究了总结合能的前级近似的准确性，并证明它与多电子原子的电子数无关。此外，还表明完全解析的主阶近似特别适合于描述高电荷离子，因为我们的波函数几乎与完整光谱的狄拉克-哈特里-福克波函数重合。最后，我们评估各种原子特性，例如散射因子和光电离截面，