charge model is a completely *ab-initio* theory and thus crucially distinct from semi-empirical models, such as those based on quantum defects of Rydberg atoms [@foot2005atomic], screened hydrogen [@hau2012high] or empirical interpolation of X-ray measurements [@genoni_can_2017]. In addition, contrary to numerical methods such as solving the Hatree-Fock equations [@hartree_1928], the effective charge model provides analytical expressions for electron densities and scattering factors.

So far, the effective charge description has only been performed for the nonrelativistic Schrödinger equation. However, it is well-known that when a product of a fine structure constant $\alpha$ and the charge of the nucleus $Z$, i.e., $\alpha Z$ is not much smaller than unity the relativistic corrections become important. Since the Dirac equation for the hydrogen-like atom can be solved exactly and the Dirac-Coulomb Green’s function is known in closed form, it is possible to develop a relativistic version of the effective charge model. Consequently, this generalization is the main achievement of the present work.

Similarly to the nonrelativistic case, we employ Dirac hydrogen basis set with a single parameter — the effective charge and require it to be identical for all wave functions of a given atom. The basis completeness allows us to work in the secondary-quantized 